%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA118-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:05 PM UTC 2026
% Result : Unsatisfiable 0.39s 0.59s
% Output : Proof 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA118-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 21:23:02 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.39/0.59 % SZS status Unsatisfiable
% 0.39/0.59 % SZS output start Proof
% 0.39/0.59 tff(f_type, type, (
% 0.39/0.59 f: $i > $i)).
% 0.39/0.59 tff(c_type, type, (
% 0.39/0.59 c: $i)).
% 0.39/0.59 tff(inj_0_type, type, (
% 0.39/0.59 inj_0: $i > $i)).
% 0.39/0.59 tff(r_type, type, (
% 0.39/0.59 r: ( $i * $i ) > $o)).
% 0.39/0.59 tff(elem_1_type, type, (
% 0.39/0.59 elem_1: $i)).
% 0.39/0.59 tff(1,plain,
% 0.39/0.59 ((f(c) = f(f(c))) <=> (f(f(c)) = f(c))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(2,plain,
% 0.39/0.59 ((f(f(c)) = f(c)) <=> (f(c) = f(f(c)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[1])).
% 0.39/0.59 tff(3,plain,
% 0.39/0.59 ((~(f(f(c)) = f(c))) <=> (~(f(c) = f(f(c))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[2])).
% 0.39/0.59 tff(4,plain,
% 0.39/0.59 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(5,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(6,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(7,axiom,(![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pfinj')).
% 0.39/0.59 tff(8,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.39/0.59 tff(9,plain,(
% 0.39/0.59 ![Y: $i, X: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.39/0.59 inference(skolemize,[status(sab)],[8])).
% 0.39/0.59 tff(10,plain,
% 0.39/0.59 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.39/0.59 tff(11,plain,
% 0.39/0.59 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.39/0.59 tff(12,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(c)) = c)),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(13,plain,
% 0.39/0.59 (inj_0(f(c)) = c),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.39/0.59 tff(14,assumption,(f(f(c)) = f(c)), introduced(assumption)).
% 0.39/0.59 tff(15,plain,
% 0.39/0.59 (f(c) = f(f(c))),
% 0.39/0.59 inference(symmetry,[status(thm)],[14])).
% 0.39/0.59 tff(16,plain,
% 0.39/0.59 (inj_0(f(c)) = inj_0(f(f(c)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[15])).
% 0.39/0.59 tff(17,plain,
% 0.39/0.59 (inj_0(f(f(c))) = inj_0(f(c))),
% 0.39/0.59 inference(symmetry,[status(thm)],[16])).
% 0.39/0.59 tff(18,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(c))) = f(c))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(19,plain,
% 0.39/0.59 (inj_0(f(f(c))) = f(c)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[18, 11])).
% 0.39/0.59 tff(20,plain,
% 0.39/0.59 (f(c) = inj_0(f(f(c)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[19])).
% 0.39/0.59 tff(21,plain,
% 0.39/0.59 (f(c) = c),
% 0.39/0.59 inference(transitivity,[status(thm)],[20, 17, 13])).
% 0.39/0.59 tff(22,plain,
% 0.39/0.59 (^[X: $i] : refl((~(f(X) = c)) <=> (~(f(X) = c)))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(23,plain,
% 0.39/0.59 (![X: $i] : (~(f(X) = c)) <=> ![X: $i] : (~(f(X) = c))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[22])).
% 0.39/0.59 tff(24,plain,
% 0.39/0.59 (![X: $i] : (~(f(X) = c)) <=> ![X: $i] : (~(f(X) = c))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(25,axiom,(![X: $i] : (~(f(X) = c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pfnc')).
% 0.39/0.59 tff(26,plain,
% 0.39/0.59 (![X: $i] : (~(f(X) = c))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.39/0.59 tff(27,plain,(
% 0.39/0.59 ![X: $i] : (~(f(X) = c))),
% 0.39/0.59 inference(skolemize,[status(sab)],[26])).
% 0.39/0.59 tff(28,plain,
% 0.39/0.59 (![X: $i] : (~(f(X) = c))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.39/0.59 tff(29,plain,
% 0.39/0.59 ((~![X: $i] : (~(f(X) = c))) | (~(f(c) = c))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(30,plain,
% 0.39/0.59 (~(f(c) = c)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.39/0.59 tff(31,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[30, 21])).
% 0.39/0.59 tff(32,plain,(~(f(f(c)) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(33,plain,
% 0.39/0.59 (~(f(c) = f(f(c)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[32, 3])).
% 0.39/0.59 tff(34,plain,
% 0.39/0.59 ((f(f(f(f(c)))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(c)))))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(35,plain,
% 0.39/0.59 ((f(f(c)) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(c)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[34])).
% 0.39/0.59 tff(36,plain,
% 0.39/0.59 ((~(f(f(c)) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(f(c))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[35])).
% 0.39/0.59 tff(37,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(c))))) = f(f(f(c))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(38,plain,
% 0.39/0.59 (inj_0(f(f(f(f(c))))) = f(f(f(c)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[37, 11])).
% 0.39/0.59 tff(39,assumption,(f(f(c)) = f(f(f(f(c))))), introduced(assumption)).
% 0.39/0.59 tff(40,plain,
% 0.39/0.59 (inj_0(f(f(c))) = inj_0(f(f(f(f(c)))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[39])).
% 0.39/0.59 tff(41,plain,
% 0.39/0.59 (f(c) = f(f(f(c)))),
% 0.39/0.59 inference(transitivity,[status(thm)],[20, 40, 38])).
% 0.39/0.59 tff(42,assumption,(f(c) = f(f(f(c)))), introduced(assumption)).
% 0.39/0.59 tff(43,plain,
% 0.39/0.59 (inj_0(f(c)) = inj_0(f(f(f(c))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[42])).
% 0.39/0.59 tff(44,plain,
% 0.39/0.59 (inj_0(f(f(f(c)))) = inj_0(f(c))),
% 0.39/0.59 inference(symmetry,[status(thm)],[43])).
% 0.39/0.59 tff(45,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(c)))) = f(f(c)))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(46,plain,
% 0.39/0.59 (inj_0(f(f(f(c)))) = f(f(c))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[45, 11])).
% 0.39/0.59 tff(47,plain,
% 0.39/0.59 (f(f(c)) = inj_0(f(f(f(c))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[46])).
% 0.39/0.59 tff(48,plain,
% 0.39/0.59 (f(f(c)) = c),
% 0.39/0.59 inference(transitivity,[status(thm)],[47, 44, 13])).
% 0.39/0.59 tff(49,plain,
% 0.39/0.59 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(c)) = c))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(50,plain,
% 0.39/0.59 (~(f(f(c)) = c)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[49, 28])).
% 0.39/0.59 tff(51,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[50, 48])).
% 0.39/0.59 tff(52,plain,(~(f(c) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(53,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[52, 41])).
% 0.39/0.59 tff(54,plain,(~(f(f(c)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(55,plain,
% 0.39/0.59 (~(f(f(f(f(c)))) = f(f(c)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[54, 36])).
% 0.39/0.59 tff(56,plain,
% 0.39/0.59 ((f(f(f(f(c)))) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(f(f(c)))))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(57,plain,
% 0.39/0.59 ((f(f(elem!1)) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(elem!1)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[56])).
% 0.39/0.59 tff(58,plain,
% 0.39/0.59 ((~(f(f(elem!1)) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(f(elem!1))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[57])).
% 0.39/0.59 tff(59,plain,
% 0.39/0.59 ((f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(60,plain,
% 0.39/0.59 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[59])).
% 0.39/0.59 tff(61,plain,
% 0.39/0.59 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> (~(f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[60])).
% 0.39/0.59 tff(62,assumption,(~(elem!1 = f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(63,plain,
% 0.39/0.59 ((f(c) = f(elem!1)) <=> (f(elem!1) = f(c))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(64,plain,
% 0.39/0.59 ((f(elem!1) = f(c)) <=> (f(c) = f(elem!1))),
% 0.39/0.59 inference(symmetry,[status(thm)],[63])).
% 0.39/0.59 tff(65,plain,
% 0.39/0.59 ((~(f(elem!1) = f(c))) <=> (~(f(c) = f(elem!1)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[64])).
% 0.39/0.59 tff(66,assumption,(~(c = elem!1)), introduced(assumption)).
% 0.39/0.59 tff(67,plain,
% 0.39/0.59 ((elem!1 = f(f(f(f(f(f(elem!1))))))) <=> (f(f(f(f(f(f(elem!1)))))) = elem!1)),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(68,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(69,plain,
% 0.39/0.59 (inj_0(f(f(f(elem!1)))) = f(f(elem!1))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[68, 11])).
% 0.39/0.59 tff(70,assumption,(f(elem!1) = f(f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(71,plain,
% 0.39/0.59 (f(f(f(elem!1))) = f(elem!1)),
% 0.39/0.59 inference(symmetry,[status(thm)],[70])).
% 0.39/0.59 tff(72,plain,
% 0.39/0.59 (inj_0(f(f(f(elem!1)))) = inj_0(f(elem!1))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[71])).
% 0.39/0.59 tff(73,plain,
% 0.39/0.59 (inj_0(f(elem!1)) = inj_0(f(f(f(elem!1))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[72])).
% 0.39/0.59 tff(74,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(elem!1)) = elem!1)),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(75,plain,
% 0.39/0.59 (inj_0(f(elem!1)) = elem!1),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[74, 11])).
% 0.39/0.59 tff(76,plain,
% 0.39/0.59 (elem!1 = inj_0(f(elem!1))),
% 0.39/0.59 inference(symmetry,[status(thm)],[75])).
% 0.39/0.59 tff(77,plain,
% 0.39/0.59 (elem!1 = f(f(elem!1))),
% 0.39/0.59 inference(transitivity,[status(thm)],[76, 73, 69])).
% 0.39/0.59 tff(78,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[62, 77])).
% 0.39/0.59 tff(79,plain,((~(f(elem!1) = f(f(f(elem!1))))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(80,plain,
% 0.39/0.59 (~(f(elem!1) = f(f(f(elem!1))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[79, 62])).
% 0.39/0.59 tff(81,assumption,(~(elem!1 = f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.59 tff(82,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(elem!1))))) = f(f(f(elem!1))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(83,plain,
% 0.39/0.59 (inj_0(f(f(f(f(elem!1))))) = f(f(f(elem!1)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[82, 11])).
% 0.39/0.59 tff(84,assumption,(f(f(f(f(elem!1)))) = f(elem!1)), introduced(assumption)).
% 0.39/0.59 tff(85,plain,
% 0.39/0.59 (inj_0(f(f(f(f(elem!1))))) = inj_0(f(elem!1))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[84])).
% 0.39/0.59 tff(86,plain,
% 0.39/0.59 (inj_0(f(elem!1)) = inj_0(f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[85])).
% 0.39/0.59 tff(87,plain,
% 0.39/0.59 (elem!1 = f(f(f(elem!1)))),
% 0.39/0.59 inference(transitivity,[status(thm)],[76, 86, 83])).
% 0.39/0.59 tff(88,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[81, 87])).
% 0.39/0.59 tff(89,plain,((~(f(f(f(f(elem!1)))) = f(elem!1))) | (elem!1 = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(90,plain,
% 0.39/0.59 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[89, 81])).
% 0.39/0.59 tff(91,assumption,(~(f(f(f(f(elem!1)))) = f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(92,assumption,(~(f(elem!1) = f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.59 tff(93,assumption,(~(elem!1 = f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.39/0.59 tff(94,assumption,(c = f(f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.59 tff(95,plain,
% 0.39/0.59 (f(f(f(f(elem!1)))) = c),
% 0.39/0.59 inference(symmetry,[status(thm)],[94])).
% 0.39/0.59 tff(96,plain,
% 0.39/0.59 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(elem!1)))) = c))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(97,plain,
% 0.39/0.59 (~(f(f(f(f(elem!1)))) = c)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[96, 28])).
% 0.39/0.59 tff(98,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[97, 95])).
% 0.39/0.59 tff(99,plain,(~(c = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(100,assumption,(~r(elem!1, f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(101,assumption,(f(f(f(elem!1))) = elem!1), introduced(assumption)).
% 0.39/0.59 tff(102,plain,
% 0.39/0.59 (f(f(f(f(elem!1)))) = f(elem!1)),
% 0.39/0.59 inference(monotonicity,[status(thm)],[101])).
% 0.39/0.59 tff(103,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[91, 102])).
% 0.39/0.59 tff(104,plain,((~(f(f(f(elem!1))) = elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(105,plain,
% 0.39/0.59 (~(f(f(f(elem!1))) = elem!1)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[104, 91])).
% 0.39/0.59 tff(106,assumption,(elem!1 = f(f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(107,plain,
% 0.39/0.59 (f(elem!1) = f(f(f(elem!1)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[106])).
% 0.39/0.59 tff(108,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[92, 107])).
% 0.39/0.59 tff(109,plain,((~(elem!1 = f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(110,plain,
% 0.39/0.59 (~(elem!1 = f(f(elem!1)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[109, 92])).
% 0.39/0.59 tff(111,assumption,(elem!1 = f(elem!1)), introduced(assumption)).
% 0.39/0.59 tff(112,plain,
% 0.39/0.59 ((elem!1 = f(f(elem!1))) <=> (f(elem!1) = f(f(elem!1)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[111])).
% 0.39/0.59 tff(113,plain,
% 0.39/0.59 ((f(elem!1) = f(f(elem!1))) <=> (elem!1 = f(f(elem!1)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[112])).
% 0.39/0.59 tff(114,plain,
% 0.39/0.59 (f(elem!1) = elem!1),
% 0.39/0.59 inference(symmetry,[status(thm)],[111])).
% 0.39/0.59 tff(115,plain,
% 0.39/0.59 (f(f(elem!1)) = f(elem!1)),
% 0.39/0.59 inference(monotonicity,[status(thm)],[114])).
% 0.39/0.59 tff(116,plain,
% 0.39/0.59 (f(elem!1) = f(f(elem!1))),
% 0.39/0.59 inference(symmetry,[status(thm)],[115])).
% 0.39/0.59 tff(117,plain,
% 0.39/0.59 (elem!1 = f(f(elem!1))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.39/0.59 tff(118,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[62, 117])).
% 0.39/0.59 tff(119,plain,((~(elem!1 = f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(120,plain,
% 0.39/0.59 (~(elem!1 = f(elem!1))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[119, 110])).
% 0.39/0.59 tff(121,plain,
% 0.39/0.59 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(elem!1))) = f(elem!1))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(122,plain,
% 0.39/0.59 (inj_0(f(f(elem!1))) = f(elem!1)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[121, 11])).
% 0.39/0.59 tff(123,assumption,(f(f(elem!1)) = f(elem!1)), introduced(assumption)).
% 0.39/0.59 tff(124,plain,
% 0.39/0.59 (f(elem!1) = f(f(elem!1))),
% 0.39/0.59 inference(symmetry,[status(thm)],[123])).
% 0.39/0.59 tff(125,plain,
% 0.39/0.59 (inj_0(f(elem!1)) = inj_0(f(f(elem!1)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[124])).
% 0.39/0.59 tff(126,plain,
% 0.39/0.59 (elem!1 = f(elem!1)),
% 0.39/0.59 inference(transitivity,[status(thm)],[76, 125, 122])).
% 0.39/0.59 tff(127,assumption,(~(elem!1 = f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(128,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.39/0.59 tff(129,plain,((~(f(f(elem!1)) = f(elem!1))) | (elem!1 = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(130,plain,
% 0.39/0.59 (~(f(f(elem!1)) = f(elem!1))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[129, 120])).
% 0.39/0.59 tff(131,plain,
% 0.39/0.59 ((f(f(elem!1)) = f(elem!1)) <=> (f(elem!1) = f(f(elem!1)))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(132,plain,
% 0.39/0.59 ((f(elem!1) = f(f(elem!1))) <=> (f(f(elem!1)) = f(elem!1))),
% 0.39/0.59 inference(symmetry,[status(thm)],[131])).
% 0.39/0.59 tff(133,assumption,(f(elem!1) = f(f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(134,plain,
% 0.39/0.59 (f(f(elem!1)) = f(elem!1)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.39/0.59 tff(135,assumption,(~(f(f(elem!1)) = f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(136,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.39/0.59 tff(137,plain,((~(f(elem!1) = f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(138,plain,
% 0.39/0.59 (~(f(elem!1) = f(f(elem!1)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.39/0.59 tff(139,assumption,(f(f(f(elem!1))) = f(f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(140,plain,
% 0.39/0.59 (f(f(elem!1)) = f(f(f(elem!1)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[139])).
% 0.39/0.59 tff(141,plain,
% 0.39/0.59 (inj_0(f(f(elem!1))) = inj_0(f(f(f(elem!1))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[140])).
% 0.39/0.59 tff(142,plain,
% 0.39/0.59 (f(elem!1) = inj_0(f(f(elem!1)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[122])).
% 0.39/0.59 tff(143,plain,
% 0.39/0.59 (f(elem!1) = f(f(elem!1))),
% 0.39/0.59 inference(transitivity,[status(thm)],[142, 141, 69])).
% 0.39/0.59 tff(144,assumption,(~(f(elem!1) = f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(145,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.39/0.59 tff(146,plain,((~(f(f(f(elem!1))) = f(f(elem!1)))) | (f(elem!1) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(147,plain,
% 0.39/0.59 (~(f(f(f(elem!1))) = f(f(elem!1)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[146, 138])).
% 0.39/0.59 tff(148,assumption,(f(f(f(f(elem!1)))) = f(f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(149,plain,
% 0.39/0.59 (f(f(f(elem!1))) = f(f(f(f(elem!1))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[148])).
% 0.39/0.59 tff(150,plain,
% 0.39/0.59 (inj_0(f(f(f(elem!1)))) = inj_0(f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[149])).
% 0.39/0.59 tff(151,plain,
% 0.39/0.59 (inj_0(f(f(f(f(elem!1))))) = inj_0(f(f(f(elem!1))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[150])).
% 0.39/0.59 tff(152,plain,
% 0.39/0.59 (f(f(f(elem!1))) = inj_0(f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[83])).
% 0.39/0.59 tff(153,plain,
% 0.39/0.59 (f(f(f(elem!1))) = f(f(elem!1))),
% 0.39/0.59 inference(transitivity,[status(thm)],[152, 151, 69])).
% 0.39/0.59 tff(154,assumption,(~(f(f(f(elem!1))) = f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(155,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.39/0.59 tff(156,plain,((~(f(f(f(f(elem!1)))) = f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(157,plain,
% 0.39/0.59 (~(f(f(f(f(elem!1)))) = f(f(f(elem!1))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[156, 147])).
% 0.39/0.59 tff(158,plain,
% 0.39/0.59 ((c = f(f(elem!1))) <=> (f(f(elem!1)) = c)),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(159,plain,
% 0.39/0.59 ((f(f(elem!1)) = c) <=> (c = f(f(elem!1)))),
% 0.39/0.59 inference(symmetry,[status(thm)],[158])).
% 0.39/0.59 tff(160,plain,
% 0.39/0.59 ((~(f(f(elem!1)) = c)) <=> (~(c = f(f(elem!1))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[159])).
% 0.39/0.59 tff(161,plain,
% 0.39/0.59 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(elem!1)) = c))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(162,plain,
% 0.39/0.59 (~(f(f(elem!1)) = c)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[161, 28])).
% 0.39/0.59 tff(163,plain,
% 0.39/0.59 (~(c = f(f(elem!1)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[162, 160])).
% 0.39/0.59 tff(164,assumption,(f(f(f(f(elem!1)))) = f(f(elem!1))), introduced(assumption)).
% 0.39/0.59 tff(165,plain,
% 0.39/0.59 (inj_0(f(f(f(f(elem!1))))) = inj_0(f(f(elem!1)))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[164])).
% 0.39/0.59 tff(166,plain,
% 0.39/0.59 (inj_0(f(f(elem!1))) = inj_0(f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[165])).
% 0.39/0.59 tff(167,plain,
% 0.39/0.59 (f(elem!1) = f(f(f(elem!1)))),
% 0.39/0.59 inference(transitivity,[status(thm)],[142, 166, 83])).
% 0.39/0.59 tff(168,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[92, 167])).
% 0.39/0.59 tff(169,plain,((~(f(f(f(f(elem!1)))) = f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(170,plain,
% 0.39/0.59 (~(f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[169, 92])).
% 0.39/0.59 tff(171,assumption,(~r(f(f(f(f(elem!1)))), elem!1)), introduced(assumption)).
% 0.39/0.59 tff(172,plain,
% 0.39/0.59 (~(elem!1 = f(elem!1))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[119, 62])).
% 0.39/0.59 tff(173,assumption,(r(elem!1, f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.39/0.59 tff(174,plain,
% 0.39/0.59 (^[Y: $i, X: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(175,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[174])).
% 0.39/0.59 tff(176,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(177,axiom,(![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rsym')).
% 0.39/0.59 tff(178,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.39/0.59 tff(179,plain,(
% 0.39/0.59 ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.39/0.59 inference(skolemize,[status(sab)],[178])).
% 0.39/0.59 tff(180,plain,
% 0.39/0.59 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.39/0.59 tff(181,plain,
% 0.39/0.59 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), elem!1))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(182,plain,
% 0.39/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), elem!1))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(183,plain,
% 0.39/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), elem!1)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.39/0.59 tff(184,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[183, 180, 173, 171])).
% 0.39/0.59 tff(185,plain,((~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(186,plain,
% 0.39/0.59 (~r(elem!1, f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[185, 171])).
% 0.39/0.59 tff(187,assumption,(~r(elem!1, f(f(elem!1)))), introduced(assumption)).
% 0.39/0.59 tff(188,plain,
% 0.39/0.59 ((f(f(f(f(elem!1)))) = elem!1) <=> (elem!1 = f(f(f(f(elem!1)))))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(189,assumption,(f(f(f(f(elem!1)))) = elem!1), introduced(assumption)).
% 0.39/0.59 tff(190,plain,
% 0.39/0.59 (elem!1 = f(f(f(f(elem!1))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.39/0.60 tff(191,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[93, 190])).
% 0.39/0.60 tff(192,plain,((~(f(f(f(f(elem!1)))) = elem!1)) | (elem!1 = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.60 tff(193,plain,
% 0.39/0.60 (~(f(f(f(f(elem!1)))) = elem!1)),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[192, 93])).
% 0.39/0.60 tff(194,assumption,(~(f(f(f(f(elem!1)))) = f(f(elem!1)))), introduced(assumption)).
% 0.39/0.60 tff(195,assumption,(~(f(f(f(f(elem!1)))) = elem!1)), introduced(assumption)).
% 0.39/0.60 tff(196,plain,
% 0.39/0.60 (^[Z: $i, Y: $i, X: $i] : refl((r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(197,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[196])).
% 0.39/0.60 tff(198,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(199,plain,
% 0.39/0.60 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((X = Y) | (X = Z)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)))), rewrite((((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> ((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)))), rewrite(((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)) <=> (r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> (r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ((r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)))), rewrite(((r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(200,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[199])).
% 0.39/0.60 tff(201,axiom,(![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rn3acl')).
% 0.39/0.60 tff(202,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.39/0.60 tff(203,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.39/0.60 tff(204,plain,(
% 0.39/0.60 ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(skolemize,[status(sab)],[203])).
% 0.39/0.60 tff(205,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.39/0.60 tff(206,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(207,plain,
% 0.39/0.60 ((r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1)) <=> (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(208,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[207])).
% 0.39/0.60 tff(209,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[208, 206])).
% 0.39/0.60 tff(210,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(211,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.39/0.60 tff(212,plain,
% 0.39/0.60 (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.39/0.60 tff(213,plain,
% 0.39/0.60 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[212, 187, 195, 62, 194, 171])).
% 0.39/0.60 tff(214,plain,
% 0.39/0.60 (~(f(f(elem!1)) = f(elem!1))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[129, 172])).
% 0.39/0.60 tff(215,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(216,plain,
% 0.39/0.60 ((r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1)))) <=> (r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(217,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[216])).
% 0.39/0.60 tff(218,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)))),
% 0.39/0.60 inference(transitivity,[status(thm)],[217, 215])).
% 0.39/0.60 tff(219,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(220,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.39/0.60 tff(221,plain,
% 0.39/0.60 (r(elem!1, f(f(elem!1))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[220, 205])).
% 0.39/0.60 tff(222,plain,
% 0.39/0.60 (r(f(f(elem!1)), f(elem!1))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[221, 187, 172, 214, 62, 100])).
% 0.39/0.60 tff(223,assumption,(r(f(f(f(f(elem!1)))), f(elem!1))), introduced(assumption)).
% 0.39/0.60 tff(224,plain,
% 0.39/0.60 (^[Z: $i, Y: $i, X: $i] : refl(((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(225,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[224])).
% 0.39/0.60 tff(226,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(227,plain,
% 0.39/0.60 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((X = Y) | (X = Z)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) <=> (((Y = Z) | (X = Z) | (X = Y)) | (~r(X, Y))))), rewrite((((Y = Z) | (X = Z) | (X = Y)) | (~r(X, Y))) <=> ((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) <=> ((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)))), ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) <=> (((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(X, Z))))), rewrite((((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(X, Z))) <=> ((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) <=> ((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> (((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))))), rewrite((((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(228,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[227])).
% 0.39/0.60 tff(229,axiom,(![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rn3cl')).
% 0.39/0.60 tff(230,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.39/0.60 tff(231,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.39/0.60 tff(232,plain,(
% 0.39/0.60 ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(skolemize,[status(sab)],[231])).
% 0.39/0.60 tff(233,plain,
% 0.39/0.60 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.39/0.60 tff(234,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(235,plain,
% 0.39/0.60 (((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> ((f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(236,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[235])).
% 0.39/0.60 tff(237,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[236, 234])).
% 0.39/0.60 tff(238,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(239,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.39/0.60 tff(240,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[239, 233, 223, 91, 222, 214, 194, 213])).
% 0.39/0.60 tff(241,plain,(r(elem!1, f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = f(f(elem!1))) | r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.60 tff(242,plain,
% 0.39/0.60 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[241, 171, 91, 194, 193, 62, 187, 100])).
% 0.39/0.60 tff(243,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(244,plain,
% 0.39/0.60 ((r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(f(f(elem!1)))))) <=> (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(245,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1)))))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[244])).
% 0.39/0.60 tff(246,plain,
% 0.39/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[245, 243])).
% 0.39/0.60 tff(247,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(248,plain,
% 0.39/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1)))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.39/0.60 tff(249,plain,
% 0.39/0.60 (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1)))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[248, 205])).
% 0.39/0.61 tff(250,plain,
% 0.39/0.61 ($false),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[249, 242, 186, 91, 172, 93, 100])).
% 0.39/0.61 tff(251,plain,(r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.61 tff(252,plain,
% 0.39/0.61 (r(elem!1, f(f(elem!1)))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[251, 171, 91, 100, 170, 110, 93])).
% 0.39/0.61 tff(253,assumption,(~r(c, elem!1)), introduced(assumption)).
% 0.39/0.61 tff(254,plain,
% 0.39/0.61 ((c = f(elem!1)) <=> (f(elem!1) = c)),
% 0.39/0.61 inference(commutativity,[status(thm)],[])).
% 0.39/0.61 tff(255,plain,
% 0.39/0.61 ((f(elem!1) = c) <=> (c = f(elem!1))),
% 0.39/0.61 inference(symmetry,[status(thm)],[254])).
% 0.39/0.61 tff(256,plain,
% 0.39/0.61 ((~(f(elem!1) = c)) <=> (~(c = f(elem!1)))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[255])).
% 0.39/0.61 tff(257,plain,
% 0.39/0.61 ((~![X: $i] : (~(f(X) = c))) | (~(f(elem!1) = c))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(258,plain,
% 0.39/0.61 (~(f(elem!1) = c)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[257, 28])).
% 0.39/0.61 tff(259,plain,
% 0.39/0.61 (~(c = f(elem!1))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[258, 256])).
% 0.39/0.61 tff(260,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(261,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(262,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1)),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.39/0.61 tff(263,plain,
% 0.39/0.61 (r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[262, 205])).
% 0.39/0.61 tff(264,plain,
% 0.39/0.61 (r(c, elem!1) | r(elem!1, f(elem!1)) | r(c, f(elem!1)) | (elem!1 = f(elem!1)) | (c = elem!1)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[263, 259])).
% 0.39/0.61 tff(265,plain,
% 0.39/0.61 (r(c, f(elem!1))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[264, 253, 100, 66, 127])).
% 0.39/0.61 tff(266,plain,
% 0.39/0.61 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(elem!1))) | r(f(elem!1), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(elem!1))) | r(f(elem!1), c))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(267,plain,
% 0.39/0.61 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(elem!1))) | r(f(elem!1), c))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(268,plain,
% 0.39/0.61 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(elem!1))) | r(f(elem!1), c)),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.39/0.61 tff(269,plain,
% 0.39/0.61 (r(f(elem!1), c)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[268, 180, 265])).
% 0.39/0.61 tff(270,plain,
% 0.39/0.61 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[249, 186, 91, 127, 93, 100])).
% 0.39/0.61 tff(271,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(272,plain,
% 0.39/0.61 (((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1))) <=> ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(273,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c))))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[272])).
% 0.39/0.61 tff(274,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)))),
% 0.39/0.61 inference(transitivity,[status(thm)],[273, 271])).
% 0.39/0.61 tff(275,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(276,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), c))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.39/0.61 tff(277,plain,
% 0.39/0.61 (~r(f(f(f(f(elem!1)))), c)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[276, 233, 258, 97, 270, 91, 269])).
% 0.39/0.61 tff(278,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(279,plain,
% 0.39/0.61 ((r(f(f(f(f(elem!1)))), c) | r(c, elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = c)) <=> (r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(280,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), c) | r(c, elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c)))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[279])).
% 0.39/0.61 tff(281,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), c) | r(c, elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c))),
% 0.39/0.61 inference(transitivity,[status(thm)],[280, 278])).
% 0.39/0.61 tff(282,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), c) | r(c, elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = c))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(283,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(f(elem!1)))), c)),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.39/0.61 tff(284,plain,
% 0.39/0.61 ($false),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[283, 205, 253, 66, 97, 171, 193, 277])).
% 0.39/0.61 tff(285,plain,(r(f(f(f(f(elem!1)))), elem!1) | r(c, elem!1) | (c = elem!1) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.61 tff(286,plain,
% 0.39/0.61 (r(c, elem!1)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[285, 171, 91, 66, 120, 93, 100])).
% 0.39/0.61 tff(287,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(288,plain,
% 0.39/0.61 (((~r(c, elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1)) <=> ((~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(289,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[288])).
% 0.39/0.61 tff(290,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.39/0.61 inference(transitivity,[status(thm)],[289, 287])).
% 0.39/0.61 tff(291,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(292,plain,
% 0.39/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (~r(c, elem!1)) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.39/0.61 tff(293,plain,
% 0.39/0.61 (~r(c, f(f(elem!1)))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[292, 233, 286, 66, 252, 110, 163])).
% 0.39/0.61 tff(294,plain,
% 0.39/0.61 ((f(f(elem!1)) = f(f(f(elem!1)))) <=> (f(f(f(elem!1))) = f(f(elem!1)))),
% 0.39/0.61 inference(commutativity,[status(thm)],[])).
% 0.39/0.61 tff(295,assumption,(f(f(elem!1)) = f(f(f(elem!1)))), introduced(assumption)).
% 0.39/0.61 tff(296,plain,
% 0.39/0.61 (f(f(f(elem!1))) = f(f(elem!1))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.39/0.61 tff(297,plain,
% 0.39/0.61 ($false),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[154, 296])).
% 0.39/0.61 tff(298,plain,((~(f(f(elem!1)) = f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.61 tff(299,plain,
% 0.39/0.61 (~(f(f(elem!1)) = f(f(f(elem!1))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[298, 147])).
% 0.39/0.61 tff(300,plain,
% 0.39/0.61 ((c = f(f(f(elem!1)))) <=> (f(f(f(elem!1))) = c)),
% 0.39/0.61 inference(commutativity,[status(thm)],[])).
% 0.39/0.61 tff(301,plain,
% 0.39/0.61 ((f(f(f(elem!1))) = c) <=> (c = f(f(f(elem!1))))),
% 0.39/0.61 inference(symmetry,[status(thm)],[300])).
% 0.39/0.61 tff(302,plain,
% 0.39/0.61 ((~(f(f(f(elem!1))) = c)) <=> (~(c = f(f(f(elem!1)))))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[301])).
% 0.39/0.61 tff(303,plain,
% 0.39/0.61 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(elem!1))) = c))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(304,plain,
% 0.39/0.61 (~(f(f(f(elem!1))) = c)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[303, 28])).
% 0.39/0.61 tff(305,plain,
% 0.39/0.61 (~(c = f(f(f(elem!1))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[304, 302])).
% 0.39/0.61 tff(306,plain,
% 0.39/0.61 ((f(f(f(elem!1))) = elem!1) <=> (elem!1 = f(f(f(elem!1))))),
% 0.39/0.61 inference(commutativity,[status(thm)],[])).
% 0.39/0.61 tff(307,plain,
% 0.39/0.61 ((elem!1 = f(f(f(elem!1)))) <=> (f(f(f(elem!1))) = elem!1)),
% 0.39/0.61 inference(symmetry,[status(thm)],[306])).
% 0.39/0.61 tff(308,assumption,(elem!1 = f(f(f(elem!1)))), introduced(assumption)).
% 0.39/0.61 tff(309,plain,
% 0.39/0.61 (f(f(f(elem!1))) = elem!1),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.39/0.61 tff(310,assumption,(~(f(f(f(elem!1))) = elem!1)), introduced(assumption)).
% 0.39/0.61 tff(311,plain,
% 0.39/0.61 ($false),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.39/0.61 tff(312,plain,((~(elem!1 = f(f(f(elem!1))))) | (f(f(f(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.61 tff(313,plain,
% 0.39/0.61 (~(elem!1 = f(f(f(elem!1))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[312, 105])).
% 0.39/0.61 tff(314,assumption,(~(f(f(f(f(elem!1)))) = f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.61 tff(315,assumption,(~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.61 tff(316,assumption,(~r(f(f(f(elem!1))), elem!1)), introduced(assumption)).
% 0.39/0.61 tff(317,plain,
% 0.39/0.61 (~(elem!1 = f(f(f(elem!1))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[312, 310])).
% 0.39/0.61 tff(318,plain,
% 0.39/0.61 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(f(elem!1))))) | r(f(f(f(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(f(elem!1))))) | r(f(f(f(elem!1))), elem!1))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(319,plain,
% 0.39/0.61 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(f(elem!1))))) | r(f(f(f(elem!1))), elem!1))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(320,plain,
% 0.39/0.61 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(f(elem!1))))) | r(f(f(f(elem!1))), elem!1)),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.39/0.61 tff(321,plain,
% 0.39/0.61 (~r(elem!1, f(f(f(elem!1))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[320, 180, 316])).
% 0.39/0.61 tff(322,plain,
% 0.39/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(323,plain,
% 0.39/0.62 ((r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(324,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1))))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[323])).
% 0.39/0.62 tff(325,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[324, 322])).
% 0.39/0.62 tff(326,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(elem!1)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(327,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.39/0.62 tff(328,plain,
% 0.39/0.62 ((f(elem!1) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(elem!1), f(f(f(elem!1))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[327, 205])).
% 0.39/0.62 tff(329,plain,
% 0.39/0.62 (r(f(elem!1), f(f(f(elem!1))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[328, 321, 317, 100, 92, 120])).
% 0.39/0.62 tff(330,plain,
% 0.39/0.62 (r(c, f(elem!1))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[264, 253, 100, 66, 120])).
% 0.39/0.62 tff(331,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(332,plain,
% 0.39/0.62 (((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(333,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1)))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[332])).
% 0.39/0.62 tff(334,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[333, 331])).
% 0.39/0.62 tff(335,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(elem!1)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(336,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (c = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(elem!1)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.39/0.62 tff(337,plain,
% 0.39/0.62 (~r(c, f(f(f(elem!1))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[336, 233, 330, 259, 92, 329, 305])).
% 0.39/0.62 tff(338,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(339,plain,
% 0.39/0.62 ((r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(c, elem!1) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1))))) <=> (r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(340,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(c, elem!1) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1))))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[339])).
% 0.39/0.62 tff(341,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(c, elem!1) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[340, 338])).
% 0.39/0.62 tff(342,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(c, elem!1) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(343,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.39/0.62 tff(344,plain,
% 0.39/0.62 ($false),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[343, 205, 253, 66, 316, 310, 337, 305])).
% 0.39/0.62 tff(345,plain,(r(c, elem!1) | (c = elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = f(f(f(elem!1)))) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.62 tff(346,plain,
% 0.39/0.62 (r(c, elem!1)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[345, 316, 66, 310, 92, 100])).
% 0.39/0.62 tff(347,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(348,plain,
% 0.39/0.62 ((r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1)) <=> (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(349,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1)))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[348])).
% 0.39/0.62 tff(350,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[349, 347])).
% 0.39/0.62 tff(351,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(352,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.39/0.62 tff(353,plain,
% 0.39/0.62 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[352, 205, 187, 110, 316, 310, 147])).
% 0.39/0.62 tff(354,plain,
% 0.39/0.62 (r(f(f(elem!1)), f(elem!1))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[221, 187, 120, 130, 110, 100])).
% 0.39/0.62 tff(355,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(356,plain,
% 0.39/0.62 (((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(357,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[356])).
% 0.39/0.62 tff(358,plain,
% 0.39/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[357, 355])).
% 0.39/0.62 tff(359,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(360,plain,
% 0.39/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.39/0.62 tff(361,plain,
% 0.39/0.62 (~r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[360, 233, 92, 329, 354, 130, 299])).
% 0.39/0.62 tff(362,assumption,(r(f(f(f(elem!1))), f(f(elem!1)))), introduced(assumption)).
% 0.39/0.62 tff(363,assumption,(~r(f(f(elem!1)), f(f(f(elem!1))))), introduced(assumption)).
% 0.39/0.62 tff(364,plain,
% 0.39/0.62 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(365,plain,
% 0.39/0.62 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(366,plain,
% 0.39/0.62 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.39/0.62 tff(367,plain,
% 0.39/0.62 ($false),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[366, 180, 363, 362])).
% 0.39/0.62 tff(368,plain,((~r(f(f(f(elem!1))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.62 tff(369,plain,
% 0.39/0.62 ($false),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[368, 361, 353])).
% 0.47/0.63 tff(370,plain,(r(elem!1, f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(371,plain,
% 0.47/0.63 (r(elem!1, f(f(elem!1)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[370, 316, 92, 310, 100])).
% 0.47/0.63 tff(372,assumption,(r(c, elem!1)), introduced(assumption)).
% 0.47/0.63 tff(373,assumption,(r(elem!1, f(f(elem!1)))), introduced(assumption)).
% 0.47/0.63 tff(374,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(375,plain,
% 0.47/0.63 ((r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(376,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[375])).
% 0.47/0.63 tff(377,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.63 inference(transitivity,[status(thm)],[376, 374])).
% 0.47/0.63 tff(378,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(379,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.47/0.63 tff(380,plain,
% 0.47/0.63 ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[379, 205])).
% 0.47/0.63 tff(381,plain,
% 0.47/0.63 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[380, 315, 316, 314, 193, 310])).
% 0.47/0.63 tff(382,plain,
% 0.47/0.63 ((c = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = c)),
% 0.47/0.63 inference(commutativity,[status(thm)],[])).
% 0.47/0.63 tff(383,plain,
% 0.47/0.63 ((f(f(f(f(elem!1)))) = c) <=> (c = f(f(f(f(elem!1)))))),
% 0.47/0.63 inference(symmetry,[status(thm)],[382])).
% 0.47/0.63 tff(384,plain,
% 0.47/0.63 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[383])).
% 0.47/0.63 tff(385,plain,
% 0.47/0.63 (~(c = f(f(f(f(elem!1)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[97, 384])).
% 0.47/0.63 tff(386,assumption,(~r(c, f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.47/0.63 tff(387,assumption,(r(f(f(f(f(elem!1)))), elem!1)), introduced(assumption)).
% 0.47/0.63 tff(388,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(389,plain,
% 0.47/0.63 (((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1)) <=> ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(390,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[389])).
% 0.47/0.63 tff(391,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[390, 388])).
% 0.47/0.63 tff(392,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(393,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.47/0.63 tff(394,plain,
% 0.47/0.63 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[393, 233, 373, 62, 387, 195, 194])).
% 0.47/0.63 tff(395,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(396,plain,
% 0.47/0.63 ((r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1)))))) <=> (r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(397,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1)))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[396])).
% 0.47/0.63 tff(398,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[397, 395])).
% 0.47/0.63 tff(399,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(400,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(elem!1))) | (c = f(f(f(f(elem!1)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.47/0.63 tff(401,plain,
% 0.47/0.63 (r(c, f(f(elem!1)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[400, 205, 194, 394, 386, 385, 163])).
% 0.47/0.63 tff(402,plain,
% 0.47/0.63 ((c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[292, 233, 372, 66, 373, 62])).
% 0.47/0.63 tff(403,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[402, 401, 163])).
% 0.47/0.63 tff(404,plain,((~r(elem!1, f(f(elem!1)))) | (~r(c, elem!1)) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(c, f(f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(405,plain,
% 0.47/0.63 (r(c, f(f(f(f(elem!1)))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[404, 381, 66, 62, 194, 373, 193, 372])).
% 0.47/0.63 tff(406,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(407,plain,
% 0.47/0.63 ((r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1)))))) <=> ((elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(408,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[407])).
% 0.47/0.63 tff(409,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[408, 406])).
% 0.47/0.63 tff(410,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(411,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.47/0.63 tff(412,plain,
% 0.47/0.63 ((elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[411, 205])).
% 0.47/0.63 tff(413,plain,
% 0.47/0.63 (r(elem!1, f(f(f(f(elem!1)))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[412, 315, 321, 93, 314, 317])).
% 0.47/0.63 tff(414,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(415,plain,
% 0.47/0.63 (((~r(c, elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = elem!1)) <=> ((c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(416,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[415])).
% 0.47/0.64 tff(417,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[416, 414])).
% 0.47/0.64 tff(418,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = elem!1))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(419,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(c, elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.47/0.64 tff(420,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[419, 233, 372, 66, 93, 413, 405, 99])).
% 0.47/0.64 tff(421,plain,(r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (~r(c, elem!1)) | (c = elem!1) | (elem!1 = f(f(f(f(elem!1))))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(422,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[421, 371, 316, 314, 93, 110, 170, 315, 66, 346, 310])).
% 0.47/0.64 tff(423,plain,(r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (elem!1 = f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (c = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = f(f(f(elem!1)))) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(424,plain,
% 0.47/0.64 (r(f(f(f(elem!1))), elem!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[423, 66, 93, 315, 314, 310, 92, 100])).
% 0.47/0.64 tff(425,assumption,(r(f(f(f(elem!1))), elem!1)), introduced(assumption)).
% 0.47/0.64 tff(426,plain,
% 0.47/0.64 (~(f(elem!1) = f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[137, 214])).
% 0.47/0.64 tff(427,plain,
% 0.47/0.64 (~(f(f(f(elem!1))) = f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[146, 426])).
% 0.47/0.64 tff(428,plain,
% 0.47/0.64 (r(c, f(elem!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[264, 253, 100, 66, 172])).
% 0.47/0.64 tff(429,plain,
% 0.47/0.64 (r(f(elem!1), c)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[268, 180, 428])).
% 0.47/0.64 tff(430,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(431,plain,
% 0.47/0.64 (((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1))) <=> ((f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(432,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[431])).
% 0.47/0.64 tff(433,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[432, 430])).
% 0.47/0.64 tff(434,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(435,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.47/0.64 tff(436,plain,
% 0.47/0.64 (~r(f(f(elem!1)), c)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[435, 233, 258, 162, 222, 214, 429])).
% 0.47/0.64 tff(437,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(elem!1)))) | r(f(f(elem!1)), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(438,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(439,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(elem!1)))) | r(f(f(elem!1)), c)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.47/0.64 tff(440,plain,
% 0.47/0.64 (~r(c, f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[439, 180, 436])).
% 0.47/0.64 tff(441,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(442,plain,
% 0.47/0.64 ((r(c, elem!1) | r(elem!1, f(f(elem!1))) | r(c, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1)) <=> (r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(443,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(elem!1))) | r(c, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[442])).
% 0.47/0.64 tff(444,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(elem!1))) | r(c, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[443, 441])).
% 0.47/0.64 tff(445,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(elem!1))) | r(c, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (c = f(f(elem!1))) | (c = elem!1))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(446,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | r(elem!1, f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.47/0.64 tff(447,plain,
% 0.47/0.64 (r(c, f(f(elem!1))) | (c = f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[446, 205, 253, 66, 187, 62])).
% 0.47/0.64 tff(448,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[447, 440, 163])).
% 0.47/0.64 tff(449,plain,(r(elem!1, f(f(elem!1))) | r(c, elem!1) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(450,plain,
% 0.47/0.64 (r(elem!1, f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[449, 253, 66, 62, 100])).
% 0.47/0.64 tff(451,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(452,plain,
% 0.47/0.64 (((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1)) <=> ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(453,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[452])).
% 0.47/0.64 tff(454,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[453, 451])).
% 0.47/0.64 tff(455,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(456,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.47/0.64 tff(457,plain,
% 0.47/0.64 ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[456, 233])).
% 0.47/0.64 tff(458,plain,
% 0.47/0.64 (~r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[457, 450, 62, 310, 427, 425])).
% 0.47/0.64 tff(459,plain,
% 0.47/0.64 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[89, 317])).
% 0.47/0.64 tff(460,plain,
% 0.47/0.64 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[285, 253, 66, 459, 172, 93, 100])).
% 0.47/0.64 tff(461,plain,
% 0.47/0.64 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[393, 233, 450, 62, 460, 193, 194])).
% 0.47/0.64 tff(462,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(463,plain,
% 0.47/0.64 ((r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(464,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[463])).
% 0.47/0.64 tff(465,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[464, 462])).
% 0.47/0.64 tff(466,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(467,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.47/0.64 tff(468,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[467, 205, 314, 315, 194, 461, 427, 458])).
% 0.47/0.64 tff(469,plain,(r(c, elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (c = elem!1) | r(elem!1, f(elem!1)) | (elem!1 = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(470,plain,
% 0.47/0.64 (r(c, elem!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[469, 424, 315, 170, 110, 310, 314, 66, 100, 93])).
% 0.47/0.64 tff(471,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(472,plain,
% 0.47/0.64 (((~r(f(f(f(elem!1))), c)) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (c = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = c)) <=> ((c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(473,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), c)) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (c = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[472])).
% 0.47/0.64 tff(474,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), c)) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (c = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[473, 471])).
% 0.47/0.64 tff(475,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), c)) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (c = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = c))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(476,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (f(f(f(elem!1))) = c) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.47/0.64 tff(477,plain,
% 0.47/0.64 ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(f(f(f(elem!1))), c))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[476, 233, 304])).
% 0.47/0.65 tff(478,plain,
% 0.47/0.65 (~r(f(f(f(elem!1))), c)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[477, 470, 66, 310, 424])).
% 0.47/0.65 tff(479,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), elem!1)) | r(elem!1, f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), elem!1)) | r(elem!1, f(f(f(elem!1)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(480,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), elem!1)) | r(elem!1, f(f(f(elem!1)))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(481,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), elem!1)) | r(elem!1, f(f(f(elem!1))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.47/0.65 tff(482,plain,
% 0.47/0.65 (r(elem!1, f(f(f(elem!1))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[481, 180, 424])).
% 0.47/0.65 tff(483,plain,
% 0.47/0.65 (~r(f(f(f(elem!1))), c)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[477, 372, 425, 310, 66])).
% 0.47/0.65 tff(484,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(485,plain,
% 0.47/0.65 ((r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(486,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[485])).
% 0.47/0.65 tff(487,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.65 inference(transitivity,[status(thm)],[486, 484])).
% 0.47/0.65 tff(488,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(489,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(f(f(elem!1)))), c)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.47/0.65 tff(490,plain,
% 0.47/0.65 (r(f(f(f(f(elem!1)))), c)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[489, 205, 304, 97, 314, 315, 483])).
% 0.47/0.65 tff(491,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, elem!1)) | r(elem!1, c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, elem!1)) | r(elem!1, c))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(492,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, elem!1)) | r(elem!1, c))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(493,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, elem!1)) | r(elem!1, c)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.47/0.65 tff(494,plain,
% 0.47/0.65 (r(elem!1, c)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[493, 180, 372])).
% 0.47/0.65 tff(495,plain,
% 0.47/0.65 ((elem!1 = c) <=> (c = elem!1)),
% 0.47/0.65 inference(commutativity,[status(thm)],[])).
% 0.47/0.65 tff(496,plain,
% 0.47/0.65 ((c = elem!1) <=> (elem!1 = c)),
% 0.47/0.65 inference(symmetry,[status(thm)],[495])).
% 0.47/0.65 tff(497,plain,
% 0.47/0.65 ((~(c = elem!1)) <=> (~(elem!1 = c))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[496])).
% 0.47/0.65 tff(498,plain,
% 0.47/0.65 (~(elem!1 = c)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[66, 497])).
% 0.47/0.65 tff(499,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(500,plain,
% 0.47/0.65 (((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, c)) | (~r(f(f(f(f(elem!1)))), c)) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1)) <=> ((f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(501,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, c)) | (~r(f(f(f(f(elem!1)))), c)) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[500])).
% 0.47/0.65 tff(502,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, c)) | (~r(f(f(f(f(elem!1)))), c)) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[501, 499])).
% 0.47/0.65 tff(503,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, c)) | (~r(f(f(f(f(elem!1)))), c)) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(504,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(elem!1, c))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.47/0.65 tff(505,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[504, 233, 97, 387, 195, 498, 494, 490])).
% 0.47/0.65 tff(506,plain,((~r(c, elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(507,plain,
% 0.47/0.65 (~r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[506, 470, 193, 314, 315, 66, 310, 424])).
% 0.47/0.65 tff(508,plain,
% 0.47/0.65 (~r(elem!1, f(f(f(f(elem!1)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[185, 507])).
% 0.47/0.65 tff(509,plain,
% 0.47/0.65 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[249, 508, 459, 120, 93, 100])).
% 0.47/0.65 tff(510,plain,
% 0.47/0.65 (r(elem!1, f(f(elem!1)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[241, 509, 459, 170, 193, 110, 507, 100])).
% 0.47/0.65 tff(511,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(512,plain,
% 0.47/0.65 (((~r(elem!1, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1)))) <=> ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(513,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[512])).
% 0.47/0.65 tff(514,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[513, 511])).
% 0.47/0.65 tff(515,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(516,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.47/0.65 tff(517,plain,
% 0.47/0.65 ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[516, 233])).
% 0.47/0.65 tff(518,plain,
% 0.47/0.65 (~r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[517, 510, 317, 110, 482, 299])).
% 0.47/0.65 tff(519,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(520,plain,
% 0.47/0.65 ((r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(elem!1)), c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1))))) <=> ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(521,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(elem!1)), c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[520])).
% 0.47/0.65 tff(522,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(elem!1)), c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.47/0.65 inference(transitivity,[status(thm)],[521, 519])).
% 0.47/0.65 tff(523,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(f(elem!1)), c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(524,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(f(elem!1)), c)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.47/0.65 tff(525,plain,
% 0.47/0.65 (r(f(f(elem!1)), c)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[524, 205, 162, 304, 518, 478, 299])).
% 0.47/0.65 tff(526,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(elem!1)))) | r(f(f(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(elem!1)))) | r(f(f(elem!1)), elem!1))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(527,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, f(f(elem!1)))) | r(f(f(elem!1)), elem!1))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(528,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, f(f(elem!1)))) | r(f(f(elem!1)), elem!1)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.47/0.65 tff(529,plain,
% 0.47/0.65 (r(f(f(elem!1)), elem!1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[528, 180, 510])).
% 0.47/0.65 tff(530,plain,
% 0.47/0.65 ((f(f(elem!1)) = elem!1) <=> (elem!1 = f(f(elem!1)))),
% 0.47/0.65 inference(commutativity,[status(thm)],[])).
% 0.47/0.65 tff(531,plain,
% 0.47/0.65 ((elem!1 = f(f(elem!1))) <=> (f(f(elem!1)) = elem!1)),
% 0.47/0.65 inference(symmetry,[status(thm)],[530])).
% 0.47/0.65 tff(532,plain,
% 0.47/0.65 ((~(elem!1 = f(f(elem!1)))) <=> (~(f(f(elem!1)) = elem!1))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[531])).
% 0.47/0.66 tff(533,plain,
% 0.47/0.66 (~(f(f(elem!1)) = elem!1)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[110, 532])).
% 0.47/0.66 tff(534,plain,
% 0.47/0.66 (r(elem!1, c)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[493, 180, 470])).
% 0.47/0.66 tff(535,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(536,plain,
% 0.47/0.66 (((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)) | (elem!1 = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = elem!1)) <=> ((f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(537,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)) | (elem!1 = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[536])).
% 0.47/0.66 tff(538,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)) | (elem!1 = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[537, 535])).
% 0.47/0.66 tff(539,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c)) | (elem!1 = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = elem!1))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(540,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (elem!1 = c) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(elem!1, c)) | (~r(f(f(elem!1)), c))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.47/0.66 tff(541,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[540, 233, 162, 498, 534, 533, 529, 525])).
% 0.47/0.66 tff(542,plain,((c = elem!1) | r(elem!1, f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(543,plain,
% 0.47/0.66 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[542, 93, 105, 157, 100, 66, 92])).
% 0.47/0.66 tff(544,plain,
% 0.47/0.66 ((f(f(f(elem!1))) = f(elem!1)) <=> (f(elem!1) = f(f(f(elem!1))))),
% 0.47/0.66 inference(commutativity,[status(thm)],[])).
% 0.47/0.66 tff(545,assumption,(f(f(f(elem!1))) = f(elem!1)), introduced(assumption)).
% 0.47/0.66 tff(546,plain,
% 0.47/0.66 (f(elem!1) = f(f(f(elem!1)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.47/0.66 tff(547,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[92, 546])).
% 0.47/0.66 tff(548,plain,((~(f(f(f(elem!1))) = f(elem!1))) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(549,plain,
% 0.47/0.66 (~(f(f(f(elem!1))) = f(elem!1))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[548, 92])).
% 0.47/0.66 tff(550,assumption,(~r(elem!1, f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.47/0.66 tff(551,assumption,(r(f(f(f(elem!1))), f(elem!1))), introduced(assumption)).
% 0.47/0.66 tff(552,assumption,(~(f(f(f(elem!1))) = f(elem!1))), introduced(assumption)).
% 0.47/0.66 tff(553,assumption,(r(f(f(f(f(elem!1)))), f(f(f(elem!1))))), introduced(assumption)).
% 0.47/0.66 tff(554,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(555,plain,
% 0.47/0.66 (((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(556,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[555])).
% 0.47/0.66 tff(557,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[556, 554])).
% 0.47/0.66 tff(558,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(559,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.47/0.66 tff(560,plain,
% 0.47/0.66 ((f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[559, 233, 314, 553, 552, 551])).
% 0.47/0.66 tff(561,plain,
% 0.47/0.66 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[560, 91])).
% 0.47/0.66 tff(562,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[249, 561, 91, 93, 127, 100, 550])).
% 0.47/0.66 tff(563,plain,((f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | (elem!1 = f(elem!1)) | r(elem!1, f(elem!1)) | r(elem!1, f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(564,plain,
% 0.47/0.66 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[563, 186, 91, 120, 157, 93, 100, 549, 543])).
% 0.47/0.66 tff(565,plain,
% 0.47/0.66 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(elem!1)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(elem!1)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(566,plain,
% 0.47/0.66 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(elem!1)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(567,plain,
% 0.47/0.66 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(elem!1))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.47/0.66 tff(568,plain,
% 0.47/0.66 (~r(f(elem!1), f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[567, 180, 564])).
% 0.47/0.66 tff(569,plain,
% 0.47/0.66 (r(elem!1, f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[328, 568, 313, 100, 92, 120])).
% 0.47/0.66 tff(570,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(571,plain,
% 0.47/0.66 (((~r(c, elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1)) <=> ((elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(572,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[571])).
% 0.47/0.66 tff(573,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[572, 570])).
% 0.47/0.66 tff(574,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(575,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.47/0.66 tff(576,plain,
% 0.47/0.66 ((elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[575, 233])).
% 0.47/0.66 tff(577,plain,
% 0.47/0.66 ((elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(elem!1, f(f(f(elem!1))))) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1)))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[576, 305])).
% 0.47/0.66 tff(578,plain,
% 0.47/0.66 (~r(c, f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[577, 569, 313, 66, 286])).
% 0.47/0.66 tff(579,plain,
% 0.47/0.66 (~r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[517, 569, 313, 110, 252, 299])).
% 0.47/0.66 tff(580,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(581,plain,
% 0.47/0.66 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(582,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[581])).
% 0.47/0.66 tff(583,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[582, 580])).
% 0.47/0.66 tff(584,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(elem!1))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(585,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.47/0.66 tff(586,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[585, 205, 579, 578, 305, 299, 163, 293])).
% 0.47/0.66 tff(587,plain,(r(f(f(f(f(elem!1)))), elem!1) | (c = elem!1) | r(elem!1, f(elem!1)) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (elem!1 = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(588,plain,
% 0.47/0.66 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[587, 93, 100, 92, 91, 66])).
% 0.47/0.66 tff(589,plain,
% 0.47/0.66 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[542, 314, 93, 66, 100, 310, 92])).
% 0.47/0.66 tff(590,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(591,plain,
% 0.47/0.67 (((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(592,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[591])).
% 0.47/0.67 tff(593,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.67 inference(transitivity,[status(thm)],[592, 590])).
% 0.47/0.67 tff(594,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(595,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.47/0.67 tff(596,plain,
% 0.47/0.67 ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[595, 233])).
% 0.47/0.67 tff(597,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[596, 589, 314, 193, 310, 425, 387])).
% 0.47/0.67 tff(598,plain,((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (elem!1 = f(f(f(f(elem!1))))) | (c = elem!1) | r(elem!1, f(elem!1)) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(599,plain,
% 0.47/0.67 (~r(f(f(f(elem!1))), elem!1)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[598, 588, 105, 157, 93, 66, 100, 92])).
% 0.47/0.67 tff(600,plain,
% 0.47/0.67 (r(elem!1, f(f(elem!1)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[370, 599, 105, 92, 100])).
% 0.47/0.67 tff(601,plain,
% 0.47/0.67 (r(c, elem!1)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[345, 599, 66, 105, 92, 100])).
% 0.47/0.67 tff(602,plain,
% 0.47/0.67 (r(c, f(f(f(f(elem!1)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[404, 601, 66, 110, 170, 588, 193, 600])).
% 0.47/0.67 tff(603,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | r(elem!1, f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), elem!1)) | r(elem!1, f(f(f(f(elem!1))))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(604,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | r(elem!1, f(f(f(f(elem!1))))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(605,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), elem!1)) | r(elem!1, f(f(f(f(elem!1)))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.47/0.67 tff(606,plain,
% 0.47/0.67 (r(elem!1, f(f(f(f(elem!1)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[605, 180, 588])).
% 0.47/0.67 tff(607,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[419, 233, 601, 66, 93, 606, 602, 99])).
% 0.47/0.67 tff(608,plain,((elem!1 = f(f(f(f(elem!1))))) | (c = elem!1) | (f(elem!1) = f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(609,plain,
% 0.47/0.67 (r(elem!1, f(elem!1))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[608, 66, 93, 92, 91])).
% 0.47/0.67 tff(610,assumption,(r(elem!1, f(elem!1))), introduced(assumption)).
% 0.47/0.67 tff(611,plain,
% 0.47/0.67 (r(c, f(f(elem!1)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[446, 205, 253, 66, 187, 62, 163])).
% 0.47/0.67 tff(612,plain,
% 0.47/0.67 (r(f(f(elem!1)), c)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[439, 180, 611])).
% 0.47/0.67 tff(613,assumption,(elem!1 = c), introduced(assumption)).
% 0.47/0.67 tff(614,plain,
% 0.47/0.67 (c = elem!1),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[613, 495])).
% 0.47/0.67 tff(615,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[66, 614])).
% 0.47/0.67 tff(616,plain,((~(elem!1 = c)) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(617,plain,
% 0.47/0.67 (~(elem!1 = c)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[616, 66])).
% 0.47/0.67 tff(618,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, c)) | r(c, elem!1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, c)) | r(c, elem!1))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(619,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(elem!1, c)) | r(c, elem!1))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(620,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(elem!1, c)) | r(c, elem!1)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.47/0.67 tff(621,plain,
% 0.47/0.67 (~r(elem!1, c)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[620, 180, 253])).
% 0.47/0.67 tff(622,assumption,(r(f(f(elem!1)), c)), introduced(assumption)).
% 0.47/0.67 tff(623,plain,
% 0.47/0.67 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[212, 171, 195, 62, 194, 187])).
% 0.47/0.67 tff(624,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(625,plain,
% 0.47/0.67 (((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(626,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[625])).
% 0.47/0.67 tff(627,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[626, 624])).
% 0.47/0.67 tff(628,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(629,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.47/0.67 tff(630,plain,
% 0.47/0.67 (~r(f(f(f(f(elem!1)))), c)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[629, 233, 162, 97, 194, 623, 622])).
% 0.47/0.67 tff(631,assumption,(~r(elem!1, c)), introduced(assumption)).
% 0.47/0.67 tff(632,assumption,(~(elem!1 = c)), introduced(assumption)).
% 0.47/0.67 tff(633,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(634,plain,
% 0.47/0.67 ((r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1)) <=> ((f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(635,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c)))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[634])).
% 0.47/0.67 tff(636,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.67 inference(transitivity,[status(thm)],[635, 633])).
% 0.47/0.67 tff(637,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c) | (elem!1 = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = elem!1))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(638,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(f(f(f(f(elem!1)))), c)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.47/0.67 tff(639,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[638, 205, 97, 171, 195, 632, 631, 630])).
% 0.47/0.67 tff(640,plain,(r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | r(elem!1, c) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(641,plain,
% 0.47/0.67 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[640, 621, 617, 195, 194, 612, 62, 187])).
% 0.47/0.67 tff(642,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(643,plain,
% 0.47/0.67 ((r(f(f(f(elem!1))), elem!1) | r(elem!1, c) | r(f(f(f(elem!1))), c) | (elem!1 = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = elem!1)) <=> ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(644,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, c) | r(f(f(f(elem!1))), c) | (elem!1 = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c)))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[643])).
% 0.47/0.67 tff(645,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, c) | r(f(f(f(elem!1))), c) | (elem!1 = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c))),
% 0.47/0.67 inference(transitivity,[status(thm)],[644, 642])).
% 0.47/0.67 tff(646,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, c) | r(f(f(f(elem!1))), c) | (elem!1 = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(647,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.47/0.67 tff(648,plain,
% 0.47/0.67 (r(f(f(f(elem!1))), c)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[647, 205, 304, 316, 310, 632, 631])).
% 0.47/0.67 tff(649,plain,
% 0.47/0.67 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[352, 205, 187, 62, 316, 310, 427])).
% 0.47/0.67 tff(650,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(651,plain,
% 0.47/0.67 (((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(elem!1))), c)) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(652,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(elem!1))), c)) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[651])).
% 0.47/0.67 tff(653,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(elem!1))), c)) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[652, 650])).
% 0.47/0.67 tff(654,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(elem!1))), c)) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(655,plain,
% 0.47/0.67 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.47/0.67 tff(656,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[655, 233, 162, 304, 427, 649, 648, 622])).
% 0.47/0.67 tff(657,plain,(r(f(f(f(elem!1))), elem!1) | (~r(f(f(elem!1)), c)) | (f(f(f(elem!1))) = elem!1) | (elem!1 = c) | r(elem!1, c) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(658,plain,
% 0.47/0.67 (r(f(f(f(elem!1))), elem!1)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[657, 612, 105, 617, 621, 187, 62])).
% 0.47/0.67 tff(659,plain,
% 0.47/0.67 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(660,plain,
% 0.47/0.68 (((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = elem!1)) <=> ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(661,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[660])).
% 0.47/0.68 tff(662,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.68 inference(transitivity,[status(thm)],[661, 659])).
% 0.47/0.68 tff(663,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = elem!1))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(664,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.47/0.68 tff(665,plain,
% 0.47/0.68 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[664, 233, 610, 172, 552, 658, 105])).
% 0.47/0.68 tff(666,plain,
% 0.47/0.68 (~(f(f(f(f(elem!1)))) = f(f(f(elem!1))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[156, 427])).
% 0.47/0.68 tff(667,plain,
% 0.47/0.68 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[596, 641, 105, 666, 195, 658])).
% 0.47/0.68 tff(668,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(669,plain,
% 0.47/0.68 ((r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(670,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[669])).
% 0.47/0.68 tff(671,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[670, 668])).
% 0.47/0.68 tff(672,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(673,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.47/0.68 tff(674,plain,
% 0.47/0.68 ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[673, 205])).
% 0.47/0.68 tff(675,plain,
% 0.47/0.68 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[674, 667, 91, 552, 666, 665])).
% 0.47/0.68 tff(676,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(677,plain,
% 0.47/0.68 (((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = elem!1)) <=> ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(678,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[677])).
% 0.47/0.68 tff(679,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[678, 676])).
% 0.47/0.68 tff(680,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = elem!1))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(681,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.47/0.68 tff(682,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[681, 233, 610, 172, 675, 91, 641, 195])).
% 0.47/0.68 tff(683,plain,(r(c, elem!1) | (~r(elem!1, f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(elem!1))) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.68 tff(684,plain,
% 0.47/0.68 (r(c, elem!1)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[683, 187, 91, 195, 552, 194, 62, 610, 66])).
% 0.47/0.68 tff(685,plain,
% 0.47/0.68 (r(elem!1, c)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[493, 180, 684])).
% 0.47/0.68 tff(686,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(687,plain,
% 0.47/0.68 (((~r(c, elem!1)) | (~r(elem!1, f(elem!1))) | (~r(c, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1)) <=> ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(688,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(elem!1))) | (~r(c, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1)))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[687])).
% 0.47/0.68 tff(689,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(elem!1))) | (~r(c, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[688, 686])).
% 0.47/0.68 tff(690,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, elem!1)) | (~r(elem!1, f(elem!1))) | (~r(c, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(691,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (c = f(elem!1)) | (c = elem!1) | (~r(c, elem!1)) | (~r(c, f(elem!1)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.47/0.68 tff(692,plain,
% 0.47/0.68 (~r(c, f(elem!1))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[691, 233, 684, 610, 172, 259, 66])).
% 0.47/0.68 tff(693,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), c)) | r(c, f(elem!1)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), c)) | r(c, f(elem!1)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(694,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), c)) | r(c, f(elem!1)))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(695,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), c)) | r(c, f(elem!1))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.47/0.68 tff(696,plain,
% 0.47/0.68 (~r(f(elem!1), c)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[695, 180, 692])).
% 0.47/0.68 tff(697,assumption,(~r(f(elem!1), c)), introduced(assumption)).
% 0.47/0.68 tff(698,assumption,(r(elem!1, c)), introduced(assumption)).
% 0.47/0.68 tff(699,plain,
% 0.47/0.68 (~r(f(f(f(f(elem!1)))), c)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[504, 233, 97, 387, 195, 632, 698])).
% 0.47/0.68 tff(700,plain,
% 0.47/0.68 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[681, 233, 610, 127, 91, 387, 195])).
% 0.47/0.68 tff(701,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(702,plain,
% 0.47/0.68 ((r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1))) <=> ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(703,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[702])).
% 0.47/0.68 tff(704,plain,
% 0.47/0.68 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c))),
% 0.47/0.68 inference(transitivity,[status(thm)],[703, 701])).
% 0.47/0.68 tff(705,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(706,plain,
% 0.47/0.68 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(f(elem!1)))) = c) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | r(f(f(f(f(elem!1)))), c)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.47/0.69 tff(707,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[706, 205, 258, 97, 700, 91, 699, 697])).
% 0.47/0.69 tff(708,plain,((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(elem!1), c) | (f(f(f(f(elem!1)))) = elem!1) | (elem!1 = c) | (~r(elem!1, c)) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(709,plain,
% 0.47/0.69 (~r(f(f(f(f(elem!1)))), elem!1)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[708, 696, 91, 195, 617, 685, 610, 172])).
% 0.47/0.69 tff(710,plain,
% 0.47/0.69 (~(f(f(elem!1)) = f(f(f(elem!1))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[298, 427])).
% 0.47/0.69 tff(711,plain,
% 0.47/0.69 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[368, 649])).
% 0.47/0.69 tff(712,plain,
% 0.47/0.69 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[380, 171, 310, 666, 195, 316])).
% 0.47/0.69 tff(713,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(714,plain,
% 0.47/0.69 (((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(715,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[714])).
% 0.47/0.69 tff(716,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[715, 713])).
% 0.47/0.69 tff(717,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(718,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.47/0.69 tff(719,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[718, 233, 666, 712, 194, 623, 711, 710])).
% 0.47/0.69 tff(720,plain,(r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | r(f(f(f(elem!1))), elem!1) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(721,plain,
% 0.47/0.69 (r(f(f(f(elem!1))), elem!1)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[720, 709, 105, 195, 194, 62, 187])).
% 0.47/0.69 tff(722,plain,
% 0.47/0.69 (~r(f(f(f(elem!1))), c)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[477, 721, 105, 66, 684])).
% 0.47/0.69 tff(723,plain,
% 0.47/0.69 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[664, 233, 610, 172, 552, 721, 105])).
% 0.47/0.69 tff(724,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(725,plain,
% 0.47/0.69 ((r(f(f(f(elem!1))), c) | r(c, f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = c)) <=> (r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(726,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), c) | r(c, f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c)))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[725])).
% 0.47/0.69 tff(727,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), c) | r(c, f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c))),
% 0.47/0.69 inference(transitivity,[status(thm)],[726, 724])).
% 0.47/0.69 tff(728,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), c) | r(c, f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = c))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(729,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.47/0.69 tff(730,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[729, 205, 692, 259, 304, 552, 723, 722])).
% 0.47/0.69 tff(731,plain,(r(elem!1, f(f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(elem!1, f(elem!1))) | (c = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(732,plain,
% 0.47/0.69 (r(elem!1, f(f(elem!1)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[731, 609, 549, 66, 193, 170, 110, 91])).
% 0.47/0.69 tff(733,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(734,plain,
% 0.47/0.69 (((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(elem!1))) <=> ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(735,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1)))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[734])).
% 0.47/0.69 tff(736,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[735, 733])).
% 0.47/0.69 tff(737,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(elem!1)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(738,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.47/0.69 tff(739,plain,
% 0.47/0.69 ((~r(elem!1, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[738, 233])).
% 0.47/0.69 tff(740,plain,
% 0.47/0.69 (~r(f(elem!1), f(f(elem!1)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[739, 732, 110, 138, 120, 609])).
% 0.47/0.69 tff(741,assumption,(r(f(f(elem!1)), f(elem!1))), introduced(assumption)).
% 0.47/0.69 tff(742,assumption,(~r(f(elem!1), f(f(elem!1)))), introduced(assumption)).
% 0.47/0.69 tff(743,plain,
% 0.47/0.69 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(elem!1))) | r(f(elem!1), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(elem!1))) | r(f(elem!1), f(f(elem!1))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(744,plain,
% 0.47/0.69 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(elem!1))) | r(f(elem!1), f(f(elem!1))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(745,plain,
% 0.47/0.69 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(elem!1))) | r(f(elem!1), f(f(elem!1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.47/0.69 tff(746,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[745, 180, 742, 741])).
% 0.47/0.69 tff(747,plain,((~r(f(f(elem!1)), f(elem!1))) | r(f(elem!1), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(748,plain,
% 0.47/0.69 (~r(f(f(elem!1)), f(elem!1))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[747, 740])).
% 0.47/0.69 tff(749,plain,
% 0.47/0.69 (~r(c, f(f(elem!1)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[292, 233, 372, 66, 373, 62, 163])).
% 0.47/0.69 tff(750,plain,
% 0.47/0.69 (~r(f(elem!1), f(f(elem!1)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[739, 373, 62, 426, 172, 610])).
% 0.47/0.69 tff(751,plain,
% 0.47/0.69 (~r(c, f(elem!1))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[691, 233, 372, 610, 172, 259, 66])).
% 0.47/0.69 tff(752,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(753,plain,
% 0.47/0.69 ((r(c, f(elem!1)) | r(f(elem!1), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1))) <=> ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(754,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | r(f(elem!1), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[753])).
% 0.47/0.69 tff(755,plain,
% 0.47/0.69 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | r(f(elem!1), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[754, 752])).
% 0.47/0.69 tff(756,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | r(f(elem!1), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(757,plain,
% 0.47/0.69 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.47/0.69 tff(758,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[757, 205, 751, 259, 750, 426, 163, 749])).
% 0.47/0.69 tff(759,plain,((~r(c, elem!1)) | (c = elem!1) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(760,plain,
% 0.47/0.69 (~r(c, elem!1)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[759, 66, 732, 110, 609])).
% 0.47/0.69 tff(761,plain,
% 0.47/0.69 (~r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[457, 425, 62, 310, 427, 373])).
% 0.47/0.70 tff(762,plain,
% 0.47/0.70 (~r(f(f(elem!1)), f(elem!1))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[747, 750])).
% 0.47/0.70 tff(763,plain,
% 0.47/0.70 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[664, 233, 610, 172, 552, 425, 310])).
% 0.47/0.70 tff(764,plain,
% 0.47/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(765,plain,
% 0.47/0.70 ((r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1)))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(766,plain,
% 0.47/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1)))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[765])).
% 0.47/0.70 tff(767,plain,
% 0.47/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.70 inference(transitivity,[status(thm)],[766, 764])).
% 0.47/0.70 tff(768,plain,
% 0.47/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(769,plain,
% 0.47/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.47/0.70 tff(770,plain,
% 0.47/0.70 ($false),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[769, 205, 552, 763, 762, 214, 427, 761])).
% 0.47/0.70 tff(771,plain,((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(elem!1, f(elem!1))) | (f(f(f(elem!1))) = elem!1) | (elem!1 = f(f(elem!1))) | (~r(elem!1, f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.70 tff(772,plain,
% 0.47/0.70 (~r(f(f(f(elem!1))), elem!1)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[771, 609, 549, 105, 110, 732])).
% 0.47/0.70 tff(773,plain,
% 0.47/0.70 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[380, 316, 310, 314, 195, 171])).
% 0.47/0.70 tff(774,assumption,(~r(f(f(f(f(elem!1)))), c)), introduced(assumption)).
% 0.54/0.70 tff(775,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[283, 205, 253, 66, 97, 171, 195, 774])).
% 0.54/0.70 tff(776,plain,(r(f(f(f(f(elem!1)))), c) | r(c, elem!1) | (c = elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(777,plain,
% 0.54/0.70 (r(f(f(f(f(elem!1)))), c)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[776, 253, 66, 171, 195])).
% 0.54/0.70 tff(778,plain,
% 0.54/0.70 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), c)) | r(c, f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), c)) | r(c, f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(779,plain,
% 0.54/0.70 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), c)) | r(c, f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(780,plain,
% 0.54/0.70 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), c)) | r(c, f(f(f(f(elem!1)))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.54/0.70 tff(781,plain,
% 0.54/0.70 (r(c, f(f(f(f(elem!1)))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[780, 180, 777])).
% 0.54/0.70 tff(782,assumption,(~r(elem!1, f(f(f(elem!1))))), introduced(assumption)).
% 0.54/0.70 tff(783,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(784,plain,
% 0.54/0.70 ((r(c, elem!1) | r(elem!1, f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1)) <=> (r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(785,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1))))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[784])).
% 0.54/0.70 tff(786,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))))),
% 0.54/0.70 inference(transitivity,[status(thm)],[785, 783])).
% 0.54/0.70 tff(787,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = elem!1))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(788,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (c = elem!1) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.54/0.70 tff(789,plain,
% 0.54/0.70 (r(c, f(f(f(elem!1))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[788, 205, 253, 66, 81, 782, 305])).
% 0.54/0.70 tff(790,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(791,plain,
% 0.54/0.70 (((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(792,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1)))))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[791])).
% 0.54/0.70 tff(793,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(transitivity,[status(thm)],[792, 790])).
% 0.54/0.70 tff(794,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(795,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (~r(c, f(f(f(f(elem!1)))))) | (c = f(f(f(f(elem!1)))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.54/0.70 tff(796,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[795, 233, 314, 553, 789, 305, 781, 99])).
% 0.54/0.70 tff(797,plain,(r(c, elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (c = elem!1) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(798,plain,
% 0.54/0.70 (r(elem!1, f(f(f(elem!1))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[797, 773, 314, 66, 317, 253, 171, 195])).
% 0.54/0.70 tff(799,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[320, 180, 798, 316])).
% 0.54/0.70 tff(800,plain,(r(f(f(f(elem!1))), elem!1) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (c = elem!1) | r(c, elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(801,plain,
% 0.54/0.70 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[800, 772, 66, 760, 157, 193, 105])).
% 0.54/0.70 tff(802,plain,
% 0.54/0.70 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[681, 233, 609, 120, 91, 801, 193])).
% 0.54/0.70 tff(803,plain,
% 0.54/0.70 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[393, 233, 732, 110, 801, 193, 170])).
% 0.54/0.70 tff(804,assumption,(~r(f(f(f(f(elem!1)))), f(f(elem!1)))), introduced(assumption)).
% 0.54/0.70 tff(805,assumption,(~r(f(f(elem!1)), f(elem!1))), introduced(assumption)).
% 0.54/0.70 tff(806,assumption,(~r(f(f(f(f(elem!1)))), f(elem!1))), introduced(assumption)).
% 0.54/0.70 tff(807,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(808,plain,
% 0.54/0.70 ((r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(809,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[808])).
% 0.54/0.70 tff(810,plain,
% 0.54/0.70 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.54/0.70 inference(transitivity,[status(thm)],[809, 807])).
% 0.54/0.70 tff(811,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(812,plain,
% 0.54/0.70 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.54/0.70 tff(813,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[812, 205, 806, 91, 805, 135, 194, 804])).
% 0.54/0.70 tff(814,plain,(r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(815,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[814, 803, 802, 170, 130, 91, 748])).
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% 0.54/0.71 inference(monotonicity,[status(thm)],[983])).
% 0.54/0.71 tff(985,plain,
% 0.54/0.71 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.71 inference(transitivity,[status(thm)],[984, 982])).
% 0.54/0.71 tff(986,plain,
% 0.54/0.71 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(987,plain,
% 0.54/0.71 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.54/0.72 tff(988,plain,
% 0.54/0.72 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(elem!1))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[987, 205, 981, 975, 974])).
% 0.54/0.72 tff(989,plain,
% 0.54/0.72 (r(f(c), f(f(f(f(f(elem!1))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[988, 973, 968])).
% 0.54/0.72 tff(990,plain,
% 0.54/0.72 ((f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) <=> (elem!1 = f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[954])).
% 0.54/0.72 tff(991,plain,
% 0.54/0.72 ((f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) <=> (f(f(f(f(f(f(elem!1)))))) = elem!1)),
% 0.54/0.72 inference(transitivity,[status(thm)],[990, 67])).
% 0.54/0.72 tff(992,plain,
% 0.54/0.72 ((f(f(f(f(f(f(elem!1)))))) = elem!1) <=> (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(symmetry,[status(thm)],[991])).
% 0.54/0.72 tff(993,plain,
% 0.54/0.72 ((~(f(f(f(f(f(f(elem!1)))))) = elem!1)) <=> (~(f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[992])).
% 0.54/0.72 tff(994,assumption,(~(f(f(f(f(f(f(elem!1)))))) = elem!1)), introduced(assumption)).
% 0.54/0.72 tff(995,plain,
% 0.54/0.72 (~(f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.54/0.72 tff(996,assumption,(~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))), introduced(assumption)).
% 0.54/0.72 tff(997,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(998,plain,
% 0.54/0.72 ((r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1)))))) <=> ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(999,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[998])).
% 0.54/0.72 tff(1000,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[999, 997])).
% 0.54/0.72 tff(1001,plain,
% 0.54/0.72 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1))))))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1002,plain,
% 0.54/0.72 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.54/0.72 tff(1003,plain,
% 0.54/0.72 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1002, 205, 996])).
% 0.54/0.72 tff(1004,plain,
% 0.54/0.72 (r(f(c), f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1003, 973, 995, 968, 875])).
% 0.54/0.72 tff(1005,assumption,(~(f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))), introduced(assumption)).
% 0.54/0.72 tff(1006,assumption,(r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))), introduced(assumption)).
% 0.54/0.72 tff(1007,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1008,plain,
% 0.54/0.72 (((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))) <=> ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1009,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1))))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[1008])).
% 0.54/0.72 tff(1010,plain,
% 0.54/0.72 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[1009, 1007])).
% 0.54/0.72 tff(1011,plain,
% 0.54/0.72 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1012,plain,
% 0.54/0.72 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.54/0.72 tff(1013,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1012, 233, 981, 1006, 1005, 1004, 875, 989])).
% 0.54/0.72 tff(1014,plain,(r(f(c), elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~(elem!1 = f(f(f(f(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(1015,plain,
% 0.54/0.72 (r(f(c), elem!1)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1014, 953, 951, 946, 940, 935, 925, 912])).
% 0.54/0.72 tff(1016,plain,
% 0.54/0.72 (r(f(c), f(f(f(f(elem!1)))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1015, 931])).
% 0.54/0.72 tff(1017,plain,
% 0.54/0.72 ((f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.54/0.72 inference(commutativity,[status(thm)],[])).
% 0.54/0.72 tff(1018,plain,
% 0.54/0.72 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.72 inference(symmetry,[status(thm)],[1017])).
% 0.54/0.72 tff(1019,plain,
% 0.54/0.72 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> (~(f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[1018])).
% 0.54/0.72 tff(1020,plain,
% 0.54/0.72 ((f(f(f(elem!1))) = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = f(f(f(elem!1))))),
% 0.54/0.72 inference(commutativity,[status(thm)],[])).
% 0.54/0.72 tff(1021,plain,
% 0.54/0.72 (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[919])).
% 0.54/0.72 tff(1022,plain,
% 0.54/0.72 (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))),
% 0.54/0.72 inference(symmetry,[status(thm)],[1021])).
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% 0.54/0.73 inference(monotonicity,[status(thm)],[1081])).
% 0.54/0.73 tff(1083,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1082, 1080])).
% 0.54/0.73 tff(1084,plain,
% 0.54/0.73 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1085,plain,
% 0.54/0.73 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.54/0.73 tff(1086,plain,
% 0.54/0.73 ((f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1085, 233, 1061])).
% 0.54/0.73 tff(1087,plain,
% 0.54/0.73 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1086, 1079, 1074, 1070, 1065])).
% 0.54/0.73 tff(1088,plain,
% 0.54/0.73 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) <=> (f(f(f(elem!1))) = f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[892])).
% 0.54/0.73 tff(1089,plain,
% 0.54/0.73 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = f(f(f(elem!1))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1088, 1020])).
% 0.54/0.73 tff(1090,plain,
% 0.54/0.73 ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[1089])).
% 0.54/0.73 tff(1091,plain,
% 0.54/0.73 ((~(f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1090])).
% 0.54/0.73 tff(1092,plain,
% 0.54/0.73 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[157, 1091])).
% 0.54/0.73 tff(1093,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1094,plain,
% 0.54/0.73 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))) <=> (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1095,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1094])).
% 0.54/0.73 tff(1096,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1095, 1093])).
% 0.54/0.73 tff(1097,plain,
% 0.54/0.73 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1098,plain,
% 0.54/0.73 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.54/0.73 tff(1099,plain,
% 0.54/0.73 ((f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1098, 205, 1092, 1087, 1061, 1055])).
% 0.54/0.73 tff(1100,plain,
% 0.54/0.73 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1099, 1054])).
% 0.54/0.73 tff(1101,plain,
% 0.54/0.73 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1102,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1103,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.54/0.73 tff(1104,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1103, 180, 1100, 1045])).
% 0.54/0.73 tff(1105,plain,(r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (~(elem!1 = f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1106,plain,
% 0.54/0.73 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1105, 1041, 912, 92, 1036, 91, 945])).
% 0.54/0.73 tff(1107,plain,
% 0.54/0.73 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1106, 1035])).
% 0.54/0.73 tff(1108,plain,
% 0.54/0.73 ((f(c) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.54/0.73 inference(commutativity,[status(thm)],[])).
% 0.54/0.73 tff(1109,plain,
% 0.54/0.73 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(c) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[1108])).
% 0.54/0.73 tff(1110,plain,
% 0.54/0.73 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(c) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1109])).
% 0.54/0.73 tff(1111,assumption,(f(f(f(f(f(f(f(elem!1))))))) = f(c)), introduced(assumption)).
% 0.54/0.73 tff(1112,plain,
% 0.54/0.73 (f(c) = f(f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[1111])).
% 0.54/0.73 tff(1113,plain,
% 0.54/0.73 (inj_0(f(c)) = inj_0(f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1112])).
% 0.54/0.73 tff(1114,plain,
% 0.54/0.73 (inj_0(f(f(f(f(f(f(f(elem!1)))))))) = inj_0(f(c))),
% 0.54/0.73 inference(symmetry,[status(thm)],[1113])).
% 0.54/0.73 tff(1115,plain,
% 0.54/0.73 (f(f(f(f(f(f(elem!1)))))) = inj_0(f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[845])).
% 0.54/0.73 tff(1116,plain,
% 0.54/0.73 (f(f(f(f(f(f(elem!1)))))) = c),
% 0.54/0.73 inference(transitivity,[status(thm)],[1115, 1114, 13])).
% 0.54/0.73 tff(1117,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[910, 1116])).
% 0.54/0.73 tff(1118,plain,(~(f(f(f(f(f(f(f(elem!1))))))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1119,plain,
% 0.54/0.73 (~(f(c) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1118, 1110])).
% 0.54/0.73 tff(1120,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(c), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1121,plain,
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% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1122,plain,
% 0.54/0.73 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(c), f(f(f(f(elem!1))))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1121])).
% 0.54/0.73 tff(1123,plain,
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% 0.54/0.73 inference(transitivity,[status(thm)],[1122, 1120])).
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% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1125,plain,
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% 0.54/0.73 inference(modus_ponens,[status(thm)],[1124, 1123])).
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% 0.54/0.73 inference(unit_resolution,[status(thm)],[1125, 233, 1119, 1107])).
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% 0.54/0.73 tff(1128,plain,
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% 0.54/0.73 inference(monotonicity,[status(thm)],[912])).
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% 0.54/0.73 inference(rewrite,[status(thm)],[])).
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% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.73 inference(modus_ponens,[status(thm)],[1132, 1131])).
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% 0.54/0.73 inference(rewrite,[status(thm)],[])).
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% 0.54/0.73 inference(rewrite,[status(thm)],[])).
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% 0.54/0.73 inference(monotonicity,[status(thm)],[1136])).
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% 0.54/0.74 tff(1147,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[1149])).
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.74 ($false),
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% 0.54/0.74 tff(1156,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[912])).
% 0.54/0.74 tff(1161,plain,
% 0.54/0.74 ((f(f(f(f(f(elem!1))))) = elem!1) <=> (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1160, 1159])).
% 0.54/0.74 tff(1162,plain,
% 0.54/0.74 ((f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) <=> (f(f(f(f(f(elem!1))))) = elem!1)),
% 0.54/0.74 inference(symmetry,[status(thm)],[1161])).
% 0.54/0.74 tff(1163,plain,
% 0.54/0.74 ((f(f(f(f(elem!1)))) = f(elem!1)) <=> (f(f(f(f(f(elem!1))))) = elem!1)),
% 0.54/0.74 inference(transitivity,[status(thm)],[938, 1162])).
% 0.54/0.74 tff(1164,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[1163])).
% 0.54/0.74 tff(1165,plain,
% 0.54/0.74 (~(f(f(f(f(f(elem!1))))) = elem!1)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[91, 1164])).
% 0.54/0.74 tff(1166,assumption,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))), introduced(assumption)).
% 0.54/0.74 tff(1167,plain,
% 0.54/0.74 (r(f(f(f(f(f(elem!1))))), elem!1) <=> r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[879, 877])).
% 0.54/0.74 tff(1168,plain,
% 0.54/0.74 (r(f(elem!1), f(f(f(f(elem!1))))) <=> r(f(f(f(f(f(elem!1))))), elem!1)),
% 0.54/0.74 inference(symmetry,[status(thm)],[1167])).
% 0.54/0.74 tff(1169,plain,
% 0.54/0.74 ((~r(f(elem!1), f(f(f(f(elem!1)))))) <=> (~r(f(f(f(f(f(elem!1))))), elem!1))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1168])).
% 0.54/0.74 tff(1170,plain,
% 0.54/0.74 (r(f(elem!1), elem!1) <=> r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[877])).
% 0.54/0.74 tff(1171,plain,
% 0.54/0.74 ((~r(f(elem!1), elem!1)) <=> (~r(f(elem!1), f(f(f(f(elem!1))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1170])).
% 0.54/0.74 tff(1172,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1173,plain,
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1174,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.54/0.74 tff(1175,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[1174, 180, 100])).
% 0.54/0.74 tff(1176,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 0.54/0.74 tff(1177,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1176, 1169])).
% 0.54/0.74 tff(1178,assumption,(~(f(f(f(f(f(elem!1))))) = elem!1)), introduced(assumption)).
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1180,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1181,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[1180])).
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% 0.54/0.74 inference(transitivity,[status(thm)],[1181, 1179])).
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1184,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 0.54/0.74 tff(1185,plain,
% 0.54/0.74 (r(c, elem!1) | (c = elem!1) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = elem!1) | r(f(f(f(f(f(elem!1))))), elem!1)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1184, 205, 872])).
% 0.54/0.74 tff(1186,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
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% 0.54/0.74 inference(monotonicity,[status(thm)],[1188])).
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% 0.54/0.74 inference(transitivity,[status(thm)],[1189, 1187])).
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.54/0.74 tff(1193,plain,
% 0.54/0.74 ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1192, 233, 872, 964, 1186, 1166])).
% 0.54/0.74 tff(1194,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[1193, 1070])).
% 0.54/0.74 tff(1195,plain,
% 0.54/0.74 (r(c, elem!1) <=> r(c, f(f(f(f(elem!1)))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[877])).
% 0.54/0.74 tff(1196,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[1195])).
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% 0.54/0.74 (r(f(f(f(f(elem!1)))), f(elem!1)) <=> r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[878])).
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% 0.54/0.74 ((~r(f(f(f(f(elem!1)))), f(elem!1))) <=> (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1198])).
% 0.54/0.74 tff(1200,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[877])).
% 0.54/0.74 tff(1201,plain,
% 0.54/0.74 ((~r(elem!1, f(elem!1))) <=> (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1200])).
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[100, 1201])).
% 0.54/0.74 tff(1203,plain,
% 0.54/0.74 (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1202, 1199])).
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% 0.54/0.74 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) <=> r(f(f(f(f(f(f(elem!1)))))), elem!1)),
% 0.54/0.75 inference(monotonicity,[status(thm)],[954])).
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% 0.54/0.75 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) <=> r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[881])).
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% 0.54/0.75 (r(f(f(f(f(elem!1)))), f(f(elem!1))) <=> r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.75 inference(symmetry,[status(thm)],[1206])).
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% 0.54/0.75 (r(elem!1, f(f(elem!1))) <=> r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[877])).
% 0.54/0.75 tff(1209,plain,
% 0.54/0.75 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[373, 1208])).
% 0.54/0.75 tff(1210,plain,
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% 0.54/0.75 inference(modus_ponens,[status(thm)],[1209, 1207])).
% 0.54/0.75 tff(1211,plain,
% 0.54/0.75 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1212,plain,
% 0.54/0.75 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1213,plain,
% 0.54/0.75 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.54/0.75 tff(1214,plain,
% 0.54/0.75 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1213, 180, 1210])).
% 0.54/0.75 tff(1215,plain,
% 0.54/0.75 (r(f(f(f(f(f(f(elem!1)))))), elem!1)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1214, 1205])).
% 0.54/0.75 tff(1216,plain,
% 0.54/0.75 ((~r(f(f(f(elem!1))), f(f(elem!1)))) <=> (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[905])).
% 0.54/0.75 tff(1217,plain,
% 0.54/0.75 (r(f(f(f(elem!1))), elem!1)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[345, 253, 66, 310, 92, 100])).
% 0.54/0.75 tff(1218,plain,
% 0.54/0.75 (~r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[457, 1217, 110, 310, 147, 373])).
% 0.54/0.75 tff(1219,plain,
% 0.54/0.75 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1218, 1216])).
% 0.54/0.75 tff(1220,assumption,(~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))), introduced(assumption)).
% 0.54/0.75 tff(1221,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))), introduced(assumption)).
% 0.54/0.75 tff(1222,assumption,(r(f(f(f(f(f(f(elem!1)))))), elem!1)), introduced(assumption)).
% 0.54/0.75 tff(1223,assumption,(~(f(c) = elem!1)), introduced(assumption)).
% 0.54/0.75 tff(1224,assumption,(~(f(f(f(f(f(f(elem!1)))))) = f(c))), introduced(assumption)).
% 0.54/0.75 tff(1225,assumption,(r(f(f(f(f(f(elem!1))))), c)), introduced(assumption)).
% 0.54/0.75 tff(1226,plain,
% 0.54/0.75 (~(f(c) = f(f(f(f(elem!1)))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1223, 957])).
% 0.54/0.75 tff(1227,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1228,plain,
% 0.54/0.75 ((r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(c), c) | (f(f(f(f(elem!1)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1229,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(c), c) | (f(f(f(f(elem!1)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1228])).
% 0.54/0.75 tff(1230,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(c), c) | (f(f(f(f(elem!1)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.54/0.75 tff(1231,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(c), c) | (f(f(f(f(elem!1)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1232,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = c) | r(f(f(f(f(elem!1)))), c) | r(f(c), c)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.54/0.75 tff(1233,plain,
% 0.54/0.75 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), c)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1232, 205, 97, 30, 774])).
% 0.54/0.75 tff(1234,plain,
% 0.54/0.75 (r(f(c), c)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1233, 973, 1226])).
% 0.54/0.75 tff(1235,plain,
% 0.54/0.75 ((elem!1 = f(f(f(f(f(elem!1)))))) <=> (f(f(f(f(f(elem!1))))) = elem!1)),
% 0.54/0.75 inference(commutativity,[status(thm)],[])).
% 0.54/0.75 tff(1236,plain,
% 0.54/0.75 ((f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) <=> (elem!1 = f(f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[954])).
% 0.54/0.75 tff(1237,plain,
% 0.54/0.75 ((f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) <=> (f(f(f(f(f(elem!1))))) = elem!1)),
% 0.54/0.75 inference(transitivity,[status(thm)],[1236, 1235])).
% 0.54/0.75 tff(1238,plain,
% 0.54/0.75 ((f(f(f(f(f(elem!1))))) = elem!1) <=> (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(symmetry,[status(thm)],[1237])).
% 0.54/0.75 tff(1239,plain,
% 0.54/0.75 ((~(f(f(f(f(f(elem!1))))) = elem!1)) <=> (~(f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1238])).
% 0.54/0.75 tff(1240,plain,
% 0.54/0.75 (~(f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1178, 1239])).
% 0.54/0.75 tff(1241,plain,
% 0.54/0.75 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[987, 205, 981, 975])).
% 0.54/0.75 tff(1242,plain,
% 0.54/0.75 (r(f(c), f(f(f(f(f(elem!1))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1241, 973, 1226, 1240])).
% 0.54/0.75 tff(1243,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1244,plain,
% 0.54/0.75 (((~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1))))))) <=> ((f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1245,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1244])).
% 0.54/0.75 tff(1246,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.54/0.75 tff(1247,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1248,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(elem!1))))), c))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.54/0.75 tff(1249,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1248, 233, 872, 1225, 30, 981, 1242, 1234])).
% 0.54/0.75 tff(1250,plain,(r(f(c), elem!1) | (~r(f(f(f(f(f(elem!1))))), c)) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = elem!1) | (~(elem!1 = f(f(f(f(elem!1)))))) | (f(c) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1251,plain,
% 0.54/0.75 (r(f(c), elem!1)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1250, 1223, 774, 975, 1178, 877, 1225])).
% 0.54/0.75 tff(1252,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1253,plain,
% 0.54/0.75 (((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(c))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1254,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1253])).
% 0.54/0.75 tff(1255,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.54/0.75 tff(1256,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(c)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1257,plain,
% 0.54/0.75 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.54/0.75 tff(1258,plain,
% 0.54/0.75 ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1257, 233])).
% 0.54/0.75 tff(1259,plain,
% 0.54/0.75 (~r(f(f(f(f(f(f(elem!1)))))), f(c))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1258, 1251, 1224, 1223, 994, 1222])).
% 0.54/0.75 tff(1260,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1261,plain,
% 0.54/0.75 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1262,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1261])).
% 0.54/0.75 tff(1263,plain,
% 0.54/0.75 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1262, 1260])).
% 0.54/0.76 tff(1264,plain,
% 0.54/0.76 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1265,plain,
% 0.54/0.76 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.54/0.76 tff(1266,plain,
% 0.54/0.76 (r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1265, 205, 1224, 1259, 1118, 1221, 1220])).
% 0.54/0.76 tff(1267,plain,
% 0.54/0.76 (r(f(c), f(f(f(f(elem!1)))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1251, 970])).
% 0.54/0.76 tff(1268,assumption,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.54/0.76 tff(1269,plain,
% 0.54/0.76 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1270,plain,
% 0.54/0.76 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> ((f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1271,plain,
% 0.54/0.76 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1))))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1270])).
% 0.54/0.76 tff(1272,plain,
% 0.54/0.76 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.54/0.76 tff(1273,plain,
% 0.54/0.76 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1274,plain,
% 0.54/0.76 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(c), f(f(f(f(elem!1))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.54/0.76 tff(1275,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1274, 233, 1118, 897, 1268, 1226, 1267, 1266])).
% 0.54/0.76 tff(1276,plain,((f(c) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~(elem!1 = f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = elem!1) | (~r(f(f(f(f(f(elem!1))))), c))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1277,plain,
% 0.54/0.76 ((f(c) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~(elem!1 = f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = elem!1) | (~r(f(f(f(f(f(elem!1))))), c))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1276, 874])).
% 0.54/0.76 tff(1278,plain,
% 0.54/0.76 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1277, 1219, 967, 877, 1215, 1061, 1053, 1186, 1204, 1203, 1178, 1092])).
% 0.54/0.76 tff(1279,plain,
% 0.54/0.76 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1280,plain,
% 0.54/0.76 ((r(f(f(f(f(f(f(f(elem!1))))))), c) | r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = c)) <=> ((f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(c, f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1281,plain,
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% 0.54/0.76 inference(monotonicity,[status(thm)],[1334])).
% 0.54/0.76 tff(1336,plain,
% 0.54/0.76 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1335, 1333])).
% 0.54/0.77 tff(1337,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1338,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 0.54/0.77 tff(1339,plain,
% 0.54/0.77 ((c = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1338, 233, 1332, 99, 1158])).
% 0.54/0.77 tff(1340,plain,
% 0.54/0.77 (~r(c, f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1339, 926, 911])).
% 0.54/0.77 tff(1341,plain,
% 0.54/0.77 (r(c, f(f(f(elem!1)))) <=> r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1021])).
% 0.54/0.77 tff(1342,plain,
% 0.54/0.77 ((~r(c, f(f(f(elem!1))))) <=> (~r(c, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1341])).
% 0.54/0.77 tff(1343,plain,
% 0.54/0.77 (r(f(f(f(elem!1))), elem!1) <=> r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[912])).
% 0.54/0.77 tff(1344,plain,
% 0.54/0.77 (r(f(f(f(elem!1))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), elem!1)),
% 0.54/0.77 inference(symmetry,[status(thm)],[1343])).
% 0.54/0.77 tff(1345,plain,
% 0.54/0.77 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1022])).
% 0.54/0.77 tff(1346,plain,
% 0.54/0.77 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), elem!1)),
% 0.54/0.77 inference(transitivity,[status(thm)],[1345, 1344])).
% 0.54/0.77 tff(1347,assumption,(r(f(c), elem!1)), introduced(assumption)).
% 0.54/0.77 tff(1348,plain,
% 0.54/0.77 (r(f(c), f(f(f(f(elem!1)))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1347, 970])).
% 0.54/0.77 tff(1349,plain,
% 0.54/0.77 ((c = f(c)) <=> (f(c) = c)),
% 0.54/0.77 inference(commutativity,[status(thm)],[])).
% 0.54/0.77 tff(1350,plain,
% 0.54/0.77 ((f(c) = c) <=> (c = f(c))),
% 0.54/0.77 inference(symmetry,[status(thm)],[1349])).
% 0.54/0.77 tff(1351,plain,
% 0.54/0.77 ((~(f(c) = c)) <=> (~(c = f(c)))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1350])).
% 0.54/0.77 tff(1352,plain,
% 0.54/0.77 (~(c = f(c))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[30, 1351])).
% 0.54/0.77 tff(1353,assumption,(r(c, f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.54/0.77 tff(1354,assumption,(~r(c, f(f(f(f(f(f(elem!1)))))))), introduced(assumption)).
% 0.54/0.77 tff(1355,plain,
% 0.54/0.77 ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1258, 874])).
% 0.54/0.77 tff(1356,plain,
% 0.54/0.77 (~r(f(f(f(f(f(f(elem!1)))))), f(c))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1355, 1347, 967, 1222, 994])).
% 0.54/0.77 tff(1357,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1358,plain,
% 0.54/0.77 ((r(c, f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1359,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1358])).
% 0.54/0.77 tff(1360,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c)))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1359, 1357])).
% 0.54/0.77 tff(1361,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1362,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | (c = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | r(c, f(c)) | (c = f(c))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 0.54/0.77 tff(1363,plain,
% 0.54/0.77 (r(c, f(c))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1362, 205, 874, 1356, 1352, 911, 1354])).
% 0.54/0.77 tff(1364,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1365,plain,
% 0.54/0.77 (((~r(c, f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(c))) <=> ((f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1366,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1365])).
% 0.54/0.77 tff(1367,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1366, 1364])).
% 0.54/0.77 tff(1368,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(c)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1369,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(f(elem!1))))) | (~r(f(c), f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.54/0.77 tff(1370,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1369, 233, 1363, 1353, 99, 1352, 968, 1348])).
% 0.54/0.77 tff(1371,plain,((~r(f(c), elem!1)) | (~r(c, f(f(f(f(elem!1)))))) | (~(elem!1 = f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1372,plain,
% 0.54/0.77 (~r(f(c), elem!1)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1371, 1332, 912, 1340, 1318, 925])).
% 0.54/0.77 tff(1373,assumption,(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.54/0.77 tff(1374,plain,
% 0.54/0.77 (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(symmetry,[status(thm)],[1373])).
% 0.54/0.77 tff(1375,plain,
% 0.54/0.77 (f(elem!1) = f(f(f(elem!1)))),
% 0.54/0.77 inference(transitivity,[status(thm)],[878, 1374, 892])).
% 0.54/0.77 tff(1376,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[92, 1375])).
% 0.54/0.77 tff(1377,plain,((~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))) | (f(elem!1) = f(f(f(elem!1)))) | (~(elem!1 = f(f(f(f(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1378,plain,
% 0.54/0.77 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1377, 912, 92])).
% 0.54/0.77 tff(1379,plain,
% 0.54/0.77 (~(f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[897, 1019])).
% 0.54/0.77 tff(1380,assumption,(~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))), introduced(assumption)).
% 0.54/0.77 tff(1381,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.54/0.77 tff(1382,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1383,plain,
% 0.54/0.77 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1384,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1383])).
% 0.54/0.77 tff(1385,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1384, 1382])).
% 0.54/0.77 tff(1386,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1387,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.54/0.77 tff(1388,plain,
% 0.54/0.77 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1387, 205, 975, 897, 1381, 974, 1380])).
% 0.54/0.77 tff(1389,plain,
% 0.54/0.77 (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1327, 180, 1381])).
% 0.54/0.77 tff(1390,assumption,(~(f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.54/0.77 tff(1391,assumption,(~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.54/0.77 tff(1392,plain,
% 0.54/0.77 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1393,plain,
% 0.54/0.77 ((r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(elem!1)))))) <=> ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1394,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1393])).
% 0.54/0.78 tff(1395,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.54/0.78 tff(1396,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(elem!1))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1397,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.54/0.78 tff(1398,plain,
% 0.54/0.78 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1397, 205, 1119, 1391, 1390])).
% 0.54/0.78 tff(1399,plain,
% 0.54/0.78 (r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1398, 968, 973])).
% 0.54/0.78 tff(1400,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1401,plain,
% 0.54/0.78 (((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1402,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1401])).
% 0.54/0.78 tff(1403,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1402, 1400])).
% 0.54/0.78 tff(1404,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1405,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.54/0.78 tff(1406,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1405, 233, 981, 1119, 1399, 1166, 1380, 989])).
% 0.54/0.78 tff(1407,plain,(r(f(c), elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))) | (~(elem!1 = f(f(f(f(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1408,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1407, 1389, 1388, 1380, 975, 974, 972, 1379, 877])).
% 0.54/0.78 tff(1409,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | r(f(c), elem!1) | (~(elem!1 = f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1410,plain,
% 0.54/0.78 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1409, 1378, 946, 940, 1372, 912, 1027])).
% 0.54/0.78 tff(1411,plain,
% 0.54/0.78 (r(f(f(f(elem!1))), elem!1)),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1410, 1346])).
% 0.54/0.78 tff(1412,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1413,plain,
% 0.54/0.78 (((~r(c, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(c, elem!1)) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1))))) <=> ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1414,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(c, elem!1)) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1413])).
% 0.54/0.78 tff(1415,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(c, elem!1)) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1414, 1412])).
% 0.54/0.78 tff(1416,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(c, elem!1)) | (f(f(f(elem!1))) = elem!1) | (c = elem!1) | (c = f(f(f(elem!1)))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1417,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.54/0.78 tff(1418,plain,
% 0.54/0.78 ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1417, 233])).
% 0.54/0.78 tff(1419,plain,
% 0.54/0.78 ((c = elem!1) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(c, elem!1)) | (~r(c, f(f(f(elem!1)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1418, 305])).
% 0.54/0.78 tff(1420,plain,
% 0.54/0.78 (~r(c, f(f(f(elem!1))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1419, 1411, 105, 66, 1331])).
% 0.54/0.78 tff(1421,plain,
% 0.54/0.78 (~r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1420, 1342])).
% 0.54/0.78 tff(1422,plain,
% 0.54/0.78 ((c = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = c)),
% 0.54/0.78 inference(commutativity,[status(thm)],[])).
% 0.54/0.78 tff(1423,plain,
% 0.54/0.78 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (c = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(symmetry,[status(thm)],[1422])).
% 0.54/0.78 tff(1424,plain,
% 0.54/0.78 ((~(f(f(f(f(f(f(f(elem!1))))))) = c)) <=> (~(c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1423])).
% 0.54/0.78 tff(1425,plain,
% 0.54/0.78 (~(c = f(f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[964, 1424])).
% 0.54/0.78 tff(1426,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1427,plain,
% 0.54/0.78 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1428,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1427])).
% 0.54/0.78 tff(1429,plain,
% 0.54/0.78 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1428, 1426])).
% 0.54/0.78 tff(1430,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1431,plain,
% 0.54/0.78 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 0.54/0.79 tff(1432,plain,
% 0.54/0.79 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1431, 233, 1027, 1410, 1315, 1158, 926])).
% 0.54/0.79 tff(1433,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(1434,plain,
% 0.54/0.79 ((r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1))))))))) <=> ((c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(1435,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[1434])).
% 0.54/0.79 tff(1436,plain,
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% 0.54/0.79 inference(transitivity,[status(thm)],[1435, 1433])).
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.54/0.79 tff(1439,plain,
% 0.54/0.79 ($false),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1438, 205, 1432, 1315, 1425, 1421, 911, 1340])).
% 0.54/0.79 tff(1440,plain,((c = elem!1) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(elem!1, f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(1441,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[1440, 100, 80, 66])).
% 0.54/0.79 tff(1442,plain,
% 0.54/0.79 (elem!1 = f(f(f(elem!1)))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[89, 1441])).
% 0.54/0.79 tff(1443,plain,
% 0.54/0.79 (r(elem!1, f(f(elem!1))) <=> r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[1442])).
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% 0.54/0.79 tff(1445,plain,
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1444])).
% 0.54/0.79 tff(1446,plain,
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% 0.54/0.79 inference(symmetry,[status(thm)],[1445])).
% 0.54/0.79 tff(1447,plain,
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1446])).
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% 0.54/0.79 inference(commutativity,[status(thm)],[])).
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1441])).
% 0.54/0.79 tff(1450,plain,
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1449])).
% 0.54/0.79 tff(1451,plain,
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% 0.54/0.79 inference(transitivity,[status(thm)],[1450, 1444])).
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1451])).
% 0.54/0.79 tff(1453,plain,
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1453])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[874, 1454])).
% 0.54/0.79 tff(1456,plain,
% 0.54/0.79 (~(f(c) = f(f(f(elem!1))))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[1455, 1447])).
% 0.54/0.79 tff(1457,plain,
% 0.54/0.79 (r(f(c), f(f(f(elem!1)))) <=> r(f(c), elem!1)),
% 0.54/0.79 inference(monotonicity,[status(thm)],[1444])).
% 0.54/0.79 tff(1458,plain,
% 0.54/0.79 (r(f(c), elem!1) <=> r(f(c), f(f(f(elem!1))))),
% 0.54/0.79 inference(symmetry,[status(thm)],[1457])).
% 0.54/0.79 tff(1459,plain,
% 0.54/0.79 (r(f(f(elem!1)), f(elem!1))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[221, 187, 62, 214, 172, 100])).
% 0.54/0.79 tff(1460,plain,
% 0.54/0.79 (r(elem!1, f(elem!1)) <=> r(f(f(f(elem!1))), f(elem!1))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[1442])).
% 0.54/0.79 tff(1461,plain,
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1460])).
% 0.54/0.79 tff(1462,plain,
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[100, 1461])).
% 0.54/0.79 tff(1463,plain,
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% 0.54/0.79 (r(elem!1, f(f(elem!1))) <=> r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[308])).
% 0.54/0.79 tff(1465,plain,
% 0.54/0.79 (r(f(f(f(elem!1))), f(f(elem!1))) <=> r(elem!1, f(f(elem!1)))),
% 0.54/0.79 inference(symmetry,[status(thm)],[1464])).
% 0.54/0.79 tff(1466,plain,
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% 0.54/0.79 tff(1468,plain,((~r(f(f(f(elem!1))), f(f(elem!1)))) | r(elem!1, f(f(elem!1))) | (~(elem!1 = f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(1469,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[1468, 187, 1442])).
% 0.54/0.79 tff(1470,assumption,(~r(f(f(f(elem!1))), f(f(elem!1)))), introduced(assumption)).
% 0.54/0.79 tff(1471,assumption,(r(f(f(elem!1)), f(f(f(elem!1))))), introduced(assumption)).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[1473, 1472])).
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% 0.54/0.79 inference(rewrite,[status(thm)],[])).
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% 0.54/0.79 inference(monotonicity,[status(thm)],[1510])).
% 0.54/0.79 tff(1512,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(c), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.54/0.79 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.54/0.79 tff(1513,plain,
% 0.54/0.79 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(c), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1))))),
% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
% 0.54/0.79 tff(1514,plain,
% 0.54/0.79 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.54/0.79 tff(1515,plain,
% 0.54/0.79 ((~r(f(c), f(elem!1))) | (f(c) = f(elem!1))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1514, 233, 741, 135, 1508, 1505])).
% 0.54/0.79 tff(1516,plain,
% 0.54/0.79 (~r(f(c), f(elem!1))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1515, 1504])).
% 0.54/0.79 tff(1517,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(1518,plain,
% 0.54/0.79 ((r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(1519,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[1518])).
% 0.54/0.79 tff(1520,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.54/0.79 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.54/0.79 tff(1521,plain,
% 0.54/0.79 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
% 0.54/0.79 tff(1522,plain,
% 0.54/0.79 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.54/0.79 tff(1523,plain,
% 0.54/0.79 (r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1522, 205, 92, 1495, 1516, 1504])).
% 0.54/0.79 tff(1524,plain,
% 0.54/0.79 ($false),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1523, 1494, 1483])).
% 0.54/0.79 tff(1525,plain,((~r(f(c), f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(c), elem!1) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~(f(f(f(f(elem!1)))) = f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(1526,plain,
% 0.54/0.79 (~r(f(c), f(f(elem!1)))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1525, 972, 1495, 92, 741, 135, 84])).
% 0.54/0.79 tff(1527,plain,
% 0.54/0.79 (~(f(elem!1) = f(f(elem!1)))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.54/0.79 tff(1528,plain,
% 0.54/0.79 (~(f(f(f(elem!1))) = f(f(elem!1)))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[146, 1527])).
% 0.54/0.79 tff(1529,plain,
% 0.54/0.79 (~(f(f(elem!1)) = f(f(f(elem!1))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[298, 1528])).
% 0.54/0.79 tff(1530,plain,
% 0.54/0.79 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(1531,plain,
% 0.54/0.79 ((r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.54/0.80 inference(rewrite,[status(thm)],[])).
% 0.54/0.80 tff(1532,plain,
% 0.54/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))))),
% 0.54/0.80 inference(monotonicity,[status(thm)],[1531])).
% 0.54/0.80 tff(1533,plain,
% 0.54/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.54/0.80 inference(transitivity,[status(thm)],[1532, 1530])).
% 0.54/0.80 tff(1534,plain,
% 0.54/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))),
% 0.54/0.80 inference(quant_inst,[status(thm)],[])).
% 0.54/0.80 tff(1535,plain,
% 0.54/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.54/0.80 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.54/0.80 tff(1536,plain,
% 0.54/0.80 (r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.54/0.80 inference(unit_resolution,[status(thm)],[1535, 205, 363, 1529, 1508, 1526])).
% 0.54/0.80 tff(1537,plain,
% 0.54/0.80 ($false),
% 0.54/0.80 inference(unit_resolution,[status(thm)],[1536, 1494, 1483])).
% 0.54/0.80 tff(1538,plain,(r(f(c), elem!1) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~(f(f(f(f(elem!1)))) = f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.80 tff(1539,plain,
% 0.54/0.80 (r(f(c), elem!1)),
% 0.54/0.80 inference(unit_resolution,[status(thm)],[1538, 1477, 1441, 80, 1463, 214, 1459])).
% 0.54/0.80 tff(1540,plain,
% 0.54/0.80 (r(f(c), f(f(f(elem!1))))),
% 0.54/0.80 inference(modus_ponens,[status(thm)],[1539, 1458])).
% 0.54/0.80 tff(1541,plain,
% 0.54/0.80 (r(c, elem!1) <=> r(c, f(f(f(elem!1))))),
% 0.54/0.80 inference(monotonicity,[status(thm)],[1442])).
% 0.54/0.80 tff(1542,plain,
% 0.54/0.80 (r(c, elem!1)),
% 0.54/0.80 inference(unit_resolution,[status(thm)],[449, 187, 66, 62, 100])).
% 0.54/0.80 tff(1543,plain,
% 0.54/0.80 (r(c, f(f(f(elem!1))))),
% 0.54/0.80 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 0.54/0.80 tff(1544,plain,
% 0.54/0.80 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(elem!1))))) | r(f(f(f(elem!1))), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(elem!1))))) | r(f(f(f(elem!1))), c))),
% 0.54/0.80 inference(rewrite,[status(thm)],[])).
% 0.54/0.80 tff(1545,plain,
% 0.54/0.80 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(elem!1))))) | r(f(f(f(elem!1))), c))),
% 0.54/0.80 inference(quant_inst,[status(thm)],[])).
% 0.54/0.80 tff(1546,plain,
% 0.54/0.80 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(elem!1))))) | r(f(f(f(elem!1))), c)),
% 0.54/0.80 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.54/0.80 tff(1547,plain,
% 0.54/0.80 (r(f(f(f(elem!1))), c)),
% 0.54/0.80 inference(unit_resolution,[status(thm)],[1546, 180, 1543])).
% 0.54/0.80 tff(1548,plain,
% 0.54/0.80 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1549,plain,
% 0.64/0.80 (((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), c)) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1550,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), c)) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1))))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1549])).
% 0.64/0.80 tff(1551,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), c)) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.80 inference(transitivity,[status(thm)],[1550, 1548])).
% 0.64/0.80 tff(1552,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), c)) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(1553,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(elem!1))), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 0.64/0.80 tff(1554,plain,
% 0.64/0.80 ((~r(f(c), c)) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1553, 233, 304, 30, 1547])).
% 0.64/0.80 tff(1555,plain,
% 0.64/0.80 (~r(f(c), c)),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1554, 1540, 1456])).
% 0.64/0.80 tff(1556,plain,
% 0.64/0.80 ((f(f(elem!1)) = f(c)) <=> (f(c) = f(f(elem!1)))),
% 0.64/0.80 inference(commutativity,[status(thm)],[])).
% 0.64/0.80 tff(1557,plain,
% 0.64/0.80 ((f(c) = f(f(elem!1))) <=> (f(f(elem!1)) = f(c))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1556])).
% 0.64/0.80 tff(1558,plain,
% 0.64/0.80 ((~(f(c) = f(f(elem!1)))) <=> (~(f(f(elem!1)) = f(c)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1557])).
% 0.64/0.80 tff(1559,plain,
% 0.64/0.80 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(c) = f(f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1449])).
% 0.64/0.80 tff(1560,plain,
% 0.64/0.80 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(c) = f(f(elem!1))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1559])).
% 0.64/0.80 tff(1561,plain,
% 0.64/0.80 (~(f(c) = f(f(elem!1)))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[981, 1560])).
% 0.64/0.80 tff(1562,plain,
% 0.64/0.80 (~(f(f(elem!1)) = f(c))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1561, 1558])).
% 0.64/0.80 tff(1563,plain,
% 0.64/0.80 (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1450])).
% 0.64/0.80 tff(1564,plain,
% 0.64/0.80 (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)),
% 0.64/0.80 inference(transitivity,[status(thm)],[1563, 1441])).
% 0.64/0.80 tff(1565,plain,
% 0.64/0.80 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) <=> r(f(elem!1), f(f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1564])).
% 0.64/0.80 tff(1566,plain,
% 0.64/0.80 (r(f(elem!1), f(f(elem!1))) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1565])).
% 0.64/0.80 tff(1567,plain,
% 0.64/0.80 (r(f(elem!1), f(f(elem!1)))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[747, 1459])).
% 0.64/0.80 tff(1568,plain,
% 0.64/0.80 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.64/0.80 tff(1569,plain,
% 0.64/0.80 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) <=> (f(elem!1) = f(f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1564])).
% 0.64/0.80 tff(1570,plain,
% 0.64/0.80 ((f(elem!1) = f(f(elem!1))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1569])).
% 0.64/0.80 tff(1571,plain,
% 0.64/0.80 ((~(f(elem!1) = f(f(elem!1)))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1570])).
% 0.64/0.80 tff(1572,plain,
% 0.64/0.80 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[426, 1571])).
% 0.64/0.80 tff(1573,plain,
% 0.64/0.80 ((f(f(f(c))) = f(elem!1)) <=> (f(elem!1) = f(f(f(c))))),
% 0.64/0.80 inference(commutativity,[status(thm)],[])).
% 0.64/0.80 tff(1574,plain,
% 0.64/0.80 ((f(elem!1) = f(f(f(c)))) <=> (f(f(f(c))) = f(elem!1))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1573])).
% 0.64/0.80 tff(1575,plain,
% 0.64/0.80 ((~(f(elem!1) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1574])).
% 0.64/0.80 tff(1576,assumption,(f(elem!1) = f(f(f(c)))), introduced(assumption)).
% 0.64/0.80 tff(1577,plain,
% 0.64/0.80 (f(f(f(c))) = f(elem!1)),
% 0.64/0.80 inference(symmetry,[status(thm)],[1576])).
% 0.64/0.80 tff(1578,plain,
% 0.64/0.80 (inj_0(f(f(f(c)))) = inj_0(f(elem!1))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1577])).
% 0.64/0.80 tff(1579,plain,
% 0.64/0.80 (f(f(c)) = f(f(f(elem!1)))),
% 0.64/0.80 inference(transitivity,[status(thm)],[47, 1578, 75, 308])).
% 0.64/0.80 tff(1580,plain,
% 0.64/0.80 (inj_0(f(f(c))) = inj_0(f(f(f(elem!1))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1579])).
% 0.64/0.80 tff(1581,plain,
% 0.64/0.80 (f(c) = f(f(elem!1))),
% 0.64/0.80 inference(transitivity,[status(thm)],[20, 1580, 69])).
% 0.64/0.80 tff(1582,assumption,(~(f(c) = f(f(elem!1)))), introduced(assumption)).
% 0.64/0.80 tff(1583,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1582, 1581])).
% 0.64/0.80 tff(1584,plain,((~(f(elem!1) = f(f(f(c))))) | (f(c) = f(f(elem!1))) | (~(elem!1 = f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(1585,plain,
% 0.64/0.80 (~(f(elem!1) = f(f(f(c))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1584, 1508, 1478])).
% 0.64/0.80 tff(1586,plain,
% 0.64/0.80 (~(f(f(f(c))) = f(elem!1))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1585, 1575])).
% 0.64/0.80 tff(1587,plain,
% 0.64/0.80 (~(f(f(elem!1)) = f(c))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1508, 1558])).
% 0.64/0.80 tff(1588,assumption,(~r(f(c), f(f(elem!1)))), introduced(assumption)).
% 0.64/0.80 tff(1589,plain,
% 0.64/0.80 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(c))) | r(f(c), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(c))) | r(f(c), f(f(elem!1))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1590,plain,
% 0.64/0.80 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(c))) | r(f(c), f(f(elem!1))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(1591,plain,
% 0.64/0.80 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(c))) | r(f(c), f(f(elem!1)))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 0.64/0.80 tff(1592,plain,
% 0.64/0.80 (~r(f(f(elem!1)), f(c))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1591, 180, 1588])).
% 0.64/0.80 tff(1593,plain,
% 0.64/0.80 (r(f(c), f(f(f(elem!1))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1347, 1481])).
% 0.64/0.80 tff(1594,assumption,(r(f(f(f(elem!1))), c)), introduced(assumption)).
% 0.64/0.80 tff(1595,plain,
% 0.64/0.80 (~r(f(c), c)),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1553, 233, 304, 30, 1594, 1593, 1494])).
% 0.64/0.80 tff(1596,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c)))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1597,plain,
% 0.64/0.80 ((r(f(f(elem!1)), f(c)) | r(f(c), c) | r(f(f(elem!1)), c) | (f(c) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(c))) <=> ((f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c)))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1598,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), c) | r(f(f(elem!1)), c) | (f(c) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1597])).
% 0.64/0.80 tff(1599,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), c) | r(f(f(elem!1)), c) | (f(c) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c)))),
% 0.64/0.80 inference(transitivity,[status(thm)],[1598, 1596])).
% 0.64/0.80 tff(1600,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), c) | r(f(f(elem!1)), c) | (f(c) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(c)))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(1601,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | r(f(c), c) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(c))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 0.64/0.80 tff(1602,plain,
% 0.64/0.80 (r(f(f(elem!1)), c)),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1601, 205, 162, 30, 1595, 1592, 1587])).
% 0.64/0.80 tff(1603,assumption,(f(f(f(c))) = f(f(elem!1))), introduced(assumption)).
% 0.64/0.80 tff(1604,plain,
% 0.64/0.80 (inj_0(f(f(f(c)))) = inj_0(f(f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1603])).
% 0.64/0.80 tff(1605,plain,
% 0.64/0.80 (f(f(c)) = f(elem!1)),
% 0.64/0.80 inference(transitivity,[status(thm)],[47, 1604, 122])).
% 0.64/0.80 tff(1606,plain,
% 0.64/0.80 (inj_0(f(f(c))) = inj_0(f(elem!1))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1605])).
% 0.64/0.80 tff(1607,plain,
% 0.64/0.80 (f(c) = elem!1),
% 0.64/0.80 inference(transitivity,[status(thm)],[20, 1606, 75])).
% 0.64/0.80 tff(1608,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1223, 1607])).
% 0.64/0.80 tff(1609,plain,((~(f(f(f(c))) = f(f(elem!1)))) | (f(c) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(1610,plain,
% 0.64/0.80 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1609, 1493])).
% 0.64/0.80 tff(1611,plain,
% 0.64/0.80 ((f(f(f(c))) = elem!1) <=> (elem!1 = f(f(f(c))))),
% 0.64/0.80 inference(commutativity,[status(thm)],[])).
% 0.64/0.80 tff(1612,plain,
% 0.64/0.80 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = elem!1)),
% 0.64/0.80 inference(symmetry,[status(thm)],[1611])).
% 0.64/0.80 tff(1613,plain,
% 0.64/0.80 ((~(elem!1 = f(f(f(c))))) <=> (~(f(f(f(c))) = elem!1))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1612])).
% 0.64/0.80 tff(1614,assumption,(elem!1 = f(f(f(c)))), introduced(assumption)).
% 0.64/0.80 tff(1615,plain,
% 0.64/0.80 (f(f(f(c))) = elem!1),
% 0.64/0.80 inference(symmetry,[status(thm)],[1614])).
% 0.64/0.80 tff(1616,plain,
% 0.64/0.80 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.64/0.80 inference(transitivity,[status(thm)],[1615, 1478])).
% 0.64/0.80 tff(1617,plain,
% 0.64/0.80 (inj_0(f(f(f(c)))) = inj_0(f(f(f(elem!1))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1616])).
% 0.64/0.80 tff(1618,plain,
% 0.64/0.80 (f(f(c)) = f(f(elem!1))),
% 0.64/0.80 inference(transitivity,[status(thm)],[47, 1617, 69])).
% 0.64/0.80 tff(1619,plain,
% 0.64/0.80 (inj_0(f(f(c))) = inj_0(f(f(elem!1)))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1618])).
% 0.64/0.80 tff(1620,plain,
% 0.64/0.80 (inj_0(f(f(elem!1))) = inj_0(f(f(c)))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1619])).
% 0.64/0.80 tff(1621,plain,
% 0.64/0.80 (f(f(f(f(f(f(f(elem!1))))))) = f(c)),
% 0.64/0.80 inference(transitivity,[status(thm)],[1496, 84, 142, 1620, 19])).
% 0.64/0.80 tff(1622,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1118, 1621])).
% 0.64/0.80 tff(1623,plain,((~(elem!1 = f(f(f(c))))) | (~(f(f(f(f(elem!1)))) = f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(1624,plain,
% 0.64/0.80 (~(elem!1 = f(f(f(c))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1623, 84])).
% 0.64/0.80 tff(1625,plain,
% 0.64/0.80 (~(f(f(f(c))) = elem!1)),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1624, 1613])).
% 0.64/0.80 tff(1626,plain,
% 0.64/0.80 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (f(f(f(c))) = elem!1)),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1479])).
% 0.64/0.80 tff(1627,plain,
% 0.64/0.80 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (elem!1 = f(f(f(c))))),
% 0.64/0.80 inference(transitivity,[status(thm)],[1626, 1611])).
% 0.64/0.80 tff(1628,plain,
% 0.64/0.80 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1627])).
% 0.64/0.80 tff(1629,plain,
% 0.64/0.80 ((~(elem!1 = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1628])).
% 0.64/0.80 tff(1630,plain,
% 0.64/0.80 (~(f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[1624, 1629])).
% 0.64/0.80 tff(1631,assumption,(~(f(f(elem!1)) = f(f(f(elem!1))))), introduced(assumption)).
% 0.64/0.80 tff(1632,plain,
% 0.64/0.80 (f(f(f(elem!1))) = elem!1),
% 0.64/0.80 inference(symmetry,[status(thm)],[308])).
% 0.64/0.80 tff(1633,plain,
% 0.64/0.80 (r(f(f(f(c))), f(f(f(elem!1)))) <=> r(f(f(f(c))), elem!1)),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1632])).
% 0.64/0.80 tff(1634,plain,
% 0.64/0.80 (r(f(f(f(c))), elem!1) <=> r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.80 inference(symmetry,[status(thm)],[1633])).
% 0.64/0.80 tff(1635,plain,
% 0.64/0.80 ((~r(f(f(f(c))), elem!1)) <=> (~r(f(f(f(c))), f(f(f(elem!1)))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1634])).
% 0.64/0.80 tff(1636,assumption,(~(f(f(f(c))) = elem!1)), introduced(assumption)).
% 0.64/0.80 tff(1637,plain,
% 0.64/0.80 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[1609, 1223])).
% 0.64/0.80 tff(1638,assumption,(~r(f(f(f(c))), f(f(elem!1)))), introduced(assumption)).
% 0.64/0.80 tff(1639,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c)))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1640,plain,
% 0.64/0.80 ((r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c))))) <=> (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c)))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(1641,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c))))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[1640])).
% 0.64/0.80 tff(1642,plain,
% 0.64/0.80 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c)))))),
% 0.64/0.80 inference(transitivity,[status(thm)],[1641, 1639])).
% 0.64/0.80 tff(1643,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(1644,plain,
% 0.64/0.80 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 0.64/0.81 tff(1645,plain,
% 0.64/0.81 (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(c))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1644, 205])).
% 0.64/0.81 tff(1646,plain,
% 0.64/0.81 (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1645, 52])).
% 0.64/0.81 tff(1647,plain,
% 0.64/0.81 (r(f(c), f(f(f(c))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1646, 1638, 1582, 1637, 1588])).
% 0.64/0.81 tff(1648,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1649,plain,
% 0.64/0.81 (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), elem!1)) | (f(f(f(c))) = elem!1) | (f(c) = elem!1) | (f(c) = f(f(f(c))))) <=> ((~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1650,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), elem!1)) | (f(f(f(c))) = elem!1) | (f(c) = elem!1) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c)))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1649])).
% 0.64/0.81 tff(1651,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), elem!1)) | (f(f(f(c))) = elem!1) | (f(c) = elem!1) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1650, 1648])).
% 0.64/0.81 tff(1652,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), elem!1)) | (f(f(f(c))) = elem!1) | (f(c) = elem!1) | (f(c) = f(f(f(c)))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1653,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (f(c) = f(f(f(c)))) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c)))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 0.64/0.81 tff(1654,plain,
% 0.64/0.81 ((~r(f(c), elem!1)) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c)))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1653, 233, 52])).
% 0.64/0.81 tff(1655,plain,
% 0.64/0.81 (~r(f(f(f(c))), elem!1)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1654, 1647, 1223, 1636, 1347])).
% 0.64/0.81 tff(1656,plain,
% 0.64/0.81 (~r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1655, 1635])).
% 0.64/0.81 tff(1657,assumption,(~(f(f(f(c))) = f(f(f(elem!1))))), introduced(assumption)).
% 0.64/0.81 tff(1658,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1659,plain,
% 0.64/0.81 ((r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1660,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1659])).
% 0.64/0.81 tff(1661,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1660, 1658])).
% 0.64/0.81 tff(1662,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1663,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 0.64/0.81 tff(1664,plain,
% 0.64/0.81 (r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1663, 205, 363, 1631, 1638, 1637, 1657])).
% 0.64/0.81 tff(1665,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1664, 1656])).
% 0.64/0.81 tff(1666,plain,(r(f(f(f(c))), f(f(elem!1))) | (~(elem!1 = f(f(f(elem!1))))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(c) = elem!1) | (f(f(f(c))) = elem!1) | (~r(f(c), elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1667,plain,
% 0.64/0.81 (r(f(f(f(c))), f(f(elem!1)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1666, 1588, 363, 1631, 1630, 1493, 1625, 1347, 1508, 1478])).
% 0.64/0.81 tff(1668,plain,
% 0.64/0.81 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(c))) = c))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1669,plain,
% 0.64/0.81 (~(f(f(f(c))) = c)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1668, 28])).
% 0.64/0.81 tff(1670,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1671,plain,
% 0.64/0.81 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), c)) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1672,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), c)) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1671])).
% 0.64/0.81 tff(1673,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), c)) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1672, 1670])).
% 0.64/0.81 tff(1674,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), c)) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1675,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 0.64/0.81 tff(1676,plain,
% 0.64/0.81 (~r(f(f(f(c))), c)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1675, 233, 162, 1669, 1667, 1610, 1602])).
% 0.64/0.81 tff(1677,plain,
% 0.64/0.81 (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)),
% 0.64/0.81 inference(transitivity,[status(thm)],[1496, 84])).
% 0.64/0.81 tff(1678,plain,
% 0.64/0.81 (r(c, f(f(f(f(f(f(f(elem!1)))))))) <=> r(c, f(elem!1))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1677])).
% 0.64/0.81 tff(1679,plain,
% 0.64/0.81 ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) <=> (~r(c, f(elem!1)))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1678])).
% 0.64/0.81 tff(1680,assumption,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))), introduced(assumption)).
% 0.64/0.81 tff(1681,assumption,(~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))), introduced(assumption)).
% 0.64/0.81 tff(1682,plain,
% 0.64/0.81 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), c)) | r(c, f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), c)) | r(c, f(f(elem!1))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1683,plain,
% 0.64/0.81 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), c)) | r(c, f(f(elem!1))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1684,plain,
% 0.64/0.81 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), c)) | r(c, f(f(elem!1)))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 0.64/0.81 tff(1685,plain,
% 0.64/0.81 (r(c, f(f(elem!1)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1684, 180, 1602])).
% 0.64/0.81 tff(1686,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1687,plain,
% 0.64/0.81 (((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1))))))))) <=> ((c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1688,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1687])).
% 0.64/0.81 tff(1689,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1688, 1686])).
% 0.64/0.81 tff(1690,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1691,plain,
% 0.64/0.81 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.64/0.81 tff(1692,plain,
% 0.64/0.81 ((c = f(f(elem!1))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1691, 233])).
% 0.64/0.81 tff(1693,plain,
% 0.64/0.81 ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1692, 163, 1425])).
% 0.64/0.81 tff(1694,plain,
% 0.64/0.81 (~r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1693, 1685, 1681, 1680])).
% 0.64/0.81 tff(1695,plain,
% 0.64/0.81 (~r(c, f(elem!1))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1694, 1679])).
% 0.64/0.81 tff(1696,plain,
% 0.64/0.81 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1697,plain,
% 0.64/0.82 ((r(f(f(f(c))), c) | r(c, f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c)) <=> (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1698,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1697])).
% 0.64/0.82 tff(1699,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1698, 1696])).
% 0.64/0.82 tff(1700,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (c = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1701,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 0.64/0.82 tff(1702,plain,
% 0.64/0.82 (r(f(f(f(c))), f(elem!1))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1701, 205, 1695, 259, 1669, 1676, 1586])).
% 0.64/0.82 tff(1703,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1704,plain,
% 0.64/0.82 ((r(f(c), c) | r(c, f(elem!1)) | r(f(c), f(elem!1)) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c)) <=> (r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1705,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(elem!1)) | r(f(c), f(elem!1)) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1704])).
% 0.64/0.82 tff(1706,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(elem!1)) | r(f(c), f(elem!1)) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1705, 1703])).
% 0.64/0.82 tff(1707,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(elem!1)) | r(f(c), f(elem!1)) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1708,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | (f(c) = c) | r(f(c), c) | r(f(c), f(elem!1)) | (f(c) = f(elem!1))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 0.64/0.82 tff(1709,plain,
% 0.64/0.82 (r(f(c), f(elem!1)) | (f(c) = f(elem!1))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1708, 205, 1695, 259, 30, 1595])).
% 0.64/0.82 tff(1710,plain,
% 0.64/0.82 (r(f(c), f(elem!1))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1709, 1504])).
% 0.64/0.82 tff(1711,plain,
% 0.64/0.82 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1712,plain,
% 0.64/0.82 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1713,plain,
% 0.64/0.82 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.64/0.82 tff(1714,plain,
% 0.64/0.82 (~r(c, f(c))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1713, 180, 1595])).
% 0.64/0.82 tff(1715,plain,
% 0.64/0.82 ((f(f(f(c))) = f(c)) <=> (f(c) = f(f(f(c))))),
% 0.64/0.82 inference(commutativity,[status(thm)],[])).
% 0.64/0.82 tff(1716,plain,
% 0.64/0.82 ((f(c) = f(f(f(c)))) <=> (f(f(f(c))) = f(c))),
% 0.64/0.82 inference(symmetry,[status(thm)],[1715])).
% 0.64/0.82 tff(1717,plain,
% 0.64/0.82 ((~(f(c) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(c)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1716])).
% 0.64/0.82 tff(1718,plain,
% 0.64/0.82 (~(f(f(f(c))) = f(c))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[52, 1717])).
% 0.64/0.82 tff(1719,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1720,plain,
% 0.64/0.82 ((r(f(f(f(c))), c) | r(c, f(c)) | r(f(f(f(c))), f(c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c)) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1721,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(c)) | r(f(f(f(c))), f(c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1720])).
% 0.64/0.82 tff(1722,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(c)) | r(f(f(f(c))), f(c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1721, 1719])).
% 0.64/0.82 tff(1723,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(c)) | r(f(f(f(c))), f(c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1724,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(c))) = c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 0.64/0.82 tff(1725,plain,
% 0.64/0.82 (r(c, f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(c))), c)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1724, 205, 1669, 1718, 1352])).
% 0.64/0.82 tff(1726,plain,
% 0.64/0.82 (r(f(f(f(c))), f(c))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1725, 1676, 1714])).
% 0.64/0.82 tff(1727,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1728,plain,
% 0.64/0.82 (((~r(f(f(f(c))), f(c))) | (~r(f(c), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(c))) <=> ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1729,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c)))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1728])).
% 0.64/0.82 tff(1730,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1729, 1727])).
% 0.64/0.82 tff(1731,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(c)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1732,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 0.64/0.82 tff(1733,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1732, 233, 1718, 1726, 1710, 1504, 1702, 1586])).
% 0.64/0.82 tff(1734,plain,(r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(c), elem!1)) | (~(f(f(f(f(elem!1)))) = f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), c))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1735,plain,
% 0.64/0.82 (r(f(c), f(f(elem!1)))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1734, 1477, 710, 1539, 1441, 1572, 1568, 1547])).
% 0.64/0.82 tff(1736,plain,
% 0.64/0.82 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(elem!1)))) | r(f(f(elem!1)), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(elem!1)))) | r(f(f(elem!1)), f(c)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1737,plain,
% 0.64/0.82 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(elem!1)))) | r(f(f(elem!1)), f(c)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1738,plain,
% 0.64/0.82 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(elem!1)))) | r(f(f(elem!1)), f(c))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 0.64/0.82 tff(1739,plain,
% 0.64/0.82 (r(f(f(elem!1)), f(c))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1738, 180, 1735])).
% 0.64/0.82 tff(1740,plain,
% 0.64/0.82 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1609, 1455])).
% 0.64/0.82 tff(1741,plain,
% 0.64/0.82 (f(f(f(f(elem!1)))) = f(f(f(f(f(f(f(elem!1)))))))),
% 0.64/0.82 inference(symmetry,[status(thm)],[1563])).
% 0.64/0.82 tff(1742,plain,
% 0.64/0.82 (f(elem!1) = f(f(f(f(elem!1))))),
% 0.64/0.82 inference(symmetry,[status(thm)],[1441])).
% 0.64/0.82 tff(1743,plain,
% 0.64/0.82 (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1742, 1741])).
% 0.64/0.82 tff(1744,plain,
% 0.64/0.82 (r(f(elem!1), f(c)) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1743])).
% 0.64/0.82 tff(1745,plain,
% 0.64/0.82 (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) <=> r(f(elem!1), f(c))),
% 0.64/0.82 inference(symmetry,[status(thm)],[1744])).
% 0.64/0.82 tff(1746,plain,
% 0.64/0.82 ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) <=> (~r(f(elem!1), f(c)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1745])).
% 0.64/0.82 tff(1747,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1748,plain,
% 0.64/0.82 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1749,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1748])).
% 0.64/0.82 tff(1750,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1749, 1747])).
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% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1752,plain,
% 0.64/0.82 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 0.64/0.82 tff(1753,plain,
% 0.64/0.82 ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1752, 233, 1118])).
% 0.64/0.82 tff(1754,plain,
% 0.64/0.82 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1753, 1735, 1561, 1572, 1568])).
% 0.64/0.82 tff(1755,plain,
% 0.64/0.82 (~r(f(elem!1), f(c))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1754, 1746])).
% 0.64/0.82 tff(1756,plain,
% 0.64/0.82 ((f(elem!1) = f(c)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1743])).
% 0.64/0.82 tff(1757,plain,
% 0.64/0.82 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(c))),
% 0.64/0.82 inference(symmetry,[status(thm)],[1756])).
% 0.64/0.82 tff(1758,plain,
% 0.64/0.82 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(c)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1757])).
% 0.64/0.82 tff(1759,plain,
% 0.64/0.82 (~(f(elem!1) = f(c))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1118, 1758])).
% 0.64/0.82 tff(1760,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1761,plain,
% 0.64/0.82 ((r(f(elem!1), f(c)) | r(f(c), c) | r(f(elem!1), c) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c))) <=> ((f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1762,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), c) | r(f(elem!1), c) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1761])).
% 0.64/0.82 tff(1763,plain,
% 0.64/0.82 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), c) | r(f(elem!1), c) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1762, 1760])).
% 0.64/0.83 tff(1764,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), c) | r(f(elem!1), c) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1765,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(c) = c) | r(f(elem!1), c) | r(f(c), c) | (f(elem!1) = f(c)) | r(f(elem!1), f(c))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 0.64/0.83 tff(1766,plain,
% 0.64/0.83 (r(f(elem!1), c)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1765, 205, 258, 30, 1555, 1759, 1755])).
% 0.64/0.83 tff(1767,plain,
% 0.64/0.83 (~r(f(f(elem!1)), c)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[435, 233, 258, 162, 1459, 214, 1766])).
% 0.64/0.83 tff(1768,plain,
% 0.64/0.83 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (f(f(f(c))) = elem!1)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1444])).
% 0.64/0.83 tff(1769,plain,
% 0.64/0.83 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (elem!1 = f(f(f(c))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1768, 1611])).
% 0.64/0.83 tff(1770,plain,
% 0.64/0.83 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[1769])).
% 0.64/0.83 tff(1771,plain,
% 0.64/0.83 ((~(elem!1 = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1770])).
% 0.64/0.83 tff(1772,plain,
% 0.64/0.83 (~(elem!1 = f(f(f(c))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1623, 1441])).
% 0.64/0.83 tff(1773,plain,
% 0.64/0.83 (~(f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 0.64/0.83 tff(1774,assumption,(~(f(f(f(c))) = f(f(elem!1)))), introduced(assumption)).
% 0.64/0.83 tff(1775,plain,
% 0.64/0.83 (r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1663, 205, 363, 1631, 1638, 1774, 1657])).
% 0.64/0.83 tff(1776,assumption,(~r(f(f(elem!1)), c)), introduced(assumption)).
% 0.64/0.83 tff(1777,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1778,plain,
% 0.64/0.83 ((r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(f(f(c))), c) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1779,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(f(f(c))), c) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1778])).
% 0.64/0.83 tff(1780,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(f(f(c))), c) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1779, 1777])).
% 0.64/0.83 tff(1781,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(f(f(c))), c) | (f(f(elem!1)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1782,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(elem!1)), c) | r(f(f(f(c))), c)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 0.64/0.83 tff(1783,plain,
% 0.64/0.83 (r(f(f(f(c))), c)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1782, 205, 162, 1669, 1638, 1774, 1776])).
% 0.64/0.83 tff(1784,assumption,(r(c, f(f(f(elem!1))))), introduced(assumption)).
% 0.64/0.83 tff(1785,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1786,plain,
% 0.64/0.83 (((~r(f(f(f(c))), c)) | (~r(c, f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = c)) <=> ((~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1787,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1786])).
% 0.64/0.83 tff(1788,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1787, 1785])).
% 0.64/0.83 tff(1789,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = c))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1790,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(elem!1))))) | (c = f(f(f(elem!1)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 0.64/0.83 tff(1791,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1790, 233, 1784, 305, 1669, 1657, 1783, 1775])).
% 0.64/0.83 tff(1792,plain,(r(f(f(f(c))), f(f(elem!1))) | (~r(c, f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(1793,plain,
% 0.64/0.83 (r(f(f(f(c))), f(f(elem!1)))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1792, 1543, 1773, 1740, 1767, 1477, 710])).
% 0.64/0.83 tff(1794,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1795,plain,
% 0.64/0.83 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1796,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c)))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1795])).
% 0.64/0.83 tff(1797,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1796, 1794])).
% 0.64/0.83 tff(1798,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1799,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(elem!1)), f(c)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.64/0.83 tff(1800,plain,
% 0.64/0.83 ((f(f(elem!1)) = f(c)) | (~r(f(f(f(c))), f(c)))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1799, 233, 1793, 1740, 1718, 1739])).
% 0.64/0.83 tff(1801,plain,
% 0.64/0.83 (~r(f(f(f(c))), f(c))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1800, 1562])).
% 0.64/0.83 tff(1802,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1803,plain,
% 0.64/0.83 ((r(f(f(f(c))), f(c)) | r(f(c), c) | r(f(f(f(c))), c) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c))) <=> ((f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1804,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), c) | r(f(f(f(c))), c) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1803])).
% 0.64/0.83 tff(1805,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), c) | r(f(f(f(c))), c) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1804, 1802])).
% 0.64/0.83 tff(1806,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), c) | r(f(f(f(c))), c) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1807,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(c))) = c) | r(f(c), c) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), c)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.64/0.83 tff(1808,plain,
% 0.64/0.83 (r(f(c), c) | r(f(f(f(c))), f(c)) | r(f(f(f(c))), c)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1807, 205, 30, 1669, 1718])).
% 0.64/0.83 tff(1809,plain,
% 0.64/0.83 (r(f(f(f(c))), c)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1808, 1801, 1555])).
% 0.64/0.83 tff(1810,plain,
% 0.64/0.83 (~r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1790, 233, 1543, 305, 1669, 1773, 1809])).
% 0.64/0.83 tff(1811,plain,
% 0.64/0.83 (~(f(elem!1) = f(f(f(c))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1584, 1561, 1442])).
% 0.64/0.83 tff(1812,plain,
% 0.64/0.83 (~(f(f(f(c))) = f(elem!1))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1811, 1575])).
% 0.64/0.83 tff(1813,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1814,plain,
% 0.64/0.83 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1815,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1814])).
% 0.64/0.83 tff(1816,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1815, 1813])).
% 0.64/0.83 tff(1817,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1818,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 0.64/0.83 tff(1819,plain,
% 0.64/0.83 ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1818, 233, 1459, 214, 1793, 1740])).
% 0.64/0.83 tff(1820,plain,
% 0.64/0.83 (~r(f(f(f(c))), f(elem!1))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1819, 1812])).
% 0.64/0.83 tff(1821,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1822,plain,
% 0.64/0.83 ((r(f(f(f(c))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1823,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1822])).
% 0.64/0.83 tff(1824,plain,
% 0.64/0.83 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1823, 1821])).
% 0.64/0.83 tff(1825,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1826,plain,
% 0.64/0.83 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 0.64/0.83 tff(1827,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1826, 205, 80, 1463, 1773, 1820, 1812, 1810])).
% 0.64/0.83 tff(1828,plain,(r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(elem!1)) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(1829,plain,
% 0.64/0.83 (r(elem!1, f(f(elem!1)))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1828, 100, 62, 66])).
% 0.64/0.83 tff(1830,plain,
% 0.64/0.83 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1829, 1443])).
% 0.64/0.83 tff(1831,plain,
% 0.64/0.83 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[366, 180, 1830])).
% 0.64/0.83 tff(1832,plain,
% 0.64/0.83 (r(f(f(f(c))), f(f(f(elem!1)))) <=> r(f(f(f(c))), elem!1)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1444])).
% 0.64/0.83 tff(1833,plain,
% 0.64/0.83 ((~r(f(f(f(c))), f(f(f(elem!1))))) <=> (~r(f(f(f(c))), elem!1))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1832])).
% 0.64/0.83 tff(1834,assumption,(~r(f(f(f(elem!1))), f(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(1835,plain,
% 0.64/0.83 (~r(f(elem!1), f(f(f(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[567, 180, 1834])).
% 0.64/0.84 tff(1836,plain,
% 0.64/0.84 ((f(elem!1) = f(c)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1499])).
% 0.64/0.84 tff(1837,plain,
% 0.64/0.84 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(c))),
% 0.64/0.84 inference(symmetry,[status(thm)],[1836])).
% 0.64/0.84 tff(1838,plain,
% 0.64/0.84 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(c)))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1837])).
% 0.64/0.84 tff(1839,plain,
% 0.64/0.84 (~(f(elem!1) = f(c))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1118, 1838])).
% 0.64/0.84 tff(1840,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1841,plain,
% 0.64/0.84 ((r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1842,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1841])).
% 0.64/0.84 tff(1843,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1842, 1840])).
% 0.64/0.84 tff(1844,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1845,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 0.64/0.84 tff(1846,plain,
% 0.64/0.84 (r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1845, 205, 549, 1834])).
% 0.64/0.84 tff(1847,plain,
% 0.64/0.84 (r(f(c), f(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1846, 1483, 1494, 1504])).
% 0.64/0.84 tff(1848,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(elem!1))) | r(f(elem!1), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(elem!1))) | r(f(elem!1), f(c)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1849,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(elem!1))) | r(f(elem!1), f(c)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1850,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(elem!1))) | r(f(elem!1), f(c))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.64/0.84 tff(1851,plain,
% 0.64/0.84 (r(f(elem!1), f(c))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1850, 180, 1847])).
% 0.64/0.84 tff(1852,plain,
% 0.64/0.84 (r(f(c), f(f(f(c))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1646, 1588, 1582, 1774, 1638])).
% 0.64/0.84 tff(1853,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1854,plain,
% 0.64/0.84 (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(c), c)) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c))))) <=> ((~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1855,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(c), c)) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1854])).
% 0.64/0.84 tff(1856,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(c), c)) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1855, 1853])).
% 0.64/0.84 tff(1857,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(c), c)) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1858,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(c) = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 0.64/0.84 tff(1859,plain,
% 0.64/0.84 (~r(f(c), c)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1858, 233, 30, 1669, 1852, 52, 1783])).
% 0.64/0.84 tff(1860,plain,
% 0.64/0.84 (~r(c, f(f(elem!1)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[439, 180, 1776])).
% 0.64/0.84 tff(1861,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1862,plain,
% 0.64/0.84 ((r(f(c), c) | r(c, f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c)) <=> ((f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1863,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c)))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1862])).
% 0.64/0.84 tff(1864,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1863, 1861])).
% 0.64/0.84 tff(1865,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1866,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 0.64/0.84 tff(1867,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1866, 205, 30, 1582, 1588, 163, 1860, 1859])).
% 0.64/0.84 tff(1868,plain,(r(f(c), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), c)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(1869,plain,
% 0.64/0.84 (r(f(f(elem!1)), c)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1868, 1588, 1638, 1774, 1582])).
% 0.64/0.84 tff(1870,assumption,(~(f(elem!1) = f(c))), introduced(assumption)).
% 0.64/0.84 tff(1871,assumption,(r(f(elem!1), f(c))), introduced(assumption)).
% 0.64/0.84 tff(1872,assumption,(~(f(elem!1) = f(f(f(c))))), introduced(assumption)).
% 0.64/0.84 tff(1873,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1874,plain,
% 0.64/0.84 (((~r(f(elem!1), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c))) <=> ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1875,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1874])).
% 0.64/0.84 tff(1876,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1875, 1873])).
% 0.64/0.84 tff(1877,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1878,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(f(f(c))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 0.64/0.84 tff(1879,plain,
% 0.64/0.84 (~r(f(elem!1), f(f(f(c))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1878, 233, 1852, 52, 1872, 1871, 1870])).
% 0.64/0.84 tff(1880,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1881,plain,
% 0.64/0.84 ((r(f(elem!1), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(c))))) <=> ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1882,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1881])).
% 0.64/0.84 tff(1883,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1882, 1880])).
% 0.64/0.84 tff(1884,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1885,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 0.64/0.84 tff(1886,plain,
% 0.64/0.84 (r(f(elem!1), f(f(elem!1)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1885, 205, 144, 1638, 1774, 1872, 1879])).
% 0.64/0.84 tff(1887,assumption,(r(f(elem!1), c)), introduced(assumption)).
% 0.64/0.84 tff(1888,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1889,plain,
% 0.64/0.84 (((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(elem!1), c)) | (f(f(elem!1)) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1)))) <=> ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1890,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(elem!1), c)) | (f(f(elem!1)) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1889])).
% 0.64/0.84 tff(1891,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(elem!1), c)) | (f(f(elem!1)) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1890, 1888])).
% 0.64/0.84 tff(1892,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(elem!1), c)) | (f(f(elem!1)) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1893,plain,
% 0.64/0.84 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = c) | (f(elem!1) = f(f(elem!1))) | (f(f(elem!1)) = c) | (~r(f(elem!1), c)) | (~r(f(f(elem!1)), c))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 0.64/0.84 tff(1894,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1893, 233, 258, 162, 1073, 144, 1887, 622])).
% 0.64/0.84 tff(1895,plain,((~r(f(elem!1), c)) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(f(elem!1)), c))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(1896,plain,
% 0.64/0.84 (~r(f(elem!1), c)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1895, 1886, 144, 1869])).
% 0.64/0.84 tff(1897,plain,
% 0.64/0.84 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1898,plain,
% 0.64/0.85 ((r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(elem!1))), c) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1))) <=> ((f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1899,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(elem!1))), c) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c)))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1898])).
% 0.64/0.85 tff(1900,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(elem!1))), c) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.85 inference(transitivity,[status(thm)],[1899, 1897])).
% 0.64/0.85 tff(1901,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(elem!1))), c) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1902,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(f(f(elem!1))) = c) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(elem!1))), c) | r(f(elem!1), c)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.64/0.85 tff(1903,plain,
% 0.64/0.85 (r(f(f(f(elem!1))), c)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1902, 205, 258, 304, 552, 1834, 1896])).
% 0.64/0.85 tff(1904,plain,
% 0.64/0.85 (~(f(f(f(elem!1))) = f(f(elem!1)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[146, 144])).
% 0.64/0.85 tff(1905,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[655, 233, 162, 304, 1904, 362, 1903, 1869])).
% 0.64/0.85 tff(1906,plain,(r(f(c), f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(elem!1) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(c)) | (f(c) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(1907,plain,
% 0.64/0.85 (r(f(c), f(f(elem!1)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1906, 1851, 549, 1834, 1527, 1638, 1610, 1585, 362, 1839, 1508])).
% 0.64/0.85 tff(1908,plain,
% 0.64/0.85 (~r(f(f(elem!1)), f(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1525, 1907, 84, 92, 1835, 135, 972])).
% 0.64/0.85 tff(1909,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1910,plain,
% 0.64/0.85 ((r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1911,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1910])).
% 0.64/0.85 tff(1912,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[1911, 1909])).
% 0.64/0.85 tff(1913,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(c))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1914,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 0.64/0.85 tff(1915,plain,
% 0.64/0.85 (r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1914, 205, 1908, 135, 1638, 1610])).
% 0.64/0.85 tff(1916,plain,
% 0.64/0.85 (r(f(f(f(c))), f(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1915, 1586])).
% 0.64/0.85 tff(1917,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(elem!1))) | r(f(elem!1), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(elem!1))) | r(f(elem!1), f(f(f(c)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1918,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(elem!1))) | r(f(elem!1), f(f(f(c)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1919,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(elem!1))) | r(f(elem!1), f(f(f(c))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 0.64/0.85 tff(1920,plain,
% 0.64/0.85 (r(f(elem!1), f(f(f(c))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1919, 180, 1916])).
% 0.64/0.85 tff(1921,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1922,plain,
% 0.64/0.85 (((~r(f(f(f(c))), f(elem!1))) | (~r(f(elem!1), f(c))) | (~r(f(f(f(c))), f(c))) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(elem!1))) <=> ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1923,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (~r(f(elem!1), f(c))) | (~r(f(f(f(c))), f(c))) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1922])).
% 0.64/0.85 tff(1924,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (~r(f(elem!1), f(c))) | (~r(f(f(f(c))), f(c))) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[1923, 1921])).
% 0.64/0.85 tff(1925,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(elem!1))) | (~r(f(elem!1), f(c))) | (~r(f(f(f(c))), f(c))) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(elem!1)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1926,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1)) | (f(elem!1) = f(c)) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(elem!1), f(c)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 0.64/0.85 tff(1927,plain,
% 0.64/0.85 (~r(f(f(f(c))), f(c))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1926, 233, 1718, 1851, 1839, 1916, 1586])).
% 0.64/0.85 tff(1928,assumption,(~r(f(f(f(c))), c)), introduced(assumption)).
% 0.64/0.85 tff(1929,assumption,(~r(f(f(f(c))), f(c))), introduced(assumption)).
% 0.64/0.85 tff(1930,plain,
% 0.64/0.85 (r(f(c), c)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1808, 1928, 1929])).
% 0.64/0.85 tff(1931,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1932,plain,
% 0.64/0.85 (((~r(f(c), c)) | (~r(c, f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c)) <=> ((~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1933,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1932])).
% 0.64/0.85 tff(1934,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[1933, 1931])).
% 0.64/0.85 tff(1935,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = c))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1936,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 0.64/0.85 tff(1937,plain,
% 0.64/0.85 ((~r(f(c), c)) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1936, 233, 30])).
% 0.64/0.85 tff(1938,plain,
% 0.64/0.85 ((~r(f(c), c)) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1937, 163])).
% 0.64/0.85 tff(1939,plain,
% 0.64/0.85 (~r(c, f(f(elem!1)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1938, 1930, 1582, 1505])).
% 0.64/0.85 tff(1940,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1941,plain,
% 0.64/0.85 ((r(f(f(f(c))), c) | r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c)) <=> (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1942,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c)))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1941])).
% 0.64/0.85 tff(1943,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.64/0.85 inference(transitivity,[status(thm)],[1942, 1940])).
% 0.64/0.85 tff(1944,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(1945,plain,
% 0.64/0.85 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 0.64/0.85 tff(1946,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1945, 205, 1669, 1638, 1774, 163, 1939, 1928])).
% 0.64/0.85 tff(1947,plain,(r(f(f(f(c))), c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(elem!1)))) | r(f(f(f(c))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(1948,plain,
% 0.64/0.85 (r(f(f(f(c))), c)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1947, 1907, 1610, 1508, 1638, 1927])).
% 0.64/0.85 tff(1949,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1950,plain,
% 0.64/0.85 (((~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(elem!1), c)) | (f(f(f(c))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(c))))) <=> ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1951,plain,
% 0.64/0.85 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(elem!1), c)) | (f(f(f(c))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1950])).
% 0.64/0.86 tff(1952,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(elem!1), c)) | (f(f(f(c))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1951, 1949])).
% 0.64/0.86 tff(1953,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(elem!1), c)) | (f(f(f(c))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1954,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(elem!1) = f(f(f(c))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 0.64/0.86 tff(1955,plain,
% 0.64/0.86 (~r(f(elem!1), c)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1954, 233, 258, 1669, 1585, 1948, 1920])).
% 0.64/0.86 tff(1956,plain,
% 0.64/0.86 (r(elem!1, c) <=> r(f(f(f(elem!1))), c)),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1478])).
% 0.64/0.86 tff(1957,plain,
% 0.64/0.86 ((~r(elem!1, c)) <=> (~r(f(f(f(elem!1))), c))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1956])).
% 0.64/0.86 tff(1958,plain,
% 0.64/0.86 (r(f(f(f(elem!1))), f(f(f(c)))) <=> r(elem!1, f(f(f(c))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1479])).
% 0.64/0.86 tff(1959,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1960,plain,
% 0.64/0.86 ((r(f(f(f(c))), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(c))) <=> (r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1961,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1960])).
% 0.64/0.86 tff(1962,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1961, 1959])).
% 0.64/0.86 tff(1963,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(c)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1964,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.64/0.86 tff(1965,plain,
% 0.64/0.86 (r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1964, 205, 1630, 1718, 1927, 1483, 1494])).
% 0.64/0.86 tff(1966,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(c)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1967,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(c)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1968,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(c))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.64/0.86 tff(1969,plain,
% 0.64/0.86 (r(f(f(f(elem!1))), f(f(f(c))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1968, 180, 1965])).
% 0.64/0.86 tff(1970,plain,
% 0.64/0.86 (r(elem!1, f(f(f(c))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1969, 1958])).
% 0.64/0.86 tff(1971,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1972,plain,
% 0.64/0.86 (((~r(elem!1, f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(elem!1, c)) | (f(f(f(c))) = c) | (elem!1 = c) | (elem!1 = f(f(f(c))))) <=> ((elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1973,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(elem!1, c)) | (f(f(f(c))) = c) | (elem!1 = c) | (elem!1 = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c)))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1972])).
% 0.64/0.86 tff(1974,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(elem!1, c)) | (f(f(f(c))) = c) | (elem!1 = c) | (elem!1 = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c))))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1973, 1971])).
% 0.64/0.86 tff(1975,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(elem!1, c)) | (f(f(f(c))) = c) | (elem!1 = c) | (elem!1 = f(f(f(c)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1976,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c)))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.64/0.86 tff(1977,plain,
% 0.64/0.86 ((elem!1 = c) | (~r(elem!1, c)) | (elem!1 = f(f(f(c)))) | (~r(f(f(f(c))), c)) | (~r(elem!1, f(f(f(c)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1976, 233, 1669])).
% 0.64/0.86 tff(1978,plain,
% 0.64/0.86 (~r(elem!1, c)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1977, 1948, 632, 1624, 1970])).
% 0.64/0.86 tff(1979,plain,
% 0.64/0.86 (~r(f(f(f(elem!1))), c)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1978, 1957])).
% 0.64/0.86 tff(1980,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1981,plain,
% 0.64/0.86 ((r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c) | (f(f(f(elem!1))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1))))) <=> ((f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1982,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c) | (f(f(f(elem!1))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c)))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1981])).
% 0.64/0.86 tff(1983,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c) | (f(f(f(elem!1))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1982, 1980])).
% 0.64/0.86 tff(1984,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c) | (f(f(f(elem!1))) = c) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1985,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = c) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(elem!1), c)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 0.64/0.86 tff(1986,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1985, 205, 258, 304, 92, 1835, 1979, 1955])).
% 0.64/0.86 tff(1987,plain,(r(f(c), elem!1) | (f(elem!1) = f(f(f(elem!1)))) | (elem!1 = c) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~(f(f(f(f(elem!1)))) = f(elem!1))) | r(f(f(f(elem!1))), f(elem!1)) | (~r(f(f(f(elem!1))), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(1988,plain,
% 0.64/0.86 (r(f(c), elem!1)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1987, 1638, 632, 92, 135, 84, 1834, 362])).
% 0.64/0.86 tff(1989,plain,
% 0.64/0.86 (r(f(c), f(f(f(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1988, 1481])).
% 0.64/0.86 tff(1990,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1991,plain,
% 0.64/0.86 (((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1992,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1991])).
% 0.64/0.86 tff(1993,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1992, 1990])).
% 0.64/0.86 tff(1994,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1995,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 0.64/0.86 tff(1996,plain,
% 0.64/0.86 ((~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1995, 233, 1528, 362, 1508])).
% 0.64/0.86 tff(1997,plain,
% 0.64/0.86 (~r(f(c), f(f(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1996, 1989, 1494])).
% 0.64/0.86 tff(1998,plain,
% 0.64/0.86 (r(f(f(elem!1)), c)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1868, 1997, 1638, 1610, 1508])).
% 0.64/0.86 tff(1999,plain,
% 0.64/0.86 (~r(f(elem!1), f(c))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1906, 1997, 549, 1834, 1527, 1638, 1610, 1585, 1839, 362, 1508])).
% 0.64/0.86 tff(2000,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(2001,plain,
% 0.64/0.86 ((r(f(elem!1), f(c)) | r(f(c), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(c))) <=> ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(2002,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[2001])).
% 0.64/0.86 tff(2003,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c)))),
% 0.64/0.86 inference(transitivity,[status(thm)],[2002, 2000])).
% 0.64/0.86 tff(2004,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(c)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(2005,plain,
% 0.64/0.86 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(elem!1) = f(c)) | r(f(elem!1), f(c))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 0.64/0.86 tff(2006,plain,
% 0.64/0.86 (r(f(elem!1), f(f(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[2005, 205, 1527, 1508, 1997, 1999, 1839])).
% 0.64/0.86 tff(2007,plain,
% 0.64/0.86 (~r(f(elem!1), c)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1895, 2006, 1527, 1998])).
% 0.64/0.86 tff(2008,plain,
% 0.64/0.86 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[366, 180, 362])).
% 0.64/0.86 tff(2009,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(2010,plain,
% 0.64/0.86 (((~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1))))) <=> ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(2011,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[2010])).
% 0.64/0.86 tff(2012,plain,
% 0.64/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2011, 2009])).
% 0.64/0.87 tff(2013,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c)) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = c) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2014,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(f(f(elem!1))) = c) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), c))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.64/0.87 tff(2015,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2014, 233, 162, 304, 1471, 1594, 1631, 622])).
% 0.64/0.87 tff(2016,plain,((~r(f(f(f(elem!1))), c)) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), c))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(2017,plain,
% 0.64/0.87 (~r(f(f(f(elem!1))), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2016, 1998, 1529, 2008])).
% 0.64/0.87 tff(2018,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1985, 205, 258, 304, 92, 1835, 2017, 2007])).
% 0.64/0.87 tff(2019,plain,(r(f(f(f(c))), f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~(f(f(f(f(elem!1)))) = f(elem!1))) | (elem!1 = c) | (f(f(elem!1)) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(2020,plain,
% 0.64/0.87 (r(f(f(f(c))), f(f(elem!1)))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2019, 1462, 80, 1830, 1441, 617, 214])).
% 0.64/0.87 tff(2021,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2022,plain,
% 0.64/0.87 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2023,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2022])).
% 0.64/0.87 tff(2024,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2023, 2021])).
% 0.64/0.87 tff(2025,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2026,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(f(elem!1))))) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.64/0.87 tff(2027,plain,
% 0.64/0.87 (~r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2026, 233, 1831, 710, 2020, 1740, 1773])).
% 0.64/0.87 tff(2028,plain,
% 0.64/0.87 (~r(f(f(f(c))), elem!1)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2027, 1833])).
% 0.64/0.87 tff(2029,plain,
% 0.64/0.87 (~(f(f(f(c))) = elem!1)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1772, 1613])).
% 0.64/0.87 tff(2030,plain,
% 0.64/0.87 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(elem!1)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2031,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(elem!1)))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2032,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(elem!1))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.64/0.87 tff(2033,plain,
% 0.64/0.87 (~r(f(f(f(elem!1))), f(f(f(c))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2032, 180, 2027])).
% 0.64/0.87 tff(2034,plain,
% 0.64/0.87 ((f(f(f(elem!1))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.64/0.87 inference(commutativity,[status(thm)],[])).
% 0.64/0.87 tff(2035,plain,
% 0.64/0.87 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (f(f(f(elem!1))) = f(f(f(c))))),
% 0.64/0.87 inference(symmetry,[status(thm)],[2034])).
% 0.64/0.87 tff(2036,plain,
% 0.64/0.87 ((~(f(f(f(c))) = f(f(f(elem!1))))) <=> (~(f(f(f(elem!1))) = f(f(f(c)))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2035])).
% 0.64/0.87 tff(2037,plain,
% 0.64/0.87 (~(f(f(f(elem!1))) = f(f(f(c))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1773, 2036])).
% 0.64/0.87 tff(2038,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2039,plain,
% 0.64/0.87 ((r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1))))) <=> ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2040,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2039])).
% 0.64/0.87 tff(2041,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2040, 2038])).
% 0.64/0.87 tff(2042,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2043,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 0.64/0.87 tff(2044,plain,
% 0.64/0.87 (r(f(elem!1), f(f(f(c))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2043, 205, 80, 1463, 1811, 2037, 2033])).
% 0.64/0.87 tff(2045,assumption,(r(f(elem!1), f(f(f(c))))), introduced(assumption)).
% 0.64/0.87 tff(2046,assumption,(~r(f(f(f(c))), elem!1)), introduced(assumption)).
% 0.64/0.87 tff(2047,assumption,(~r(f(f(f(elem!1))), c)), introduced(assumption)).
% 0.64/0.87 tff(2048,plain,
% 0.64/0.87 (r(elem!1, c) <=> r(f(f(f(elem!1))), c)),
% 0.64/0.87 inference(monotonicity,[status(thm)],[308])).
% 0.64/0.87 tff(2049,plain,
% 0.64/0.87 (r(f(f(f(elem!1))), c)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[698, 2048])).
% 0.64/0.87 tff(2050,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2047, 2049])).
% 0.64/0.87 tff(2051,plain,((~r(elem!1, c)) | r(f(f(f(elem!1))), c) | (~(elem!1 = f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(2052,plain,
% 0.64/0.87 (~r(elem!1, c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2051, 2047, 308])).
% 0.64/0.87 tff(2053,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2054,plain,
% 0.64/0.87 ((r(f(f(f(c))), elem!1) | r(elem!1, c) | r(f(f(f(c))), c) | (elem!1 = c) | (f(f(f(c))) = c) | (f(f(f(c))) = elem!1)) <=> ((elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2055,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), elem!1) | r(elem!1, c) | r(f(f(f(c))), c) | (elem!1 = c) | (f(f(f(c))) = c) | (f(f(f(c))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c)))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2054])).
% 0.64/0.87 tff(2056,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), elem!1) | r(elem!1, c) | r(f(f(f(c))), c) | (elem!1 = c) | (f(f(f(c))) = c) | (f(f(f(c))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2055, 2053])).
% 0.64/0.87 tff(2057,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), elem!1) | r(elem!1, c) | r(f(f(f(c))), c) | (elem!1 = c) | (f(f(f(c))) = c) | (f(f(f(c))) = elem!1))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2058,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | (f(f(f(c))) = c) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 0.64/0.87 tff(2059,plain,
% 0.64/0.87 ((elem!1 = c) | r(elem!1, c) | (f(f(f(c))) = elem!1) | r(f(f(f(c))), elem!1) | r(f(f(f(c))), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2058, 205, 1669])).
% 0.64/0.87 tff(2060,plain,
% 0.64/0.87 (r(f(f(f(c))), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2059, 2052, 632, 1636, 2046])).
% 0.64/0.87 tff(2061,plain,
% 0.64/0.87 (r(f(elem!1), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1985, 205, 258, 304, 92, 1495, 2047])).
% 0.64/0.87 tff(2062,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1954, 233, 258, 1669, 2061, 1872, 2060, 2045])).
% 0.64/0.87 tff(2063,plain,(r(f(f(f(elem!1))), c) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(f(f(c))))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (elem!1 = c) | (f(f(f(c))) = elem!1) | r(f(f(f(c))), elem!1) | (~(elem!1 = f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(2064,plain,
% 0.64/0.87 (r(f(f(f(elem!1))), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2063, 1811, 2044, 80, 1463, 617, 2029, 2028, 1442])).
% 0.64/0.87 tff(2065,plain,
% 0.64/0.87 (~r(f(f(elem!1)), c)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2016, 2064, 710, 1831])).
% 0.64/0.87 tff(2066,plain,
% 0.64/0.87 (~(f(f(f(elem!1))) = f(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[548, 80])).
% 0.64/0.87 tff(2067,assumption,(~r(f(c), f(f(f(elem!1))))), introduced(assumption)).
% 0.64/0.87 tff(2068,plain,
% 0.64/0.87 (r(f(c), f(elem!1)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1845, 205, 552, 1834])).
% 0.64/0.87 tff(2069,plain,
% 0.64/0.87 (r(f(c), f(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2068, 2067, 1494, 1504])).
% 0.64/0.87 tff(2070,assumption,(~r(f(f(f(elem!1))), f(f(f(c))))), introduced(assumption)).
% 0.64/0.87 tff(2071,plain,
% 0.64/0.87 (~(f(f(f(elem!1))) = f(f(f(c))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1630, 2036])).
% 0.64/0.87 tff(2072,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2073,plain,
% 0.64/0.87 ((r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(elem!1))))) <=> (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2074,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2073])).
% 0.64/0.87 tff(2075,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2074, 2072])).
% 0.64/0.87 tff(2076,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(elem!1)))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(2077,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 0.64/0.87 tff(2078,plain,
% 0.64/0.87 (r(f(c), f(f(f(c)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2077, 205, 52, 2071, 2070])).
% 0.64/0.87 tff(2079,plain,
% 0.64/0.87 (r(f(c), f(f(f(c))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[2078, 2067, 1494])).
% 0.64/0.87 tff(2080,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2081,plain,
% 0.64/0.87 (((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1))) <=> ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(2082,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[2081])).
% 0.64/0.87 tff(2083,plain,
% 0.64/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c)))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[2082, 2080])).
% 0.64/0.87 tff(2084,plain,
% 0.64/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(2085,plain,
% 0.64/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)) | (f(elem!1) = f(f(f(c))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 0.64/0.88 tff(2086,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2085, 233, 2079, 52, 1585, 2045, 2069, 1504])).
% 0.64/0.88 tff(2087,plain,(r(f(c), f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(c))))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (~(f(f(f(f(elem!1)))) = f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(2088,plain,
% 0.64/0.88 (r(f(c), f(f(f(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2087, 2044, 2033, 2066, 1462, 1441])).
% 0.64/0.88 tff(2089,plain,
% 0.64/0.88 (~r(f(c), c)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1553, 233, 304, 30, 2064, 2088, 1456])).
% 0.64/0.88 tff(2090,plain,
% 0.64/0.88 ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1995, 233, 427, 1830, 1561, 2088])).
% 0.64/0.88 tff(2091,plain,
% 0.64/0.88 (~r(f(c), f(f(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2090, 1456])).
% 0.64/0.88 tff(2092,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2093,plain,
% 0.64/0.88 ((r(f(c), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(c), c) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2094,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(c), c) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c)))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2093])).
% 0.64/0.88 tff(2095,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(c), c) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c))),
% 0.64/0.88 inference(transitivity,[status(thm)],[2094, 2092])).
% 0.64/0.88 tff(2096,plain,
% 0.64/0.88 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), c) | r(f(c), c) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(2097,plain,
% 0.64/0.88 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (f(c) = c) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), c) | r(f(f(elem!1)), c)),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 0.64/0.88 tff(2098,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2097, 205, 162, 30, 1561, 2091, 2089, 2065])).
% 0.64/0.88 tff(2099,plain,(r(elem!1, f(elem!1)) | (elem!1 = f(f(elem!1))) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(2100,plain,
% 0.64/0.88 (r(elem!1, f(elem!1))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2099, 62, 66])).
% 0.64/0.88 tff(2101,plain,
% 0.64/0.88 ((~r(f(elem!1), f(f(elem!1)))) <=> (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[1072])).
% 0.64/0.88 tff(2102,plain,
% 0.64/0.88 (r(f(f(f(f(elem!1)))), f(f(elem!1))) <=> r(elem!1, f(f(elem!1)))),
% 0.64/0.88 inference(symmetry,[status(thm)],[1208])).
% 0.64/0.88 tff(2103,plain,
% 0.64/0.88 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) <=> r(elem!1, f(f(elem!1)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[1206, 2102])).
% 0.64/0.88 tff(2104,plain,
% 0.64/0.88 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | r(f(c), f(f(f(f(f(f(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | r(f(c), f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2105,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | r(f(c), f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(2106,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | r(f(c), f(f(f(f(f(f(elem!1)))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 0.64/0.88 tff(2107,plain,
% 0.64/0.88 (~r(f(f(f(f(f(f(elem!1)))))), f(c))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2106, 180, 876])).
% 0.64/0.88 tff(2108,plain,
% 0.64/0.88 (~(f(f(f(f(f(f(elem!1)))))) = elem!1)),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[831, 1052])).
% 0.64/0.88 tff(2109,plain,
% 0.64/0.88 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1470, 1216])).
% 0.64/0.88 tff(2110,plain,
% 0.64/0.88 ((f(f(f(f(elem!1)))) = f(c)) <=> (elem!1 = f(c))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[954])).
% 0.64/0.88 tff(2111,plain,
% 0.64/0.88 ((f(f(f(f(elem!1)))) = f(c)) <=> (f(c) = elem!1)),
% 0.64/0.88 inference(transitivity,[status(thm)],[2110, 1448])).
% 0.64/0.88 tff(2112,plain,
% 0.64/0.88 ((f(c) = elem!1) <=> (f(f(f(f(elem!1)))) = f(c))),
% 0.64/0.88 inference(symmetry,[status(thm)],[2111])).
% 0.64/0.88 tff(2113,plain,
% 0.64/0.88 ((~(f(c) = elem!1)) <=> (~(f(f(f(f(elem!1)))) = f(c)))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2112])).
% 0.64/0.88 tff(2114,plain,
% 0.64/0.88 (~(f(f(f(f(elem!1)))) = f(c))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[967, 2113])).
% 0.64/0.88 tff(2115,assumption,(~r(f(f(f(f(f(f(elem!1)))))), f(c))), introduced(assumption)).
% 0.64/0.88 tff(2116,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2117,plain,
% 0.64/0.88 ((r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2118,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2117])).
% 0.64/0.88 tff(2119,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(c)) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | r(f(f(f(f(f(f(elem!1)))))), f(c)) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[2118, 2116])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 0.64/0.88 tff(2122,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[2121, 205, 874, 2115, 996, 2114])).
% 0.64/0.88 tff(2123,plain,
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(2126,plain,
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 0.64/0.88 tff(2127,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[2126, 180, 2123])).
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[1265, 205, 874, 2115, 1118, 1221, 903])).
% 0.64/0.88 tff(2129,plain,
% 0.64/0.88 (~(f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1)))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[994, 1048])).
% 0.64/0.88 tff(2130,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[1039, 180, 996])).
% 0.64/0.88 tff(2131,plain,
% 0.64/0.88 ((f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1098, 205, 897, 1221, 903, 2130])).
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[1274, 233, 1118, 897, 2132, 2128, 968, 2127])).
% 0.64/0.88 tff(2134,plain,(r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))) | (~(elem!1 = f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | r(f(f(f(f(f(f(elem!1)))))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(2135,plain,
% 0.64/0.88 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))),
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% 0.64/0.88 tff(2136,plain,
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[2135, 2103])).
% 0.64/0.88 tff(2137,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[739, 2136, 62, 426, 172, 610])).
% 0.64/0.88 tff(2138,plain,
% 0.64/0.88 (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[2137, 2101])).
% 0.64/0.88 tff(2139,plain,
% 0.64/0.88 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(2141,plain,
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.64/0.88 tff(2142,plain,
% 0.64/0.88 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[2141, 180, 2138])).
% 0.64/0.88 tff(2143,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 ((r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))) <=> (r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(2145,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2144])).
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% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[2145, 2143])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[2147, 2146])).
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% 0.64/0.88 tff(2150,plain,
% 0.64/0.88 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))),
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% 0.64/0.88 ((f(f(f(elem!1))) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(f(elem!1))))),
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% 0.64/0.88 tff(2154,plain,
% 0.64/0.88 ((~(f(f(f(elem!1))) = f(f(elem!1)))) <=> (~(f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2153])).
% 0.64/0.88 tff(2155,plain,
% 0.64/0.88 ((~(f(f(elem!1)) = f(elem!1))) <=> (~(f(elem!1) = f(f(elem!1))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[131])).
% 0.64/0.88 tff(2156,plain,
% 0.64/0.88 (~(f(elem!1) = f(f(elem!1)))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[135, 2155])).
% 0.64/0.88 tff(2157,plain,
% 0.64/0.88 (~(f(f(f(elem!1))) = f(f(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[146, 2156])).
% 0.64/0.88 tff(2158,plain,
% 0.64/0.88 (~(f(f(elem!1)) = f(f(f(elem!1))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[2157, 2154])).
% 0.64/0.88 tff(2159,plain,
% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 ((r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(elem!1)) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[2160])).
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% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.89 inference(rewrite,[status(thm)],[])).
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% 0.64/0.89 inference(monotonicity,[status(thm)],[2218])).
% 0.64/0.89 tff(2220,plain,
% 0.64/0.89 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[2219, 2217])).
% 0.64/0.89 tff(2221,plain,
% 0.64/0.89 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(2222,plain,
% 0.64/0.89 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 0.64/0.89 tff(2223,plain,
% 0.64/0.89 (r(c, f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[2222, 205, 1425, 2216, 1289, 1380])).
% 0.64/0.89 tff(2224,plain,
% 0.64/0.89 (r(c, f(f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[2223, 2215])).
% 0.64/0.89 tff(2225,plain,
% 0.64/0.89 (r(f(f(f(f(f(f(elem!1)))))), elem!1) <=> r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[877])).
% 0.64/0.89 tff(2226,plain,
% 0.64/0.89 ((~r(f(f(f(f(f(f(elem!1)))))), elem!1)) <=> (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[2225])).
% 0.64/0.89 tff(2227,assumption,(r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))), introduced(assumption)).
% 0.64/0.89 tff(2228,plain,
% 0.64/0.89 (r(f(f(f(elem!1))), elem!1) <=> r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[877])).
% 0.64/0.89 tff(2229,plain,
% 0.64/0.89 (r(f(f(f(elem!1))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), elem!1)),
% 0.64/0.89 inference(symmetry,[status(thm)],[2228])).
% 0.64/0.89 tff(2230,plain,
% 0.64/0.89 (r(f(f(f(elem!1))), f(f(f(f(elem!1))))) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[891])).
% 0.64/0.89 tff(2231,plain,
% 0.64/0.89 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(symmetry,[status(thm)],[2230])).
% 0.64/0.89 tff(2232,plain,
% 0.64/0.89 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) <=> r(f(f(f(elem!1))), elem!1)),
% 0.64/0.89 inference(transitivity,[status(thm)],[2231, 2229])).
% 0.64/0.89 tff(2233,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | r(c, f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | r(c, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(2234,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | r(c, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(2235,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 0.64/0.89 tff(2236,plain,
% 0.64/0.89 (~r(f(f(f(f(f(f(f(elem!1))))))), c)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[2235, 180, 2216])).
% 0.64/0.89 tff(2237,plain,
% 0.64/0.89 (r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))) <=> r(f(f(f(f(f(elem!1))))), elem!1)),
% 0.64/0.89 inference(monotonicity,[status(thm)],[954])).
% 0.64/0.89 tff(2238,plain,
% 0.64/0.89 (r(f(f(f(f(f(elem!1))))), elem!1) <=> r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(symmetry,[status(thm)],[2237])).
% 0.64/0.89 tff(2239,plain,
% 0.64/0.89 (r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[2207, 2238])).
% 0.64/0.89 tff(2240,plain,
% 0.64/0.89 ((f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) <=> (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(symmetry,[status(thm)],[1159])).
% 0.64/0.89 tff(2241,plain,
% 0.64/0.89 ((~(f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))) <=> (~(f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[2240])).
% 0.64/0.89 tff(2242,plain,
% 0.64/0.89 (~(f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[974, 2241])).
% 0.64/0.89 tff(2243,plain,
% 0.64/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(2244,plain,
% 0.64/0.89 (((~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(f(f(f(f(elem!1))))))) <=> ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(2245,plain,
% 0.64/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[2244])).
% 0.64/0.89 tff(2246,plain,
% 0.64/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[2245, 2243])).
% 0.64/0.89 tff(2247,plain,
% 0.64/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (c = f(f(f(f(f(elem!1)))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(2248,plain,
% 0.64/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 0.64/0.89 tff(2249,plain,
% 0.64/0.89 ((~r(c, f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[2248, 233, 99, 2224, 2215])).
% 0.64/0.89 tff(2250,plain,
% 0.64/0.89 (~r(c, f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[2249, 2242, 2239])).
% 0.64/0.89 tff(2251,plain,
% 0.64/0.89 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1284, 205, 964, 897, 2250, 99, 2236])).
% 0.64/0.89 tff(2252,plain,
% 0.64/0.89 (r(f(f(f(elem!1))), elem!1)),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[2251, 2232])).
% 0.64/0.89 tff(2253,plain,
% 0.64/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))))),
% 0.64/0.90 inference(rewrite,[status(thm)],[])).
% 0.64/0.90 tff(2254,plain,
% 0.64/0.90 (((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1))))) <=> ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))))),
% 0.64/0.90 inference(rewrite,[status(thm)],[])).
% 0.64/0.90 tff(2255,plain,
% 0.64/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1)))))))),
% 0.64/0.90 inference(monotonicity,[status(thm)],[2254])).
% 0.64/0.90 tff(2256,plain,
% 0.64/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))))),
% 0.64/0.90 inference(transitivity,[status(thm)],[2255, 2253])).
% 0.64/0.90 tff(2257,plain,
% 0.64/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))))),
% 0.64/0.90 inference(quant_inst,[status(thm)],[])).
% 0.64/0.90 tff(2258,plain,
% 0.64/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1)))))),
% 0.64/0.90 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 0.64/0.90 tff(2259,plain,
% 0.64/0.90 ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~r(f(f(f(f(f(f(elem!1)))))), elem!1)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(elem!1)))))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[2258, 233])).
% 0.64/0.90 tff(2260,plain,
% 0.64/0.90 (~r(f(f(f(f(f(f(elem!1)))))), elem!1)),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[2259, 2252, 310, 902, 994, 2227])).
% 0.64/0.90 tff(2261,plain,
% 0.64/0.90 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[2260, 2226])).
% 0.74/0.90 tff(2262,plain,
% 0.74/0.90 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), c))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2263,plain,
% 0.74/0.90 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), c))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(2264,plain,
% 0.74/0.90 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), c)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 0.74/0.90 tff(2265,plain,
% 0.74/0.90 (r(f(f(f(f(f(elem!1))))), c)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2264, 180, 2224])).
% 0.74/0.90 tff(2266,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2267,plain,
% 0.74/0.90 (((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2268,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[2267])).
% 0.74/0.90 tff(2269,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[2268, 2266])).
% 0.74/0.90 tff(2270,plain,
% 0.74/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(2271,plain,
% 0.74/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 0.74/0.90 tff(2272,plain,
% 0.74/0.90 (~r(f(f(f(f(elem!1)))), c)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2271, 233, 97, 872, 2265, 2206, 974])).
% 0.74/0.90 tff(2273,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2274,plain,
% 0.74/0.90 ((r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2275,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[2274])).
% 0.74/0.90 tff(2276,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/0.90 inference(transitivity,[status(thm)],[2275, 2273])).
% 0.74/0.90 tff(2277,plain,
% 0.74/0.90 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(2278,plain,
% 0.74/0.90 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 0.74/0.90 tff(2279,plain,
% 0.74/0.90 (r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2278, 205, 97, 910, 2272, 2261, 2129])).
% 0.74/0.90 tff(2280,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2281,plain,
% 0.74/0.90 (((~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = c)) <=> ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2282,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[2281])).
% 0.74/0.90 tff(2283,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[2282, 2280])).
% 0.74/0.90 tff(2284,plain,
% 0.74/0.90 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(c, f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = c))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(2285,plain,
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 0.74/0.90 tff(2286,plain,
% 0.74/0.90 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2285, 233, 910, 2279, 1005, 2224, 2215])).
% 0.74/0.90 tff(2287,plain,
% 0.74/0.90 (r(f(c), f(f(f(f(f(elem!1))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2148, 205, 981, 2286, 1005, 876, 875])).
% 0.74/0.90 tff(2288,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(2289,plain,
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% 0.74/0.90 inference(rewrite,[status(thm)],[])).
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% 0.74/0.90 inference(monotonicity,[status(thm)],[2289])).
% 0.74/0.90 tff(2291,plain,
% 0.74/0.90 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[2290, 2288])).
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% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 0.74/0.90 tff(2294,plain,
% 0.74/0.90 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2293, 205, 2261, 876, 2129])).
% 0.74/0.90 tff(2295,plain,
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% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2298,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2297])).
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% 0.74/0.91 inference(transitivity,[status(thm)],[2298, 2296])).
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% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(elem!1))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(2301,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(c), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.74/0.91 tff(2302,plain,
% 0.74/0.91 ($false),
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% 0.74/0.91 tff(2304,plain,
% 0.74/0.91 (r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2303, 1289, 974, 1005, 876, 877, 994, 310, 2211, 897, 2207, 2206, 1380])).
% 0.74/0.91 tff(2305,plain,
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% 0.74/0.91 tff(2308,plain,
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% 0.74/0.91 tff(2309,plain,
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% 0.74/0.91 inference(monotonicity,[status(thm)],[880])).
% 0.74/0.91 tff(2310,plain,
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% 0.74/0.91 inference(monotonicity,[status(thm)],[2309])).
% 0.74/0.91 tff(2311,plain,
% 0.74/0.91 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))),
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% 0.74/0.91 tff(2312,plain,
% 0.74/0.91 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
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% 0.74/0.91 ((~(f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1))))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2313])).
% 0.74/0.91 tff(2315,plain,
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% 0.74/0.91 tff(2316,plain,
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% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2321,plain,
% 0.74/0.91 (((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (c = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = c)) <=> ((f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (c = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2322,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (c = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (c = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2321])).
% 0.74/0.91 tff(2323,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (c = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (c = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[2322, 2320])).
% 0.74/0.91 tff(2324,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (c = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = c))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(2325,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (c = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 0.74/0.91 tff(2326,plain,
% 0.74/0.91 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2325, 233, 964, 1118, 2319, 2308, 1352])).
% 0.74/0.91 tff(2327,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2328,plain,
% 0.74/0.91 ((r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2329,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2328])).
% 0.74/0.91 tff(2330,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[2329, 2327])).
% 0.74/0.91 tff(2331,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(2332,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 0.74/0.91 tff(2333,plain,
% 0.74/0.91 ((f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2332, 205, 1118, 2326, 2205])).
% 0.74/0.91 tff(2334,plain,
% 0.74/0.91 (r(f(f(f(f(f(elem!1))))), f(c))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2333, 2197, 2201])).
% 0.74/0.91 tff(2335,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2336,plain,
% 0.74/0.91 (((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1))))))) <=> ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2337,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2336])).
% 0.74/0.91 tff(2338,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[2337, 2335])).
% 0.74/0.91 tff(2339,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(2340,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 0.74/0.91 tff(2341,plain,
% 0.74/0.91 (~r(f(f(f(f(elem!1)))), f(c))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2340, 233, 2206, 2334, 974, 2114, 2197])).
% 0.74/0.91 tff(2342,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2343,plain,
% 0.74/0.91 ((r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c))) <=> (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2344,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[2343])).
% 0.74/0.91 tff(2345,plain,
% 0.74/0.91 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[2344, 2342])).
% 0.74/0.91 tff(2346,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(2347,plain,
% 0.74/0.91 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(c)) | r(f(f(f(f(elem!1)))), f(c)) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 0.74/0.92 tff(2348,plain,
% 0.74/0.92 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2347, 205, 876, 2114, 2341, 875])).
% 0.74/0.92 tff(2349,plain,
% 0.74/0.92 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2348, 995])).
% 0.74/0.92 tff(2350,plain,
% 0.74/0.92 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(c)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2351,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(c)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(2352,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(c))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 0.74/0.92 tff(2353,plain,
% 0.74/0.92 (~r(f(c), f(f(f(f(elem!1)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2352, 180, 2341])).
% 0.74/0.92 tff(2354,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2355,plain,
% 0.74/0.92 ((r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2356,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2355])).
% 0.74/0.92 tff(2357,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[2356, 2354])).
% 0.74/0.92 tff(2358,plain,
% 0.74/0.92 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(f(c), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(2359,plain,
% 0.74/0.92 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 0.74/0.92 tff(2360,plain,
% 0.74/0.92 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2359, 205, 1118, 897, 2326, 968, 2353])).
% 0.74/0.92 tff(2361,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1431, 233, 897, 2360, 2209, 903, 2349, 995])).
% 0.74/0.92 tff(2362,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = elem!1) | (~(elem!1 = f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(elem!1))) = elem!1) | (~r(f(f(f(f(f(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(2363,plain,
% 0.74/0.92 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2362, 2177, 897, 876, 2108, 877, 2193, 974, 2150, 2191, 886, 310, 2187])).
% 0.74/0.92 tff(2364,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2365,plain,
% 0.74/0.92 (((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2366,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2365])).
% 0.74/0.92 tff(2367,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[2366, 2364])).
% 0.74/0.92 tff(2368,plain,
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% 0.74/0.92 tff(2373,plain,
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% 0.74/0.92 tff(2376,plain,
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% 0.74/0.92 tff(2377,plain,
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% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2399,plain,
% 0.74/0.92 (((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(c, f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1)))))) <=> ((~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2400,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(c, f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1)))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2399])).
% 0.74/0.92 tff(2401,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(c, f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[2400, 2398])).
% 0.74/0.92 tff(2402,plain,
% 0.74/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(c, f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(2403,plain,
% 0.74/0.92 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(elem!1)))))) | (~r(c, f(c))) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(elem!1)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 0.74/0.92 tff(2404,plain,
% 0.74/0.92 (~r(c, f(c))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2403, 233, 2392, 99, 1352, 2114, 2397])).
% 0.74/0.92 tff(2405,plain,
% 0.74/0.92 (r(f(f(f(f(elem!1)))), c)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1133, 180, 2392])).
% 0.74/0.92 tff(2406,plain,
% 0.74/0.92 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2407,plain,
% 0.74/0.93 (((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2408,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[2407])).
% 0.74/0.93 tff(2409,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[2408, 2406])).
% 0.74/0.93 tff(2410,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(2411,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), c)) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 0.74/0.93 tff(2412,plain,
% 0.74/0.93 (~r(f(f(f(f(f(elem!1))))), c)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2411, 233, 97, 872, 2405, 2242, 2377])).
% 0.74/0.93 tff(2413,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2414,plain,
% 0.74/0.93 ((r(f(f(f(f(f(elem!1))))), c) | r(c, f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (c = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = c)) <=> (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2415,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | r(c, f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (c = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[2414])).
% 0.74/0.93 tff(2416,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | r(c, f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (c = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[2415, 2413])).
% 0.74/0.93 tff(2417,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | r(c, f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | (c = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = c))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(2418,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(c)) | r(f(f(f(f(f(elem!1))))), f(c)) | r(c, f(c)) | (c = f(c))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 0.74/0.93 tff(2419,plain,
% 0.74/0.93 (r(f(f(f(f(f(elem!1))))), f(c))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2418, 205, 872, 2412, 2404, 1352, 2197])).
% 0.74/0.93 tff(2420,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2421,plain,
% 0.74/0.93 (((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2422,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[2421])).
% 0.74/0.93 tff(2423,plain,
% 0.74/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[2422, 2420])).
% 0.74/0.93 tff(2424,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(2425,plain,
% 0.74/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | (f(f(f(f(elem!1)))) = f(c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))),
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% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2529,plain,
% 0.74/0.94 ((r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))) <=> (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2530,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[2529])).
% 0.74/0.94 tff(2531,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[2530, 2528])).
% 0.74/0.94 tff(2532,plain,
% 0.74/0.94 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(2533,plain,
% 0.74/0.94 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 0.74/0.94 tff(2534,plain,
% 0.74/0.94 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2533, 205, 1005, 1289, 1380, 2512, 2527])).
% 0.74/0.94 tff(2535,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2536,plain,
% 0.74/0.94 (((~r(c, f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(elem!1)))))))) <=> ((c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2537,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[2536])).
% 0.74/0.94 tff(2538,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[2537, 2535])).
% 0.74/0.94 tff(2539,plain,
% 0.74/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(2540,plain,
% 0.74/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 0.74/0.94 tff(2541,plain,
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% 0.74/0.94 tff(2542,plain,
% 0.74/0.94 ($false),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2223, 2541, 2215])).
% 0.74/0.94 tff(2543,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (~r(c, f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2544,plain,
% 0.74/0.94 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2543, 2525, 1380, 1005, 2524, 2512, 904])).
% 0.74/0.94 tff(2545,plain,
% 0.74/0.94 ((f(c) = f(f(elem!1))) <=> (f(c) = f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[880])).
% 0.74/0.94 tff(2546,plain,
% 0.74/0.94 ((f(c) = f(f(elem!1))) <=> (f(f(f(f(f(f(elem!1)))))) = f(c))),
% 0.74/0.94 inference(transitivity,[status(thm)],[2545, 862])).
% 0.74/0.94 tff(2547,plain,
% 0.74/0.94 ((f(f(f(f(f(f(elem!1)))))) = f(c)) <=> (f(c) = f(f(elem!1)))),
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% 0.74/0.94 tff(2548,plain,
% 0.74/0.94 ((~(f(f(f(f(f(f(elem!1)))))) = f(c))) <=> (~(f(c) = f(f(elem!1))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[2547])).
% 0.74/0.94 tff(2549,plain,
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% 0.74/0.94 inference(modus_ponens,[status(thm)],[874, 2548])).
% 0.74/0.94 tff(2550,plain,
% 0.74/0.94 (r(c, f(f(f(f(f(f(elem!1))))))) <=> r(c, f(f(elem!1)))),
% 0.74/0.94 inference(symmetry,[status(thm)],[2309])).
% 0.74/0.94 tff(2551,plain,
% 0.74/0.94 (r(c, f(f(elem!1)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[2524, 2550])).
% 0.74/0.94 tff(2552,plain,
% 0.74/0.94 (~r(f(c), c)),
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% 0.74/0.94 tff(2553,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), c))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2554,plain,
% 0.74/0.94 ((r(f(c), c) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c)) <=> ((f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), c))),
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% 0.74/0.94 tff(2555,plain,
% 0.74/0.94 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), c)))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[2554])).
% 0.74/0.94 tff(2556,plain,
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% 0.74/0.94 inference(transitivity,[status(thm)],[2555, 2553])).
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% 0.74/0.94 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = c))),
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% 0.74/0.94 tff(2558,plain,
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[2605, 2603])).
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% 0.74/0.95 tff(2610,plain,
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% 0.74/0.95 tff(2612,plain,
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% 0.74/0.95 tff(2613,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[577, 2612, 81, 66, 1784])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[2613, 2601])).
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% 0.74/0.95 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(c, f(f(f(f(elem!1))))) | (c = f(f(f(f(elem!1))))))),
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% 0.74/0.95 inference(transitivity,[status(thm)],[2617, 2615])).
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 tff(2631,plain,
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% 0.74/0.95 tff(2632,plain,
% 0.74/0.95 ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2540, 233, 2588, 2511, 2622, 911])).
% 0.74/0.95 tff(2633,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[2632, 2631, 2215])).
% 0.74/0.95 tff(2634,plain,(r(f(f(f(elem!1))), f(elem!1)) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(elem!1)))) | (c = elem!1) | (~r(c, f(f(f(elem!1))))) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(2635,plain,
% 0.74/0.95 (r(f(f(f(elem!1))), f(elem!1))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2634, 2583, 81, 66, 2476, 62, 1470])).
% 0.74/0.95 tff(2636,plain,
% 0.74/0.95 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))),
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% 0.74/0.95 tff(2638,plain,
% 0.74/0.95 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2637, 2499, 2498])).
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% 0.74/0.95 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(2640,plain,
% 0.74/0.95 ((r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(2641,plain,
% 0.74/0.95 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[2640])).
% 0.74/0.96 tff(2642,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[2641, 2639])).
% 0.74/0.96 tff(2643,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2644,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2643, 2642])).
% 0.74/0.96 tff(2645,plain,
% 0.74/0.96 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2644, 205, 861, 2638, 2490, 2470])).
% 0.74/0.96 tff(2646,plain,
% 0.74/0.96 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2645, 2483])).
% 0.74/0.96 tff(2647,plain,
% 0.74/0.96 (r(f(f(f(f(f(f(elem!1)))))), elem!1)),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2646, 2479])).
% 0.74/0.96 tff(2648,plain,
% 0.74/0.96 (~r(f(c), elem!1)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1355, 2647, 2456, 832, 2478])).
% 0.74/0.96 tff(2649,plain,
% 0.74/0.96 (~r(f(c), f(f(f(f(elem!1)))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2648, 2474])).
% 0.74/0.96 tff(2650,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2651,plain,
% 0.74/0.96 (((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2652,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[2651])).
% 0.74/0.96 tff(2653,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[2652, 2650])).
% 0.74/0.96 tff(2654,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2655,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 0.74/0.96 tff(2656,plain,
% 0.74/0.96 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2655, 233, 2506, 2511, 841, 2646, 2483])).
% 0.74/0.96 tff(2657,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2658,plain,
% 0.74/0.96 (((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1))))))))) <=> ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2659,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1)))))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[2658])).
% 0.74/0.96 tff(2660,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[2659, 2657])).
% 0.74/0.96 tff(2661,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2662,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | (~r(c, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 0.74/0.96 tff(2663,plain,
% 0.74/0.96 ((~r(c, f(f(f(f(f(elem!1))))))) | (c = f(f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2662, 233, 1425, 2582, 2636, 2500])).
% 0.74/0.96 tff(2664,plain,
% 0.74/0.96 (~r(c, f(f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2663, 2215])).
% 0.74/0.96 tff(2665,plain,
% 0.74/0.96 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(elem!1))))), c)) | r(c, f(f(f(f(f(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(elem!1))))), c)) | r(c, f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2666,plain,
% 0.74/0.96 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(elem!1))))), c)) | r(c, f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2667,plain,
% 0.74/0.96 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(elem!1))))), c)) | r(c, f(f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 0.74/0.96 tff(2668,plain,
% 0.74/0.96 (~r(f(f(f(f(f(elem!1))))), c)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2667, 180, 2664])).
% 0.74/0.96 tff(2669,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2670,plain,
% 0.74/0.96 ((r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))) <=> (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2671,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[2670])).
% 0.74/0.96 tff(2672,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[2671, 2669])).
% 0.74/0.96 tff(2673,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2674,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(elem!1)))))), c) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 0.74/0.96 tff(2675,plain,
% 0.74/0.96 (r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2674, 205, 872, 910, 2668, 2656, 2511])).
% 0.74/0.96 tff(2676,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2677,plain,
% 0.74/0.96 (((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2678,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1))))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[2677])).
% 0.74/0.96 tff(2679,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[2678, 2676])).
% 0.74/0.96 tff(2680,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(c), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(2681,plain,
% 0.74/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 0.74/0.96 tff(2682,plain,
% 0.74/0.96 (~r(f(c), c)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2681, 233, 910, 30, 2675, 2476, 875])).
% 0.74/0.96 tff(2683,plain,
% 0.74/0.96 (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1039, 180, 2646])).
% 0.74/0.96 tff(2684,plain,
% 0.74/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(2685,plain,
% 0.74/0.96 (((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2686,plain,
% 0.74/0.97 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[2685])).
% 0.74/0.97 tff(2687,plain,
% 0.74/0.97 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.74/0.97 inference(transitivity,[status(thm)],[2686, 2684])).
% 0.74/0.97 tff(2688,plain,
% 0.74/0.97 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
% 0.74/0.97 tff(2689,plain,
% 0.74/0.97 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (~r(f(f(f(f(elem!1)))), c)) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 0.74/0.97 tff(2690,plain,
% 0.74/0.97 (~r(f(f(f(f(elem!1)))), c)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2689, 233, 97, 910, 2675, 2683, 833])).
% 0.74/0.97 tff(2691,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[2820])).
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% 0.74/0.98 inference(monotonicity,[status(thm)],[2835])).
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% 0.74/0.98 tff(2851,plain,
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% 0.74/0.98 (~(f(f(f(f(f(elem!1))))) = f(f(f(c))))),
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% 0.74/0.98 inference(rewrite,[status(thm)],[])).
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% 0.74/0.98 inference(rewrite,[status(thm)],[])).
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% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 0.74/0.99 tff(2899,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[2898, 233])).
% 0.74/0.99 tff(2900,plain,
% 0.74/0.99 ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2899, 1119])).
% 0.74/0.99 tff(2901,plain,
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% 0.74/0.99 tff(2902,plain,
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% 0.74/0.99 inference(monotonicity,[status(thm)],[881])).
% 0.74/0.99 tff(2903,plain,
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% 0.74/0.99 inference(symmetry,[status(thm)],[2902])).
% 0.74/0.99 tff(2904,plain,
% 0.74/0.99 ((~(f(f(f(c))) = f(f(elem!1)))) <=> (~(f(f(f(c))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2903])).
% 0.74/0.99 tff(2905,plain,
% 0.74/0.99 (~(f(f(f(c))) = f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2762, 2904])).
% 0.74/0.99 tff(2906,plain,
% 0.74/0.99 ((f(f(f(c))) = f(f(f(f(f(elem!1)))))) <=> (f(f(f(c))) = f(elem!1))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[879])).
% 0.74/0.99 tff(2907,plain,
% 0.74/0.99 ((f(f(f(c))) = f(f(f(f(f(elem!1)))))) <=> (f(elem!1) = f(f(f(c))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2906, 1573])).
% 0.74/0.99 tff(2908,plain,
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% 0.74/0.99 inference(symmetry,[status(thm)],[2907])).
% 0.74/0.99 tff(2909,plain,
% 0.74/0.99 ((~(f(elem!1) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2908])).
% 0.74/0.99 tff(2910,plain,
% 0.74/0.99 (~(f(f(f(c))) = f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2759, 2909])).
% 0.74/0.99 tff(2911,plain,
% 0.74/0.99 (r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) <=> r(f(f(f(c))), f(f(elem!1)))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[881])).
% 0.74/0.99 tff(2912,plain,
% 0.74/0.99 (r(f(f(f(c))), f(f(elem!1))) <=> r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(symmetry,[status(thm)],[2911])).
% 0.74/0.99 tff(2913,plain,
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% 0.74/0.99 inference(monotonicity,[status(thm)],[2912])).
% 0.74/0.99 tff(2914,plain,
% 0.74/0.99 (~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1638, 2913])).
% 0.74/0.99 tff(2915,assumption,(~r(f(c), f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.74/0.99 tff(2916,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2917,plain,
% 0.74/0.99 ((r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1))))))))) <=> (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2918,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2917])).
% 0.74/0.99 tff(2919,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2918, 2916])).
% 0.74/0.99 tff(2920,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2921,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 0.74/0.99 tff(2922,plain,
% 0.74/0.99 (r(f(c), f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2921, 205, 981, 1119, 2915, 1289, 1380])).
% 0.74/0.99 tff(2923,plain,
% 0.74/0.99 (r(f(c), f(f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1505, 2778])).
% 0.74/0.99 tff(2924,plain,
% 0.74/0.99 (r(f(f(f(f(f(f(elem!1)))))), f(c))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2477, 2923])).
% 0.74/0.99 tff(2925,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2926,plain,
% 0.74/0.99 (((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(c))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2927,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2926])).
% 0.74/0.99 tff(2928,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2927, 2925])).
% 0.74/0.99 tff(2929,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(c)))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2930,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | (f(c) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 0.74/0.99 tff(2931,plain,
% 0.74/0.99 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2930, 233, 874, 2924, 981, 1005, 2922])).
% 0.74/0.99 tff(2932,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2933,plain,
% 0.74/0.99 ((r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1)))))))) <=> (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2934,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2933])).
% 0.74/0.99 tff(2935,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2934, 2932])).
% 0.74/0.99 tff(2936,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2937,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 0.74/0.99 tff(2938,plain,
% 0.74/0.99 ((f(f(f(c))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2937, 205, 2931, 1005, 2914])).
% 0.74/0.99 tff(2939,plain,
% 0.74/0.99 (r(f(f(f(c))), f(f(f(f(f(elem!1))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2938, 2910, 2905])).
% 0.74/0.99 tff(2940,plain,
% 0.74/0.99 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(c)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2941,plain,
% 0.74/0.99 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(c)))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2942,plain,
% 0.74/0.99 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(c))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2941, 2940])).
% 0.74/0.99 tff(2943,plain,
% 0.74/0.99 (r(f(f(f(f(f(elem!1))))), f(f(f(c))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2942, 180, 2939])).
% 0.74/0.99 tff(2944,plain,
% 0.74/0.99 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(c)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2945,plain,
% 0.74/0.99 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(c)))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2946,plain,
% 0.74/0.99 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(c))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 0.74/0.99 tff(2947,plain,
% 0.74/0.99 (r(f(f(f(f(f(elem!1))))), f(c))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2946, 180, 2922])).
% 0.74/0.99 tff(2948,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2949,plain,
% 0.74/0.99 (((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(f(f(elem!1))))))) <=> ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2950,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1)))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2949])).
% 0.74/0.99 tff(2951,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1))))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2950, 2948])).
% 0.74/0.99 tff(2952,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (~r(f(f(f(c))), f(c))) | (f(f(f(f(f(elem!1))))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2953,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = f(c)) | (~r(f(f(f(f(f(elem!1))))), f(c))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(f(elem!1)))))) | (~r(f(f(f(c))), f(f(f(f(f(elem!1)))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 0.74/0.99 tff(2954,plain,
% 0.74/0.99 (~r(f(f(f(c))), f(c))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2953, 233, 2947, 1718, 2910, 2939, 2197])).
% 0.74/0.99 tff(2955,plain,
% 0.74/0.99 (r(f(f(f(c))), c)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1947, 2954, 2762, 2549, 1638, 1505])).
% 0.74/0.99 tff(2956,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2957,plain,
% 0.74/0.99 (((~r(f(f(f(f(f(elem!1))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(c))))) <=> ((f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2958,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c)))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2957])).
% 0.74/0.99 tff(2959,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2958, 2956])).
% 0.74/0.99 tff(2960,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2961,plain,
% 0.74/0.99 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(c)))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(c)))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 0.74/0.99 tff(2962,plain,
% 0.74/0.99 (~r(f(f(f(f(f(elem!1))))), c)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2961, 233, 872, 1669, 2955, 2758, 2943])).
% 0.74/0.99 tff(2963,plain,
% 0.74/0.99 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2964,plain,
% 0.74/1.00 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))) <=> (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2965,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2964])).
% 0.74/1.00 tff(2966,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(elem!1))))), c) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2965, 2963])).
% 0.74/1.00 tff(2967,plain,
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2968,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | r(f(f(f(f(f(f(f(elem!1))))))), c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 0.74/1.00 tff(2969,plain,
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% 0.74/1.00 tff(2970,plain,
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% 0.74/1.00 inference(unit_resolution,[status(thm)],[2674, 205, 872, 910, 2962, 2931, 1005])).
% 0.74/1.00 tff(2971,plain,
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% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2972,plain,
% 0.74/1.00 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2973,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2972])).
% 0.74/1.00 tff(2974,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2973, 2971])).
% 0.74/1.00 tff(2975,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2976,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(f(elem!1)))))), c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 0.74/1.00 tff(2977,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2976, 233, 910, 964, 2209, 1220, 2970, 2969])).
% 0.74/1.00 tff(2978,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(f(f(elem!1)))))) | r(f(f(f(c))), f(f(elem!1))) | (~r(f(c), f(f(elem!1)))) | (~(elem!1 = f(f(f(f(elem!1)))))) | r(f(c), f(f(f(f(f(f(f(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2979,plain,
% 0.74/1.00 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2978, 2882, 2469, 2500, 2511, 1638, 2880, 817, 2901])).
% 0.74/1.00 tff(2980,plain,
% 0.74/1.00 (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2369, 233, 2511, 2979, 2500, 2883, 2470])).
% 0.74/1.00 tff(2981,plain,
% 0.74/1.00 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2982,plain,
% 0.74/1.00 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2983,plain,
% 0.74/1.00 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 0.74/1.00 tff(2984,plain,
% 0.74/1.00 (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2983, 180, 2980])).
% 0.74/1.00 tff(2985,plain,
% 0.74/1.00 (r(c, f(f(elem!1))) <=> r(c, f(f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[825])).
% 0.74/1.00 tff(2986,plain,
% 0.74/1.00 ((~r(c, f(f(elem!1)))) <=> (~r(c, f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2985])).
% 0.74/1.00 tff(2987,plain,
% 0.74/1.00 ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(elem!1))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2383, 233, 861, 2979, 2500])).
% 0.74/1.00 tff(2988,plain,
% 0.74/1.00 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2987, 2499, 2498])).
% 0.74/1.00 tff(2989,plain,
% 0.74/1.00 (r(f(c), f(f(f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2880, 2475])).
% 0.74/1.00 tff(2990,plain,
% 0.74/1.00 (r(f(f(f(f(f(f(elem!1)))))), f(c))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2477, 2989])).
% 0.74/1.00 tff(2991,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2992,plain,
% 0.74/1.00 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2993,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2992])).
% 0.74/1.00 tff(2994,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2993, 2991])).
% 0.74/1.00 tff(2995,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2996,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(elem!1)))))) = f(c)) | (~r(f(f(f(f(f(f(elem!1)))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(f(f(elem!1))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 0.74/1.00 tff(2997,plain,
% 0.74/1.00 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2996, 233, 874, 2990, 1118, 2882, 2469])).
% 0.74/1.00 tff(2998,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2999,plain,
% 0.74/1.00 ((r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(3000,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2999])).
% 0.74/1.00 tff(3001,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[3000, 2998])).
% 0.74/1.00 tff(3002,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(3003,plain,
% 0.74/1.00 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(elem!1))))) | (f(c) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(c), f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 0.74/1.00 tff(3004,plain,
% 0.74/1.00 ((f(c) = f(f(f(f(elem!1))))) | r(f(c), f(f(f(f(elem!1)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[3003, 205, 861, 2988, 1119, 2901])).
% 0.74/1.00 tff(3005,plain,
% 0.74/1.00 (r(f(c), f(f(f(f(elem!1)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[3004, 2461])).
% 0.74/1.00 tff(3006,plain,
% 0.74/1.00 (r(f(f(f(f(elem!1)))), f(c))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2352, 180, 3005])).
% 0.74/1.00 tff(3007,plain,
% 0.74/1.00 ((f(f(f(f(elem!1)))) = f(c)) <=> (elem!1 = f(c))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[818])).
% 0.74/1.00 tff(3008,plain,
% 0.74/1.00 ((f(f(f(f(elem!1)))) = f(c)) <=> (f(c) = elem!1)),
% 0.74/1.00 inference(transitivity,[status(thm)],[3007, 1448])).
% 0.74/1.00 tff(3009,plain,
% 0.74/1.00 ((f(c) = elem!1) <=> (f(f(f(f(elem!1)))) = f(c))),
% 0.74/1.00 inference(symmetry,[status(thm)],[3008])).
% 0.74/1.00 tff(3010,plain,
% 0.74/1.00 ((~(f(c) = elem!1)) <=> (~(f(f(f(f(elem!1)))) = f(c)))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[3009])).
% 0.74/1.00 tff(3011,plain,
% 0.74/1.00 (~(f(f(f(f(elem!1)))) = f(c))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2456, 3010])).
% 0.74/1.00 tff(3012,assumption,(r(f(f(f(f(elem!1)))), f(c))), introduced(assumption)).
% 0.74/1.00 tff(3013,assumption,(~(f(f(f(f(elem!1)))) = f(c))), introduced(assumption)).
% 0.74/1.00 tff(3014,plain,
% 0.74/1.00 (r(c, f(f(f(f(elem!1)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2391, 205, 897, 1381, 99, 1425, 2216])).
% 0.74/1.00 tff(3015,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), f(c))), introduced(assumption)).
% 0.74/1.00 tff(3016,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(3017,plain,
% 0.74/1.00 ((r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(f(elem!1))))))))) <=> (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(3018,plain,
% 0.74/1.00 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[3017])).
% 0.74/1.01 tff(3019,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)))),
% 0.74/1.01 inference(transitivity,[status(thm)],[3018, 3016])).
% 0.74/1.01 tff(3020,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(3021,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(f(f(elem!1)))))))) | r(c, f(c)) | (c = f(f(f(f(f(f(f(elem!1)))))))) | (c = f(c)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 0.74/1.01 tff(3022,plain,
% 0.74/1.01 (r(c, f(c))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3021, 205, 1118, 3015, 1352, 1425, 2216])).
% 0.74/1.01 tff(3023,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2403, 233, 3022, 3014, 99, 1352, 3013, 3012])).
% 0.74/1.01 tff(3024,plain,(r(c, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(f(elem!1)))) = f(c)) | (~r(f(f(f(f(elem!1)))), f(c))) | r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(3025,plain,
% 0.74/1.01 (r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3024, 3011, 3006, 2997, 861, 2988])).
% 0.74/1.01 tff(3026,plain,
% 0.74/1.01 (~r(c, f(f(elem!1)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1693, 3025, 2888, 2892])).
% 0.74/1.01 tff(3027,plain,
% 0.74/1.01 (~r(c, f(f(f(f(f(f(elem!1)))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3026, 2986])).
% 0.74/1.01 tff(3028,plain,
% 0.74/1.01 (~r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2523, 180, 3027])).
% 0.74/1.01 tff(3029,plain,
% 0.74/1.01 (~(f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2500, 2200])).
% 0.74/1.01 tff(3030,plain,
% 0.74/1.01 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3031,plain,
% 0.74/1.01 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(3032,plain,
% 0.74/1.01 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 0.74/1.01 tff(3033,plain,
% 0.74/1.01 (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3032, 180, 2979])).
% 0.74/1.01 tff(3034,plain,
% 0.74/1.01 (r(f(f(f(f(f(f(f(elem!1))))))), c)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2307, 180, 3025])).
% 0.74/1.01 tff(3035,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3036,plain,
% 0.74/1.01 (((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1))))))))) <=> ((f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3037,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[3036])).
% 0.74/1.01 tff(3038,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c)))),
% 0.74/1.01 inference(transitivity,[status(thm)],[3037, 3035])).
% 0.74/1.01 tff(3039,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (~r(f(f(f(f(f(elem!1))))), c)) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(3040,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(f(elem!1))))))) = c) | (~r(f(f(f(f(f(f(f(elem!1))))))), c)) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(elem!1))))), c))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 0.74/1.01 tff(3041,plain,
% 0.74/1.01 (~r(f(f(f(f(f(elem!1))))), c)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3040, 233, 872, 964, 3034, 3033, 3029])).
% 0.74/1.01 tff(3042,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3043,plain,
% 0.74/1.01 ((r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1)))))))) <=> (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3044,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[3043])).
% 0.74/1.01 tff(3045,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.74/1.01 inference(transitivity,[status(thm)],[3044, 3042])).
% 0.74/1.01 tff(3046,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(3047,plain,
% 0.74/1.01 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(elem!1))))), c) | (f(f(f(f(f(elem!1))))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(f(elem!1))))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(elem!1))))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 0.74/1.01 tff(3048,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3047, 205, 872, 910, 3041, 3028, 2984, 2734])).
% 0.74/1.01 tff(3049,plain,(r(f(f(f(c))), f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(3050,plain,
% 0.74/1.01 (r(f(f(f(c))), f(f(elem!1)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3049, 81, 62, 66])).
% 0.74/1.01 tff(3051,plain,
% 0.74/1.01 (r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3050, 2733])).
% 0.74/1.01 tff(3052,plain,
% 0.74/1.01 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(c)))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3053,plain,
% 0.74/1.01 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(c)))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(3054,plain,
% 0.74/1.01 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 0.74/1.01 tff(3055,plain,
% 0.74/1.01 ((~r(f(f(f(c))), f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3054, 180])).
% 0.74/1.01 tff(3056,plain,
% 0.74/1.01 (r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[3055, 3051])).
% 0.74/1.01 tff(3057,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c)))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3058,plain,
% 0.74/1.01 (((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c)))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(3059,plain,
% 0.74/1.01 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(f(f(f(elem!1))))))) | (~r(f(c), f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(f(f(f(elem!1)))))), f(f(f(c))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(f(c))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[3058])).
% 0.74/1.01 tff(3060,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[2271, 233, 97, 872, 3195, 2506, 841])).
% 0.86/1.03 tff(3197,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3198,plain,
% 0.86/1.03 ((r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1)))))))) <=> ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3199,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3198])).
% 0.86/1.03 tff(3200,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3199, 3197])).
% 0.86/1.03 tff(3201,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(f(f(elem!1)))))) = c) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3202,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = c) | (f(f(f(f(f(f(elem!1)))))) = c) | r(f(f(f(f(elem!1)))), f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(elem!1)))), c) | (f(f(f(f(elem!1)))) = f(f(f(f(f(f(elem!1))))))) | r(f(f(f(f(f(f(elem!1)))))), c)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 0.86/1.03 tff(3203,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3202, 205, 97, 910, 3196, 3192, 3177, 833])).
% 0.86/1.03 tff(3204,plain,((elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(3205,plain,
% 0.86/1.03 (elem!1 = f(f(f(elem!1)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3204, 62, 66])).
% 0.86/1.03 tff(3206,plain,
% 0.86/1.03 (f(f(f(elem!1))) = elem!1),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[312, 3205])).
% 0.86/1.03 tff(3207,plain,
% 0.86/1.03 (f(f(f(f(elem!1)))) = f(elem!1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[104, 3206])).
% 0.86/1.03 tff(3208,plain,
% 0.86/1.03 (f(f(f(f(f(elem!1))))) = f(f(elem!1))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3207])).
% 0.86/1.03 tff(3209,plain,
% 0.86/1.03 (f(f(f(f(f(f(elem!1)))))) = f(f(f(elem!1)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3208])).
% 0.86/1.03 tff(3210,plain,
% 0.86/1.03 (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3209])).
% 0.86/1.03 tff(3211,plain,
% 0.86/1.03 (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)),
% 0.86/1.03 inference(transitivity,[status(thm)],[3210, 3207])).
% 0.86/1.03 tff(3212,plain,
% 0.86/1.03 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(c))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3211])).
% 0.86/1.03 tff(3213,plain,
% 0.86/1.03 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(c)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3212])).
% 0.86/1.03 tff(3214,plain,
% 0.86/1.03 (~(f(elem!1) = f(c))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1118, 3213])).
% 0.86/1.03 tff(3215,plain,
% 0.86/1.03 (~(f(c) = f(elem!1))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3214, 65])).
% 0.86/1.03 tff(3216,plain,
% 0.86/1.03 (f(f(f(elem!1))) = elem!1),
% 0.86/1.03 inference(symmetry,[status(thm)],[3205])).
% 0.86/1.03 tff(3217,plain,
% 0.86/1.03 ((f(f(f(elem!1))) = f(c)) <=> (elem!1 = f(c))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3216])).
% 0.86/1.03 tff(3218,plain,
% 0.86/1.03 ((f(f(f(elem!1))) = f(c)) <=> (f(c) = elem!1)),
% 0.86/1.03 inference(transitivity,[status(thm)],[3217, 1448])).
% 0.86/1.03 tff(3219,plain,
% 0.86/1.03 ((f(c) = elem!1) <=> (f(f(f(elem!1))) = f(c))),
% 0.86/1.03 inference(symmetry,[status(thm)],[3218])).
% 0.86/1.03 tff(3220,plain,
% 0.86/1.03 ((~(f(c) = elem!1)) <=> (~(f(f(f(elem!1))) = f(c)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3219])).
% 0.86/1.03 tff(3221,plain,
% 0.86/1.03 (f(f(f(f(f(f(elem!1)))))) = elem!1),
% 0.86/1.03 inference(transitivity,[status(thm)],[3209, 3216])).
% 0.86/1.03 tff(3222,plain,
% 0.86/1.03 ((f(f(f(f(f(f(elem!1)))))) = f(c)) <=> (elem!1 = f(c))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3221])).
% 0.86/1.03 tff(3223,plain,
% 0.86/1.03 ((f(f(f(f(f(f(elem!1)))))) = f(c)) <=> (f(c) = elem!1)),
% 0.86/1.03 inference(transitivity,[status(thm)],[3222, 1448])).
% 0.86/1.03 tff(3224,plain,
% 0.86/1.03 ((~(f(f(f(f(f(f(elem!1)))))) = f(c))) <=> (~(f(c) = elem!1))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3223])).
% 0.86/1.03 tff(3225,plain,
% 0.86/1.03 (~(f(c) = elem!1)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[874, 3224])).
% 0.86/1.03 tff(3226,plain,
% 0.86/1.03 (~(f(f(f(elem!1))) = f(c))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3225, 3220])).
% 0.86/1.03 tff(3227,plain,
% 0.86/1.03 ((f(c) = f(f(f(elem!1)))) <=> (f(c) = elem!1)),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3216])).
% 0.86/1.03 tff(3228,plain,
% 0.86/1.03 ((f(c) = elem!1) <=> (f(c) = f(f(f(elem!1))))),
% 0.86/1.03 inference(symmetry,[status(thm)],[3227])).
% 0.86/1.03 tff(3229,plain,
% 0.86/1.03 ((~(f(c) = elem!1)) <=> (~(f(c) = f(f(f(elem!1)))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3228])).
% 0.86/1.03 tff(3230,plain,
% 0.86/1.03 (~(f(c) = f(f(f(elem!1))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3225, 3229])).
% 0.86/1.03 tff(3231,plain,
% 0.86/1.03 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(c) = f(f(elem!1)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3208])).
% 0.86/1.03 tff(3232,plain,
% 0.86/1.03 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(c) = f(f(elem!1))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3231])).
% 0.86/1.03 tff(3233,plain,
% 0.86/1.03 (~(f(c) = f(f(elem!1)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[981, 3232])).
% 0.86/1.03 tff(3234,plain,
% 0.86/1.03 (~(f(elem!1) = f(f(f(c))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1584, 3233, 3205])).
% 0.86/1.03 tff(3235,plain,
% 0.86/1.03 (~(f(f(f(c))) = f(elem!1))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3234, 1575])).
% 0.86/1.03 tff(3236,plain,
% 0.86/1.03 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1609, 3225])).
% 0.86/1.03 tff(3237,plain,
% 0.86/1.03 (~(f(f(elem!1)) = f(c))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3233, 1558])).
% 0.86/1.03 tff(3238,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3239,plain,
% 0.86/1.03 ((r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3240,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3239])).
% 0.86/1.03 tff(3241,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3240, 3238])).
% 0.86/1.03 tff(3242,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(c), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = f(f(elem!1))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3243,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3242, 3241])).
% 0.86/1.03 tff(3244,plain,
% 0.86/1.03 (r(f(c), f(elem!1)) | (f(c) = f(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3243, 205, 805, 214, 3233, 1588])).
% 0.86/1.03 tff(3245,plain,
% 0.86/1.03 (r(f(c), f(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3244, 3215])).
% 0.86/1.03 tff(3246,plain,
% 0.86/1.03 (r(f(elem!1), elem!1) <=> r(f(elem!1), f(f(f(elem!1))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3205])).
% 0.86/1.03 tff(3247,plain,
% 0.86/1.03 (r(f(elem!1), f(f(f(elem!1))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2185, 3246])).
% 0.86/1.03 tff(3248,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3249,plain,
% 0.86/1.03 (((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3250,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3249])).
% 0.86/1.03 tff(3251,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3250, 3248])).
% 0.86/1.03 tff(3252,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(elem!1)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3253,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1)))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 0.86/1.03 tff(3254,plain,
% 0.86/1.03 ((~r(f(c), f(f(f(elem!1))))) | (f(c) = f(f(f(elem!1))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3253, 233, 80, 3247, 3245, 3215])).
% 0.86/1.03 tff(3255,plain,
% 0.86/1.03 (~r(f(c), f(f(f(elem!1))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3254, 3230])).
% 0.86/1.03 tff(3256,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3257,plain,
% 0.86/1.03 ((r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c))) <=> (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3258,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3257])).
% 0.86/1.03 tff(3259,plain,
% 0.86/1.03 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3258, 3256])).
% 0.86/1.03 tff(3260,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3261,plain,
% 0.86/1.03 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 0.86/1.03 tff(3262,plain,
% 0.86/1.03 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3261, 205, 710, 1592, 3255, 3237, 3230])).
% 0.86/1.03 tff(3263,plain,
% 0.86/1.03 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1476, 3262])).
% 0.86/1.03 tff(3264,plain,
% 0.86/1.03 (r(elem!1, f(f(elem!1)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1468, 3263, 3205])).
% 0.86/1.03 tff(3265,plain,
% 0.86/1.03 (~r(c, elem!1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[759, 3264, 66, 62, 2100])).
% 0.86/1.03 tff(3266,plain,
% 0.86/1.03 (~(elem!1 = f(f(f(c))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1623, 3207])).
% 0.86/1.03 tff(3267,plain,
% 0.86/1.03 (r(elem!1, f(f(f(c)))) <=> r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3205])).
% 0.86/1.03 tff(3268,plain,
% 0.86/1.03 (r(f(f(f(elem!1))), f(f(f(c)))) <=> r(elem!1, f(f(f(c))))),
% 0.86/1.03 inference(symmetry,[status(thm)],[3267])).
% 0.86/1.03 tff(3269,plain,
% 0.86/1.03 ((~r(f(f(f(elem!1))), f(f(f(c))))) <=> (~r(elem!1, f(f(f(c)))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3268])).
% 0.86/1.03 tff(3270,plain,
% 0.86/1.03 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (f(f(f(c))) = elem!1)),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3216])).
% 0.86/1.03 tff(3271,plain,
% 0.86/1.03 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (elem!1 = f(f(f(c))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3270, 1611])).
% 0.86/1.03 tff(3272,plain,
% 0.86/1.03 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.86/1.03 inference(symmetry,[status(thm)],[3271])).
% 0.86/1.03 tff(3273,plain,
% 0.86/1.03 ((~(elem!1 = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3272])).
% 0.86/1.03 tff(3274,plain,
% 0.86/1.03 (~(f(f(f(c))) = f(f(f(elem!1))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3266, 3273])).
% 0.86/1.03 tff(3275,plain,
% 0.86/1.03 (r(f(elem!1), f(c))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1850, 180, 3245])).
% 0.86/1.03 tff(3276,plain,
% 0.86/1.03 (r(f(c), f(f(f(c))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1646, 1638, 1582, 1774, 1588])).
% 0.86/1.03 tff(3277,assumption,(~(f(c) = f(f(f(elem!1))))), introduced(assumption)).
% 0.86/1.03 tff(3278,plain,
% 0.86/1.03 (~(f(f(elem!1)) = f(c))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1582, 1558])).
% 0.86/1.03 tff(3279,plain,
% 0.86/1.03 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3261, 205, 1631, 1592, 2067, 3278, 3277])).
% 0.86/1.03 tff(3280,plain,
% 0.86/1.03 (r(f(f(elem!1)), c)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1868, 1638, 1588, 1774, 1582])).
% 0.86/1.03 tff(3281,plain,
% 0.86/1.03 (~r(f(f(f(elem!1))), c)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2016, 3280, 1631, 3279])).
% 0.86/1.04 tff(3282,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3283,plain,
% 0.86/1.04 ((r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(c), c) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3284,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(c), c) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3283])).
% 0.86/1.04 tff(3285,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(c), c) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3284, 3282])).
% 0.86/1.04 tff(3286,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(elem!1)))) | r(f(f(f(elem!1))), c) | r(f(c), c) | (f(f(f(elem!1))) = c) | (f(c) = c) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3287,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = c) | r(f(f(f(elem!1))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 0.86/1.04 tff(3288,plain,
% 0.86/1.04 (r(f(c), c)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3287, 205, 304, 30, 3281, 2067, 3277])).
% 0.86/1.04 tff(3289,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3290,plain,
% 0.86/1.04 (((~r(f(elem!1), f(c))) | (~r(f(c), c)) | (~r(f(elem!1), c)) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c))) <=> ((f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3291,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), c)) | (~r(f(elem!1), c)) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3290])).
% 0.86/1.04 tff(3292,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), c)) | (~r(f(elem!1), c)) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3291, 3289])).
% 0.86/1.04 tff(3293,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(c))) | (~r(f(c), c)) | (~r(f(elem!1), c)) | (f(c) = c) | (f(elem!1) = c) | (f(elem!1) = f(c)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3294,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(c), c)) | (f(c) = c) | (~r(f(elem!1), c)) | (f(elem!1) = f(c)) | (~r(f(elem!1), f(c)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3293, 3292])).
% 0.86/1.04 tff(3295,plain,
% 0.86/1.04 (~r(f(elem!1), c)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3294, 233, 258, 30, 3288, 1871, 1870])).
% 0.86/1.04 tff(3296,plain,
% 0.86/1.04 (r(c, f(c))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2828, 180, 3288])).
% 0.86/1.04 tff(3297,assumption,(r(f(c), f(f(f(c))))), introduced(assumption)).
% 0.86/1.04 tff(3298,plain,
% 0.86/1.04 (~r(f(elem!1), f(f(f(c))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1878, 233, 3297, 52, 1872, 1871, 1870])).
% 0.86/1.04 tff(3299,assumption,(r(c, f(c))), introduced(assumption)).
% 0.86/1.04 tff(3300,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3301,plain,
% 0.86/1.04 (((~r(c, f(c))) | (~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c))) <=> ((~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3302,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3301])).
% 0.86/1.04 tff(3303,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3302, 3300])).
% 0.86/1.04 tff(3304,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3305,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3304, 3303])).
% 0.86/1.04 tff(3306,plain,
% 0.86/1.04 (~r(c, f(f(f(c))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3305, 233, 3299, 3297, 52, 3130, 1352])).
% 0.86/1.04 tff(3307,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3308,plain,
% 0.86/1.04 ((r(f(elem!1), c) | r(c, f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c)) <=> ((f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3309,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), c) | r(c, f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3308])).
% 0.86/1.04 tff(3310,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), c) | r(c, f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3309, 3307])).
% 0.86/1.04 tff(3311,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), c) | r(c, f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3312,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 0.86/1.04 tff(3313,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3312, 205, 258, 697, 1872, 3130, 3306, 3298])).
% 0.86/1.04 tff(3314,plain,((~r(f(c), f(f(f(c))))) | r(f(elem!1), c) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(c)) | (~r(c, f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3315,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3314, 3296, 3295, 1872, 1871, 1870, 3276])).
% 0.86/1.04 tff(3316,plain,(r(f(f(f(c))), f(f(elem!1))) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(c))) | (f(elem!1) = f(c)) | r(f(c), f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3317,plain,
% 0.86/1.04 (r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3316, 3275, 3234, 3214, 3255, 3230, 710, 3233, 3236, 1588])).
% 0.86/1.04 tff(3318,plain,
% 0.86/1.04 (~r(f(f(f(c))), f(f(f(elem!1))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2026, 233, 3262, 710, 3317, 3236, 3274])).
% 0.86/1.04 tff(3319,plain,
% 0.86/1.04 (~r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2032, 180, 3318])).
% 0.86/1.04 tff(3320,plain,
% 0.86/1.04 (~r(elem!1, f(f(f(c))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3319, 3269])).
% 0.86/1.04 tff(3321,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3322,plain,
% 0.86/1.04 ((r(c, elem!1) | r(elem!1, f(f(f(c)))) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | (c = elem!1)) <=> (r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3323,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(c)))) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3322])).
% 0.86/1.04 tff(3324,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(c)))) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | (c = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c)))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3323, 3321])).
% 0.86/1.04 tff(3325,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, elem!1) | r(elem!1, f(f(f(c)))) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | (c = elem!1))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3326,plain,
% 0.86/1.04 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | (c = f(f(f(c)))) | r(elem!1, f(f(f(c))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3325, 3324])).
% 0.86/1.04 tff(3327,plain,
% 0.86/1.04 (r(c, elem!1) | (c = elem!1) | r(c, f(f(f(c)))) | (elem!1 = f(f(f(c)))) | r(elem!1, f(f(f(c))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3326, 205, 3130])).
% 0.86/1.04 tff(3328,plain,
% 0.86/1.04 (r(c, f(f(f(c))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3327, 3320, 66, 3266, 3265])).
% 0.86/1.04 tff(3329,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3330,plain,
% 0.86/1.04 (((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c))))) <=> ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3331,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3330])).
% 0.86/1.04 tff(3332,plain,
% 0.86/1.04 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3331, 3329])).
% 0.86/1.05 tff(3333,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3334,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(c)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3333, 3332])).
% 0.86/1.05 tff(3335,plain,
% 0.86/1.05 (~r(c, f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3334, 233, 3317, 3236, 163, 3130, 3328])).
% 0.86/1.05 tff(3336,plain,
% 0.86/1.05 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(c))) | r(f(c), f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(c))) | r(f(c), f(f(f(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3337,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(c))) | r(f(c), f(f(f(elem!1)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3338,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(c))) | r(f(c), f(f(f(elem!1))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 0.86/1.05 tff(3339,plain,
% 0.86/1.05 (~r(f(f(f(elem!1))), f(c))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3338, 180, 3255])).
% 0.86/1.05 tff(3340,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3341,plain,
% 0.86/1.05 ((r(f(f(f(c))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(elem!1))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(elem!1))))) <=> (r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3342,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(elem!1))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3341])).
% 0.86/1.05 tff(3343,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(elem!1))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3342, 3340])).
% 0.86/1.05 tff(3344,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(elem!1))) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3345,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(elem!1))) = f(c)) | r(f(f(f(c))), f(f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 0.86/1.05 tff(3346,plain,
% 0.86/1.05 (r(f(f(f(c))), f(c))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3345, 205, 3274, 1718, 3339, 3226, 3318])).
% 0.86/1.05 tff(3347,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3348,plain,
% 0.86/1.05 (((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (c = f(f(f(c))))) <=> ((~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3349,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c)))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3348])).
% 0.86/1.05 tff(3350,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3349, 3347])).
% 0.86/1.05 tff(3351,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (c = f(f(f(c)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3352,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (c = f(f(f(c)))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(f(f(c)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 0.86/1.05 tff(3353,plain,
% 0.86/1.05 (~r(c, f(c))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3352, 233, 1718, 3346, 3130, 3328, 1352])).
% 0.86/1.05 tff(3354,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3355,plain,
% 0.86/1.05 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(c)) | r(c, f(c)) | (f(f(elem!1)) = f(c)) | (c = f(c)) | (c = f(f(elem!1)))) <=> (r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3356,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(c)) | r(c, f(c)) | (f(f(elem!1)) = f(c)) | (c = f(c)) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3355])).
% 0.86/1.05 tff(3357,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(c)) | r(c, f(c)) | (f(f(elem!1)) = f(c)) | (c = f(c)) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3356, 3354])).
% 0.86/1.05 tff(3358,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(c)) | r(c, f(c)) | (f(f(elem!1)) = f(c)) | (c = f(c)) | (c = f(f(elem!1))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3359,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | (c = f(c)) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3358, 3357])).
% 0.86/1.05 tff(3360,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3359, 205, 3353, 163, 3335, 1352, 1592, 3237])).
% 0.86/1.05 tff(3361,plain,(r(f(c), f(f(elem!1))) | (c = elem!1) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3362,plain,
% 0.86/1.05 (r(f(f(elem!1)), f(elem!1))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3361, 1588, 62, 66])).
% 0.86/1.05 tff(3363,plain,
% 0.86/1.05 (r(f(elem!1), f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[747, 3362])).
% 0.86/1.05 tff(3364,plain,
% 0.86/1.05 (~r(elem!1, f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[739, 3363, 62, 426, 172, 2100])).
% 0.86/1.05 tff(3365,plain,
% 0.86/1.05 (~r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1468, 3364, 3205])).
% 0.86/1.05 tff(3366,plain,
% 0.86/1.05 (~r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1476, 3365])).
% 0.86/1.05 tff(3367,plain,
% 0.86/1.05 (~(f(f(f(c))) = elem!1)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3266, 1613])).
% 0.86/1.05 tff(3368,plain,
% 0.86/1.05 (r(f(c), elem!1) <=> r(f(c), f(f(f(elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3205])).
% 0.86/1.05 tff(3369,plain,
% 0.86/1.05 (r(f(c), f(f(f(elem!1)))) <=> r(f(c), elem!1)),
% 0.86/1.05 inference(symmetry,[status(thm)],[3368])).
% 0.86/1.05 tff(3370,plain,
% 0.86/1.05 (r(f(c), f(f(f(elem!1))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1535, 205, 3366, 710, 3233, 1588, 3230])).
% 0.86/1.05 tff(3371,plain,
% 0.86/1.05 (r(f(c), elem!1)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 0.86/1.05 tff(3372,plain,
% 0.86/1.05 (r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1666, 3371, 3274, 710, 3367, 3225, 1588, 3366, 3233, 3205])).
% 0.86/1.05 tff(3373,plain,
% 0.86/1.05 ((~r(f(f(f(c))), f(elem!1))) | (f(f(f(c))) = f(elem!1))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1818, 233, 3362, 214, 3372, 3236])).
% 0.86/1.05 tff(3374,plain,
% 0.86/1.05 (~r(f(f(f(c))), f(elem!1))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3373, 3235])).
% 0.86/1.05 tff(3375,plain,
% 0.86/1.05 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) <=> (f(elem!1) = f(f(elem!1)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3211])).
% 0.86/1.05 tff(3376,plain,
% 0.86/1.05 ((f(elem!1) = f(f(elem!1))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.05 inference(symmetry,[status(thm)],[3375])).
% 0.86/1.05 tff(3377,plain,
% 0.86/1.05 ((~(f(elem!1) = f(f(elem!1)))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3376])).
% 0.86/1.05 tff(3378,plain,
% 0.86/1.05 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[426, 3377])).
% 0.86/1.05 tff(3379,plain,
% 0.86/1.05 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) <=> r(f(elem!1), f(f(elem!1)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3211])).
% 0.86/1.05 tff(3380,plain,
% 0.86/1.05 (r(f(elem!1), f(f(elem!1))) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.86/1.05 inference(symmetry,[status(thm)],[3379])).
% 0.86/1.05 tff(3381,plain,
% 0.86/1.05 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3363, 3380])).
% 0.86/1.05 tff(3382,plain,
% 0.86/1.05 (~r(f(f(f(elem!1))), c)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1734, 3381, 710, 3207, 1588, 3378, 3366, 3371])).
% 0.86/1.05 tff(3383,plain,
% 0.86/1.05 (r(f(f(elem!1)), c)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[524, 205, 162, 304, 3366, 3382, 710])).
% 0.86/1.05 tff(3384,plain,
% 0.86/1.05 (~r(f(f(f(c))), c)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1675, 233, 162, 1669, 3372, 3236, 3383])).
% 0.86/1.05 tff(3385,plain,
% 0.86/1.05 (~r(f(elem!1), c)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1895, 3383, 426, 3363])).
% 0.86/1.05 tff(3386,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3387,plain,
% 0.86/1.05 ((r(f(f(f(c))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(c))), c) | (f(elem!1) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(elem!1))) <=> ((f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3388,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(c))), c) | (f(elem!1) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3387])).
% 0.86/1.05 tff(3389,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(c))), c) | (f(elem!1) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3388, 3386])).
% 0.86/1.05 tff(3390,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(elem!1)) | r(f(elem!1), c) | r(f(f(f(c))), c) | (f(elem!1) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(elem!1)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3391,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | r(f(elem!1), c) | r(f(f(f(c))), f(elem!1)) | (f(f(f(c))) = f(elem!1)) | (f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 0.86/1.05 tff(3392,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3391, 205, 258, 1669, 3385, 3384, 3374, 3235])).
% 0.86/1.05 tff(3393,plain,(r(f(c), f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3394,plain,
% 0.86/1.05 (r(f(c), f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3393, 62, 66])).
% 0.86/1.05 tff(3395,plain,
% 0.86/1.05 (r(elem!1, f(elem!1)) <=> r(f(f(f(elem!1))), f(elem!1))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3205])).
% 0.86/1.05 tff(3396,plain,
% 0.86/1.05 (r(f(f(f(elem!1))), f(elem!1))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2100, 3395])).
% 0.86/1.05 tff(3397,plain,
% 0.86/1.05 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) <=> (f(elem!1) = f(f(elem!1)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1677])).
% 0.86/1.05 tff(3398,plain,
% 0.86/1.05 ((f(elem!1) = f(f(elem!1))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.05 inference(symmetry,[status(thm)],[3397])).
% 0.86/1.05 tff(3399,plain,
% 0.86/1.05 ((~(f(elem!1) = f(f(elem!1)))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3398])).
% 0.86/1.05 tff(3400,plain,
% 0.86/1.05 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1527, 3399])).
% 0.86/1.05 tff(3401,plain,
% 0.86/1.05 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) <=> r(f(elem!1), f(f(elem!1)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1677])).
% 0.86/1.05 tff(3402,plain,
% 0.86/1.05 (r(f(elem!1), f(f(elem!1))) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.86/1.05 inference(symmetry,[status(thm)],[3401])).
% 0.86/1.05 tff(3403,assumption,(f(f(f(elem!1))) = f(f(f(c)))), introduced(assumption)).
% 0.86/1.05 tff(3404,plain,
% 0.86/1.05 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.86/1.05 inference(symmetry,[status(thm)],[3403])).
% 0.86/1.05 tff(3405,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1657, 3404])).
% 0.86/1.05 tff(3406,plain,((~(f(f(f(elem!1))) = f(f(f(c))))) | (f(f(f(c))) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3407,plain,
% 0.86/1.05 (~(f(f(f(elem!1))) = f(f(f(c))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3406, 1657])).
% 0.86/1.05 tff(3408,assumption,(r(f(elem!1), f(f(f(elem!1))))), introduced(assumption)).
% 0.86/1.05 tff(3409,plain,
% 0.86/1.05 (~r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[368, 363])).
% 0.86/1.05 tff(3410,assumption,(~(f(f(f(elem!1))) = f(f(f(c))))), introduced(assumption)).
% 0.86/1.05 tff(3411,assumption,(~r(f(elem!1), f(f(f(c))))), introduced(assumption)).
% 0.86/1.05 tff(3412,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1885, 205, 742, 144, 1638, 1774, 1872, 3411])).
% 0.86/1.05 tff(3413,plain,(r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(f(elem!1))) | (f(elem!1) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(elem!1) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3414,plain,
% 0.86/1.05 (r(f(elem!1), f(f(f(c))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3413, 1638, 144, 742, 1774, 1872])).
% 0.86/1.05 tff(3415,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3416,plain,
% 0.86/1.05 (((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1))) <=> ((f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3417,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c)))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3416])).
% 0.86/1.05 tff(3418,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3417, 3415])).
% 0.86/1.05 tff(3419,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (f(elem!1) = f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3420,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 0.86/1.05 tff(3421,plain,
% 0.86/1.05 (~r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3420, 233, 552, 551, 1872, 3414, 3410])).
% 0.86/1.05 tff(3422,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3423,plain,
% 0.86/1.05 ((r(f(f(f(elem!1))), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(f(c))))) <=> (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3424,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3423])).
% 0.86/1.05 tff(3425,plain,
% 0.86/1.05 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3424, 3422])).
% 0.86/1.05 tff(3426,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(f(c)))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(f(c)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3427,plain,
% 0.86/1.05 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(f(c)))) | (f(f(f(elem!1))) = f(f(f(c))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 0.86/1.05 tff(3428,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3427, 205, 1904, 1470, 1638, 1774, 3421, 3410])).
% 0.86/1.06 tff(3429,plain,(r(f(f(f(c))), f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(elem!1))) | r(f(elem!1), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3430,plain,
% 0.86/1.06 (r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3429, 742, 1774, 3410, 549, 551, 1872, 1527, 3409])).
% 0.86/1.06 tff(3431,plain,
% 0.86/1.06 (r(f(f(elem!1)), f(c))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1738, 180, 1505])).
% 0.86/1.06 tff(3432,assumption,(r(f(f(f(c))), f(f(elem!1)))), introduced(assumption)).
% 0.86/1.06 tff(3433,plain,
% 0.86/1.06 ((f(f(elem!1)) = f(c)) | (~r(f(f(f(c))), f(c)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1799, 233, 3432, 1774, 1718, 3431])).
% 0.86/1.06 tff(3434,plain,
% 0.86/1.06 (~r(f(f(f(c))), f(c))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3433, 3278])).
% 0.86/1.06 tff(3435,assumption,(r(c, f(f(elem!1)))), introduced(assumption)).
% 0.86/1.06 tff(3436,plain,
% 0.86/1.06 (~r(f(c), c)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1938, 3435, 1582, 1505])).
% 0.86/1.06 tff(3437,plain,
% 0.86/1.06 (r(f(f(f(c))), c)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1808, 3436, 3434])).
% 0.86/1.06 tff(3438,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3439,plain,
% 0.86/1.06 (((~r(f(f(f(c))), c)) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c)) <=> ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3440,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3439])).
% 0.86/1.06 tff(3441,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3440, 3438])).
% 0.86/1.06 tff(3442,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = c))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3443,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (c = f(f(elem!1))) | (f(f(f(c))) = c) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), c))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 0.86/1.06 tff(3444,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3443, 233, 1669, 3432, 1774, 163, 3435, 3437])).
% 0.86/1.06 tff(3445,plain,((~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3446,plain,
% 0.86/1.06 (~r(c, f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3445, 3430, 1774, 1582, 1505])).
% 0.86/1.06 tff(3447,plain,
% 0.86/1.06 (~r(f(f(elem!1)), c)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1684, 180, 3446])).
% 0.86/1.06 tff(3448,plain,
% 0.86/1.06 (~r(f(f(elem!1)), f(elem!1))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[747, 742])).
% 0.86/1.06 tff(3449,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3450,plain,
% 0.86/1.06 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(c, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (c = f(elem!1)) | (c = f(f(elem!1)))) <=> (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3451,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(c, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (c = f(elem!1)) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3450])).
% 0.86/1.06 tff(3452,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(c, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (c = f(elem!1)) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3451, 3449])).
% 0.86/1.06 tff(3453,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(c, f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (c = f(elem!1)) | (c = f(f(elem!1))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3454,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(elem!1)) | (c = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(c, f(f(elem!1))) | (c = f(f(elem!1)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 0.86/1.06 tff(3455,plain,
% 0.86/1.06 (r(c, f(elem!1))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3454, 205, 259, 3448, 135, 163, 3446])).
% 0.86/1.06 tff(3456,plain,
% 0.86/1.06 (~r(c, f(f(f(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[336, 233, 3455, 259, 92, 3408, 305])).
% 0.86/1.06 tff(3457,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3458,plain,
% 0.86/1.06 ((r(f(f(elem!1)), c) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = c)) <=> ((f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3459,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), c) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3458])).
% 0.86/1.06 tff(3460,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), c) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3459, 3457])).
% 0.86/1.06 tff(3461,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), c) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = c))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3462,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (c = f(f(f(elem!1)))) | r(c, f(f(f(elem!1)))) | r(f(f(elem!1)), c)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 0.86/1.06 tff(3463,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3462, 205, 162, 363, 3456, 305, 1529, 3447])).
% 0.86/1.06 tff(3464,plain,(r(f(elem!1), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(c))) = f(f(elem!1))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(elem!1) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3465,plain,
% 0.86/1.06 (r(f(elem!1), f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3464, 363, 92, 3408, 135, 1774, 1508, 1505, 3407, 551, 1872])).
% 0.86/1.06 tff(3466,plain,
% 0.86/1.06 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3465, 3402])).
% 0.86/1.06 tff(3467,plain,
% 0.86/1.06 (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2900, 3466, 1508, 3400, 1505])).
% 0.86/1.06 tff(3468,assumption,(r(c, f(elem!1))), introduced(assumption)).
% 0.86/1.06 tff(3469,plain,
% 0.86/1.06 (~r(c, f(f(f(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[336, 233, 3468, 259, 92, 3408, 305])).
% 0.86/1.06 tff(3470,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3471,plain,
% 0.86/1.06 ((r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(elem!1))))) <=> (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3472,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3471])).
% 0.86/1.06 tff(3473,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3472, 3470])).
% 0.86/1.06 tff(3474,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(elem!1)))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3475,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (c = f(f(f(elem!1)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(elem!1))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 0.86/1.06 tff(3476,plain,
% 0.86/1.06 (r(c, f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3475, 205, 1904, 1470, 3469, 305, 163])).
% 0.86/1.06 tff(3477,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3478,plain,
% 0.86/1.06 (((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1))) <=> ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3479,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3478])).
% 0.86/1.06 tff(3480,plain,
% 0.86/1.06 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3479, 3477])).
% 0.86/1.06 tff(3481,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(elem!1)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3482,plain,
% 0.86/1.06 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (c = f(elem!1)) | (~r(c, f(elem!1))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 0.86/1.06 tff(3483,plain,
% 0.86/1.06 ((c = f(f(elem!1))) | (~r(c, f(f(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3482, 233, 3468, 259, 1073, 144])).
% 0.86/1.06 tff(3484,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3483, 3476, 163])).
% 0.86/1.06 tff(3485,plain,((~r(c, f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | r(f(f(f(elem!1))), f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3486,plain,
% 0.86/1.06 (~r(c, f(elem!1))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3485, 3465, 1527, 3408, 92, 3409])).
% 0.86/1.06 tff(3487,plain,
% 0.86/1.06 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(c))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1677])).
% 0.86/1.06 tff(3488,plain,
% 0.86/1.06 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(c)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3487])).
% 0.86/1.06 tff(3489,plain,
% 0.86/1.06 (~(f(elem!1) = f(c))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1118, 3488])).
% 0.86/1.06 tff(3490,plain,
% 0.86/1.06 (~(f(c) = f(elem!1))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3489, 65])).
% 0.86/1.06 tff(3491,plain,
% 0.86/1.06 (r(f(c), f(elem!1)) <=> r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1499])).
% 0.86/1.06 tff(3492,plain,
% 0.86/1.06 (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) <=> r(f(c), f(elem!1))),
% 0.86/1.06 inference(symmetry,[status(thm)],[3491])).
% 0.86/1.06 tff(3493,plain,
% 0.86/1.06 ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) <=> (~r(f(c), f(elem!1)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3492])).
% 0.86/1.06 tff(3494,plain,
% 0.86/1.06 (~r(f(c), f(elem!1))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2915, 3493])).
% 0.86/1.06 tff(3495,assumption,(~r(c, f(f(elem!1)))), introduced(assumption)).
% 0.86/1.06 tff(3496,plain,
% 0.86/1.06 (r(c, f(f(f(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[585, 205, 363, 305, 1631, 163, 3495])).
% 0.86/1.06 tff(3497,plain,
% 0.86/1.06 (~r(f(f(elem!1)), c)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1684, 180, 3495])).
% 0.86/1.06 tff(3498,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1792, 3497, 3496, 1657, 1774, 1638, 363, 1631])).
% 0.86/1.06 tff(3499,plain,(r(c, f(f(elem!1))) | (f(f(f(c))) = f(f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3500,plain,
% 0.86/1.06 (r(c, f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3499, 1638, 1774, 1657, 363, 1631])).
% 0.86/1.06 tff(3501,plain,
% 0.86/1.06 (~r(f(c), c)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1938, 3500, 1508, 1505])).
% 0.86/1.06 tff(3502,assumption,(~r(c, f(elem!1))), introduced(assumption)).
% 0.86/1.06 tff(3503,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1708, 205, 3502, 259, 30, 3501, 3494, 3490])).
% 0.86/1.06 tff(3504,plain,(r(f(f(f(c))), f(f(elem!1))) | r(c, f(elem!1)) | (~r(f(c), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(c))) = f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | r(f(c), f(f(f(f(f(f(f(elem!1)))))))) | (~(f(f(f(f(elem!1)))) = f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3505,plain,
% 0.86/1.06 (r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3504, 3486, 1505, 1774, 1657, 363, 1529, 3467, 84])).
% 0.86/1.06 tff(3506,plain,
% 0.86/1.06 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(c)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3507,plain,
% 0.86/1.06 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(c)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3508,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(c))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 0.86/1.07 tff(3509,plain,
% 0.86/1.07 (r(f(f(elem!1)), f(f(f(c))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3508, 180, 3505])).
% 0.86/1.07 tff(3510,plain,
% 0.86/1.07 ((f(f(f(c))) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(f(c))))),
% 0.86/1.07 inference(symmetry,[status(thm)],[2725])).
% 0.86/1.07 tff(3511,plain,
% 0.86/1.07 ((~(f(f(f(c))) = f(f(elem!1)))) <=> (~(f(f(elem!1)) = f(f(f(c)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3510])).
% 0.86/1.07 tff(3512,plain,
% 0.86/1.07 (~(f(f(elem!1)) = f(f(f(c))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1774, 3511])).
% 0.86/1.07 tff(3513,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3514,plain,
% 0.86/1.07 (((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(elem!1)))) <=> ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3515,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3514])).
% 0.86/1.07 tff(3516,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3515, 3513])).
% 0.86/1.07 tff(3517,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(elem!1))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3518,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (~r(f(elem!1), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 0.86/1.07 tff(3519,plain,
% 0.86/1.07 (~r(f(elem!1), f(f(f(c))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3518, 233, 3465, 1527, 1872, 3512, 3509])).
% 0.86/1.07 tff(3520,plain,
% 0.86/1.07 (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) <=> r(f(elem!1), f(c))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1677])).
% 0.86/1.07 tff(3521,plain,
% 0.86/1.07 ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) <=> (~r(f(elem!1), f(c)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3520])).
% 0.86/1.07 tff(3522,plain,
% 0.86/1.07 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1753, 3466, 1508, 3400, 1505])).
% 0.86/1.07 tff(3523,plain,
% 0.86/1.07 (~r(f(elem!1), f(c))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 0.86/1.07 tff(3524,plain,
% 0.86/1.07 (~r(f(f(f(c))), f(c))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1799, 233, 3505, 1774, 1718, 3431, 1587])).
% 0.86/1.07 tff(3525,plain,
% 0.86/1.07 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3526,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3527,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 0.86/1.07 tff(3528,plain,
% 0.86/1.07 (~r(f(c), f(f(f(c))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3527, 180, 3524])).
% 0.86/1.07 tff(3529,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3530,plain,
% 0.86/1.07 ((r(f(elem!1), f(c)) | r(f(c), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c))) <=> (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3531,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3530])).
% 0.86/1.07 tff(3532,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3531, 3529])).
% 0.86/1.07 tff(3533,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(c)) | r(f(c), f(f(f(c)))) | r(f(elem!1), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(c)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3534,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(elem!1) = f(c)) | r(f(elem!1), f(f(f(c)))) | r(f(elem!1), f(c)) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 0.86/1.07 tff(3535,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3534, 205, 3528, 52, 1872, 3523, 3489, 3519])).
% 0.86/1.07 tff(3536,plain,(r(f(f(elem!1)), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(c)))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(c), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(elem!1)))) | (~(f(f(f(f(elem!1)))) = f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3537,plain,
% 0.86/1.07 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3536, 3234, 3236, 3394, 3274, 3207, 3247, 80, 214, 3396])).
% 0.86/1.07 tff(3538,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3539,plain,
% 0.86/1.07 (((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3540,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3539])).
% 0.86/1.07 tff(3541,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3540, 3538])).
% 0.86/1.07 tff(3542,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(c) = f(f(f(elem!1)))) | (f(c) = f(f(elem!1))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3543,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(c), f(f(f(elem!1))))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(elem!1))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 0.86/1.07 tff(3544,plain,
% 0.86/1.07 (~r(f(c), f(f(f(elem!1))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3543, 233, 3537, 710, 3233, 3394, 3230])).
% 0.86/1.07 tff(3545,plain,
% 0.86/1.07 (~r(f(f(f(elem!1))), f(c))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3338, 180, 3544])).
% 0.86/1.07 tff(3546,plain,
% 0.86/1.07 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1476, 3537])).
% 0.86/1.07 tff(3547,plain,
% 0.86/1.07 (r(elem!1, f(f(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1468, 3546, 3205])).
% 0.86/1.07 tff(3548,plain,
% 0.86/1.07 (~r(c, elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[759, 3547, 66, 62, 2100])).
% 0.86/1.07 tff(3549,plain,
% 0.86/1.07 (r(c, elem!1) <=> r(c, f(f(f(elem!1))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[308])).
% 0.86/1.07 tff(3550,plain,
% 0.86/1.07 (r(c, f(f(f(elem!1)))) <=> r(c, elem!1)),
% 0.86/1.07 inference(symmetry,[status(thm)],[3549])).
% 0.86/1.07 tff(3551,plain,
% 0.86/1.07 (r(c, elem!1)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1784, 3550])).
% 0.86/1.07 tff(3552,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[253, 3551])).
% 0.86/1.07 tff(3553,plain,((~r(c, f(f(f(elem!1))))) | r(c, elem!1) | (~(elem!1 = f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3554,plain,
% 0.86/1.07 (~r(c, f(f(f(elem!1))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3553, 3548, 3205])).
% 0.86/1.07 tff(3555,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3556,plain,
% 0.86/1.07 ((r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(c, f(c)) | (f(f(f(elem!1))) = f(c)) | (c = f(c)) | (c = f(f(f(elem!1))))) <=> ((c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3557,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(c, f(c)) | (f(f(f(elem!1))) = f(c)) | (c = f(c)) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3556])).
% 0.86/1.07 tff(3558,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(c, f(c)) | (f(f(f(elem!1))) = f(c)) | (c = f(c)) | (c = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3557, 3555])).
% 0.86/1.07 tff(3559,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(c)) | r(c, f(c)) | (f(f(f(elem!1))) = f(c)) | (c = f(c)) | (c = f(f(f(elem!1)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3560,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(elem!1)))) | r(c, f(c)) | r(f(f(f(elem!1))), f(c)) | (c = f(c)) | r(c, f(f(f(elem!1)))) | (f(f(f(elem!1))) = f(c))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3559, 3558])).
% 0.86/1.07 tff(3561,plain,
% 0.86/1.07 (r(c, f(c))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3560, 205, 3554, 305, 1352, 3545, 3226])).
% 0.86/1.07 tff(3562,plain,
% 0.86/1.07 (r(f(c), c)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1713, 180, 3561])).
% 0.86/1.07 tff(3563,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3564,plain,
% 0.86/1.07 (((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c))) <=> ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3565,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3564])).
% 0.86/1.07 tff(3566,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3565, 3563])).
% 0.86/1.07 tff(3567,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (~r(c, f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3568,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)) | (~r(c, f(f(elem!1))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 0.86/1.07 tff(3569,plain,
% 0.86/1.07 (~r(c, f(f(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3568, 233, 3561, 3233, 3394, 163, 1352])).
% 0.86/1.07 tff(3570,plain,
% 0.86/1.07 (~r(f(elem!1), f(f(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[739, 3547, 62, 426, 172, 2100])).
% 0.86/1.07 tff(3571,plain,
% 0.86/1.07 (~r(f(f(elem!1)), f(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[747, 3570])).
% 0.86/1.07 tff(3572,plain,
% 0.86/1.07 (r(c, f(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3454, 205, 259, 3571, 214, 163, 3569])).
% 0.86/1.07 tff(3573,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3574,plain,
% 0.86/1.07 (((~r(f(c), c)) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c)) <=> ((c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3575,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3574])).
% 0.86/1.07 tff(3576,plain,
% 0.86/1.07 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3575, 3573])).
% 0.86/1.07 tff(3577,plain,
% 0.86/1.07 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (c = f(elem!1)) | (f(c) = f(elem!1)) | (f(c) = c))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3578,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(elem!1)) | (~r(f(c), c)) | (f(c) = c) | (~r(c, f(elem!1))) | (~r(f(c), f(elem!1))) | (f(c) = f(elem!1))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 0.86/1.08 tff(3579,plain,
% 0.86/1.08 ((~r(f(c), f(elem!1))) | (f(c) = f(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3578, 233, 3572, 259, 30, 3562])).
% 0.86/1.08 tff(3580,plain,
% 0.86/1.08 (~r(f(c), f(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3579, 3215])).
% 0.86/1.08 tff(3581,plain,
% 0.86/1.08 (r(f(elem!1), c)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[268, 180, 3572])).
% 0.86/1.08 tff(3582,plain,
% 0.86/1.08 (r(elem!1, f(f(f(c)))) <=> r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[308])).
% 0.86/1.08 tff(3583,plain,
% 0.86/1.08 (f(f(f(elem!1))) = elem!1),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[312, 308])).
% 0.86/1.08 tff(3584,plain,
% 0.86/1.08 (f(f(f(f(elem!1)))) = f(elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[104, 3583])).
% 0.86/1.08 tff(3585,plain,
% 0.86/1.08 (~(elem!1 = f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1623, 3584])).
% 0.86/1.08 tff(3586,plain,
% 0.86/1.08 (f(f(f(f(f(elem!1))))) = f(f(elem!1))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3584])).
% 0.86/1.08 tff(3587,plain,
% 0.86/1.08 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(c) = f(f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3586])).
% 0.86/1.08 tff(3588,plain,
% 0.86/1.08 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(c) = f(f(elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3587])).
% 0.86/1.08 tff(3589,plain,
% 0.86/1.08 (~(f(c) = f(f(elem!1)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[981, 3588])).
% 0.86/1.08 tff(3590,plain,
% 0.86/1.08 (~(f(elem!1) = f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1584, 3589, 308])).
% 0.86/1.08 tff(3591,assumption,(r(c, f(f(f(c))))), introduced(assumption)).
% 0.86/1.08 tff(3592,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3593,plain,
% 0.86/1.08 (((~r(f(elem!1), c)) | (~r(c, f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c)) <=> ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3594,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), c)) | (~r(c, f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3593])).
% 0.86/1.08 tff(3595,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), c)) | (~r(c, f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3594, 3592])).
% 0.86/1.08 tff(3596,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), c)) | (~r(c, f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = c))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3597,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = c) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 0.86/1.08 tff(3598,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3597, 233, 258, 1887, 1872, 3130, 3591, 2045])).
% 0.86/1.08 tff(3599,plain,((~r(c, f(f(f(c))))) | (~r(f(elem!1), c)) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3600,plain,
% 0.86/1.08 (~r(c, f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3599, 2045, 3590, 1887])).
% 0.86/1.08 tff(3601,plain,
% 0.86/1.08 (r(elem!1, f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3327, 3600, 66, 3585, 253])).
% 0.86/1.08 tff(3602,plain,
% 0.86/1.08 (r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3601, 3582])).
% 0.86/1.08 tff(3603,plain,
% 0.86/1.08 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (f(f(f(c))) = elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1632])).
% 0.86/1.08 tff(3604,plain,
% 0.86/1.08 ((f(f(f(c))) = f(f(f(elem!1)))) <=> (elem!1 = f(f(f(c))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3603, 1611])).
% 0.86/1.08 tff(3605,plain,
% 0.86/1.08 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3604])).
% 0.86/1.08 tff(3606,plain,
% 0.86/1.08 ((~(elem!1 = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(elem!1)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3605])).
% 0.86/1.08 tff(3607,plain,
% 0.86/1.08 (~(f(f(f(c))) = f(f(f(elem!1))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3585, 3606])).
% 0.86/1.08 tff(3608,plain,
% 0.86/1.08 (~(f(f(f(elem!1))) = f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3406, 3607])).
% 0.86/1.08 tff(3609,assumption,(r(f(f(f(elem!1))), f(f(f(c))))), introduced(assumption)).
% 0.86/1.08 tff(3610,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3611,plain,
% 0.86/1.08 (((~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1))))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3612,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c)))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3611])).
% 0.86/1.08 tff(3613,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3612, 3610])).
% 0.86/1.08 tff(3614,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(c))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(elem!1) = f(f(f(elem!1)))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3615,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (~r(f(f(f(elem!1))), f(f(f(c)))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 0.86/1.08 tff(3616,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3615, 233, 92, 3408, 1872, 2045, 3609, 3410])).
% 0.86/1.08 tff(3617,plain,((~r(f(f(f(elem!1))), f(f(f(c))))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(c)))) | (~r(f(elem!1), f(f(f(c))))) | (f(f(f(elem!1))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3618,plain,
% 0.86/1.08 (~r(f(f(f(elem!1))), f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3617, 2045, 3408, 3590, 92, 3608])).
% 0.86/1.08 tff(3619,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3618, 3602])).
% 0.86/1.08 tff(3620,plain,((~r(f(elem!1), f(f(f(c))))) | (~(elem!1 = f(f(f(elem!1))))) | (c = elem!1) | r(c, elem!1) | (~r(f(elem!1), c)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3621,plain,
% 0.86/1.08 (~r(f(elem!1), f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3620, 3205, 66, 3548, 3581, 3247, 80])).
% 0.86/1.08 tff(3622,plain,
% 0.86/1.08 (~(f(f(elem!1)) = f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3236, 3511])).
% 0.86/1.08 tff(3623,assumption,(~r(f(f(elem!1)), f(f(f(c))))), introduced(assumption)).
% 0.86/1.08 tff(3624,assumption,(~(f(f(elem!1)) = f(f(f(c))))), introduced(assumption)).
% 0.86/1.08 tff(3625,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3626,plain,
% 0.86/1.08 ((r(f(f(elem!1)), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(f(elem!1)) = f(elem!1))) <=> (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3627,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3626])).
% 0.86/1.08 tff(3628,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3627, 3625])).
% 0.86/1.08 tff(3629,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(f(elem!1)) = f(elem!1)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3630,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 0.86/1.08 tff(3631,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3630, 205, 805, 135, 1872, 3624, 3623, 3411])).
% 0.86/1.08 tff(3632,plain,(r(f(f(elem!1)), f(f(f(c)))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(elem!1) = f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | r(f(elem!1), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3633,plain,
% 0.86/1.08 (r(f(f(elem!1)), f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3632, 3571, 214, 3234, 3622, 3621])).
% 0.86/1.08 tff(3634,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3635,plain,
% 0.86/1.08 (((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(elem!1)))) <=> ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3636,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3635])).
% 0.86/1.08 tff(3637,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3636, 3634])).
% 0.86/1.08 tff(3638,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(elem!1))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3639,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(c))))) | (f(f(elem!1)) = f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3638, 3637])).
% 0.86/1.08 tff(3640,plain,
% 0.86/1.08 (~r(f(c), f(f(f(c))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3639, 233, 3233, 3394, 52, 3622, 3633])).
% 0.86/1.08 tff(3641,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3642,plain,
% 0.86/1.08 ((r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1))) <=> (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3643,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3642])).
% 0.86/1.08 tff(3644,plain,
% 0.86/1.08 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3643, 3641])).
% 0.86/1.08 tff(3645,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(elem!1)) | r(f(elem!1), f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(elem!1) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(elem!1)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3646,plain,
% 0.86/1.08 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(elem!1)) | (f(c) = f(elem!1)) | r(f(elem!1), f(f(f(c)))) | (f(elem!1) = f(f(f(c))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 0.86/1.08 tff(3647,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3646, 205, 3640, 52, 3234, 3621, 3580, 3215])).
% 0.86/1.08 tff(3648,plain,((elem!1 = f(f(elem!1))) | (c = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3649,plain,
% 0.86/1.08 (c = elem!1),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3648, 62])).
% 0.86/1.08 tff(3650,assumption,(c = elem!1), introduced(assumption)).
% 0.86/1.08 tff(3651,plain,
% 0.86/1.08 (f(c) = f(elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3650])).
% 0.86/1.08 tff(3652,plain,
% 0.86/1.08 (f(elem!1) = f(c)),
% 0.86/1.08 inference(symmetry,[status(thm)],[3651])).
% 0.86/1.08 tff(3653,assumption,(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))), introduced(assumption)).
% 0.86/1.08 tff(3654,plain,
% 0.86/1.08 (inj_0(f(f(f(f(f(f(f(elem!1)))))))) = inj_0(f(f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3653])).
% 0.86/1.08 tff(3655,plain,
% 0.86/1.08 (f(f(f(f(f(f(elem!1)))))) = f(c)),
% 0.86/1.08 inference(transitivity,[status(thm)],[1115, 3654, 122, 3652])).
% 0.86/1.08 tff(3656,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[874, 3655])).
% 0.86/1.08 tff(3657,plain,((~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) | (~(c = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3658,plain,
% 0.86/1.08 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3657, 3649])).
% 0.86/1.08 tff(3659,plain,
% 0.86/1.08 (~(f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3658, 61])).
% 0.86/1.08 tff(3660,plain,
% 0.86/1.08 (f(c) = f(elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3649])).
% 0.86/1.08 tff(3661,plain,
% 0.86/1.08 (r(f(c), f(f(f(f(f(f(f(elem!1)))))))) <=> r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3660])).
% 0.86/1.08 tff(3662,plain,
% 0.86/1.08 ((~r(f(c), f(f(f(f(f(f(f(elem!1))))))))) <=> (~r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3661])).
% 0.86/1.08 tff(3663,plain,
% 0.86/1.08 (r(f(c), f(f(elem!1))) <=> r(f(elem!1), f(f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3660])).
% 0.86/1.08 tff(3664,plain,
% 0.86/1.08 ((~r(f(c), f(f(elem!1)))) <=> (~r(f(elem!1), f(f(elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3663])).
% 0.86/1.08 tff(3665,plain,
% 0.86/1.08 (~r(f(elem!1), f(f(elem!1)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1588, 3664])).
% 0.86/1.08 tff(3666,plain,
% 0.86/1.08 (~r(f(f(elem!1)), f(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[745, 180, 3665])).
% 0.86/1.08 tff(3667,plain,
% 0.86/1.08 (f(f(c)) = f(f(elem!1))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3660])).
% 0.86/1.08 tff(3668,plain,
% 0.86/1.08 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3667])).
% 0.86/1.08 tff(3669,plain,
% 0.86/1.08 (f(f(f(f(c)))) = f(f(f(f(elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3668])).
% 0.86/1.08 tff(3670,plain,
% 0.86/1.08 ((f(c) = f(f(f(f(c))))) <=> (f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3660, 3669])).
% 0.86/1.08 tff(3671,plain,
% 0.86/1.08 ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3670, 2711])).
% 0.86/1.08 tff(3672,plain,
% 0.86/1.08 ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3671])).
% 0.86/1.08 tff(3673,assumption,(f(c) = f(f(f(f(c))))), introduced(assumption)).
% 0.86/1.08 tff(3674,plain,
% 0.86/1.08 (inj_0(f(c)) = inj_0(f(f(f(f(c)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3673])).
% 0.86/1.08 tff(3675,plain,
% 0.86/1.08 (inj_0(f(f(f(f(c))))) = inj_0(f(c))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3674])).
% 0.86/1.08 tff(3676,plain,
% 0.86/1.08 (f(f(f(c))) = inj_0(f(f(f(f(c)))))),
% 0.86/1.08 inference(symmetry,[status(thm)],[38])).
% 0.86/1.08 tff(3677,plain,
% 0.86/1.08 (f(f(f(c))) = c),
% 0.86/1.08 inference(transitivity,[status(thm)],[3676, 3675, 13])).
% 0.86/1.08 tff(3678,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1669, 3677])).
% 0.86/1.08 tff(3679,plain,(~(f(c) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3680,plain,
% 0.86/1.08 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3679, 3672])).
% 0.86/1.08 tff(3681,plain,
% 0.86/1.08 ((f(c) = f(f(elem!1))) <=> (f(elem!1) = f(f(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3660])).
% 0.86/1.08 tff(3682,plain,
% 0.86/1.08 ((f(elem!1) = f(f(elem!1))) <=> (f(c) = f(f(elem!1)))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3681])).
% 0.86/1.08 tff(3683,plain,
% 0.86/1.08 ((~(f(elem!1) = f(f(elem!1)))) <=> (~(f(c) = f(f(elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3682])).
% 0.86/1.08 tff(3684,plain,
% 0.86/1.08 (~(f(c) = f(f(elem!1)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[426, 3683])).
% 0.86/1.08 tff(3685,plain,
% 0.86/1.08 ((f(f(f(f(f(f(f(elem!1))))))) = elem!1) <=> (elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(commutativity,[status(thm)],[])).
% 0.86/1.08 tff(3686,plain,
% 0.86/1.08 (c = elem!1),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3393, 62, 1588])).
% 0.86/1.08 tff(3687,plain,
% 0.86/1.08 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3686])).
% 0.86/1.08 tff(3688,plain,
% 0.86/1.08 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3687, 3685])).
% 0.86/1.08 tff(3689,plain,
% 0.86/1.08 ((~(f(f(f(f(f(f(f(elem!1))))))) = c)) <=> (~(elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3688])).
% 0.86/1.08 tff(3690,plain,
% 0.86/1.08 (~(elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[964, 3689])).
% 0.86/1.08 tff(3691,plain,
% 0.86/1.08 (r(c, f(f(f(f(f(f(f(elem!1)))))))) <=> r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3686])).
% 0.86/1.08 tff(3692,plain,
% 0.86/1.08 ((~r(c, f(f(f(f(f(f(f(elem!1))))))))) <=> (~r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3691])).
% 0.86/1.09 tff(3693,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3657, 3686])).
% 0.86/1.09 tff(3694,plain,
% 0.86/1.09 (r(c, f(f(elem!1))) <=> r(elem!1, f(f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3686])).
% 0.86/1.09 tff(3695,plain,
% 0.86/1.09 (r(elem!1, f(f(elem!1))) <=> r(c, f(f(elem!1)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3694])).
% 0.86/1.09 tff(3696,plain,
% 0.86/1.09 (f(c) = f(elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3686])).
% 0.86/1.09 tff(3697,plain,
% 0.86/1.09 (f(f(c)) = f(f(elem!1))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3696])).
% 0.86/1.09 tff(3698,plain,
% 0.86/1.09 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3697])).
% 0.86/1.09 tff(3699,plain,
% 0.86/1.09 ((f(f(f(c))) = f(f(elem!1))) <=> (f(f(f(elem!1))) = f(f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3698])).
% 0.86/1.09 tff(3700,plain,
% 0.86/1.09 ((f(f(f(elem!1))) = f(f(elem!1))) <=> (f(f(f(c))) = f(f(elem!1)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3699])).
% 0.86/1.09 tff(3701,plain,
% 0.86/1.09 ((~(f(f(f(elem!1))) = f(f(elem!1)))) <=> (~(f(f(f(c))) = f(f(elem!1))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3700])).
% 0.86/1.09 tff(3702,plain,
% 0.86/1.09 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[427, 3701])).
% 0.86/1.09 tff(3703,plain,
% 0.86/1.09 (r(f(f(elem!1)), c)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1868, 3702, 1588, 1638, 1582])).
% 0.86/1.09 tff(3704,plain,
% 0.86/1.09 (r(f(f(elem!1)), c) <=> r(f(f(elem!1)), elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3650])).
% 0.86/1.09 tff(3705,plain,
% 0.86/1.09 (r(f(f(elem!1)), elem!1) <=> r(f(f(elem!1)), c)),
% 0.86/1.09 inference(symmetry,[status(thm)],[3704])).
% 0.86/1.09 tff(3706,plain,
% 0.86/1.09 ((~r(f(f(elem!1)), elem!1)) <=> (~r(f(f(elem!1)), c))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3705])).
% 0.86/1.09 tff(3707,assumption,(~r(f(f(elem!1)), elem!1)), introduced(assumption)).
% 0.86/1.09 tff(3708,plain,
% 0.86/1.09 (~r(f(f(elem!1)), c)),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 0.86/1.09 tff(3709,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[622, 3708])).
% 0.86/1.09 tff(3710,plain,(r(f(f(elem!1)), elem!1) | (~r(f(f(elem!1)), c)) | (~(c = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3711,plain,
% 0.86/1.09 (r(f(f(elem!1)), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3710, 3703, 3686])).
% 0.86/1.09 tff(3712,plain,
% 0.86/1.09 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), elem!1)) | r(elem!1, f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), elem!1)) | r(elem!1, f(f(elem!1))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3713,plain,
% 0.86/1.09 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), elem!1)) | r(elem!1, f(f(elem!1))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3714,plain,
% 0.86/1.09 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), elem!1)) | r(elem!1, f(f(elem!1)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 0.86/1.09 tff(3715,plain,
% 0.86/1.09 (r(elem!1, f(f(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3714, 180, 3711])).
% 0.86/1.09 tff(3716,plain,
% 0.86/1.09 (r(c, f(f(elem!1)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3715, 3695])).
% 0.86/1.09 tff(3717,plain,
% 0.86/1.09 (r(f(f(elem!1)), f(c)) <=> r(f(f(elem!1)), f(elem!1))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3696])).
% 0.86/1.09 tff(3718,plain,
% 0.86/1.09 ((~r(f(f(elem!1)), f(c))) <=> (~r(f(f(elem!1)), f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3717])).
% 0.86/1.09 tff(3719,plain,
% 0.86/1.09 (~r(f(f(elem!1)), f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1592, 3718])).
% 0.86/1.09 tff(3720,plain,
% 0.86/1.09 (r(f(f(elem!1)), f(f(f(c)))) <=> r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3698])).
% 0.86/1.09 tff(3721,plain,
% 0.86/1.09 ((~r(f(f(elem!1)), f(f(f(c))))) <=> (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3720])).
% 0.86/1.09 tff(3722,assumption,(r(f(f(elem!1)), f(f(f(c))))), introduced(assumption)).
% 0.86/1.09 tff(3723,plain,
% 0.86/1.09 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(c))))) | r(f(f(f(c))), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(c))))) | r(f(f(f(c))), f(f(elem!1))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3724,plain,
% 0.86/1.09 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(c))))) | r(f(f(f(c))), f(f(elem!1))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3725,plain,
% 0.86/1.09 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(c))))) | r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3724, 3723])).
% 0.86/1.09 tff(3726,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3725, 180, 1638, 3722])).
% 0.86/1.09 tff(3727,plain,((~r(f(f(elem!1)), f(f(f(c))))) | r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3728,plain,
% 0.86/1.09 (~r(f(f(elem!1)), f(f(f(c))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3727, 1638])).
% 0.86/1.09 tff(3729,plain,
% 0.86/1.09 (~r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3728, 3721])).
% 0.86/1.09 tff(3730,plain,
% 0.86/1.09 (r(f(c), f(f(elem!1))) <=> r(f(elem!1), f(f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3696])).
% 0.86/1.09 tff(3731,plain,
% 0.86/1.09 ((~r(f(c), f(f(elem!1)))) <=> (~r(f(elem!1), f(f(elem!1))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3730])).
% 0.86/1.09 tff(3732,plain,
% 0.86/1.09 (~r(f(elem!1), f(f(elem!1)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1588, 3731])).
% 0.86/1.09 tff(3733,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3734,plain,
% 0.86/1.09 ((r(f(elem!1), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1)))) <=> ((f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3735,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3734])).
% 0.86/1.09 tff(3736,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3735, 3733])).
% 0.86/1.09 tff(3737,plain,
% 0.86/1.09 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3738,plain,
% 0.86/1.09 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 0.86/1.09 tff(3739,plain,
% 0.86/1.09 (r(f(elem!1), f(f(f(elem!1))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3738, 205, 3732, 426, 80, 3729, 710])).
% 0.86/1.09 tff(3740,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) <=> (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.09 inference(commutativity,[status(thm)],[])).
% 0.86/1.09 tff(3741,plain,
% 0.86/1.09 ((f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3740])).
% 0.86/1.09 tff(3742,plain,
% 0.86/1.09 ((~(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3741])).
% 0.86/1.09 tff(3743,plain,
% 0.86/1.09 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(elem!1) = f(f(f(f(f(elem!1))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3651])).
% 0.86/1.09 tff(3744,plain,
% 0.86/1.09 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(elem!1) = f(f(f(f(f(elem!1)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3743])).
% 0.86/1.09 tff(3745,plain,
% 0.86/1.09 (~(f(elem!1) = f(f(f(f(f(elem!1))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[981, 3744])).
% 0.86/1.09 tff(3746,assumption,(f(f(f(f(f(f(elem!1)))))) = f(f(elem!1))), introduced(assumption)).
% 0.86/1.09 tff(3747,plain,
% 0.86/1.09 (inj_0(f(f(f(f(f(f(elem!1))))))) = inj_0(f(f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3746])).
% 0.86/1.09 tff(3748,plain,
% 0.86/1.09 (inj_0(f(f(elem!1))) = inj_0(f(f(f(f(f(f(elem!1)))))))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3747])).
% 0.86/1.09 tff(3749,plain,
% 0.86/1.09 (f(elem!1) = f(f(f(f(f(elem!1)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[142, 3748, 843])).
% 0.86/1.09 tff(3750,assumption,(~(f(elem!1) = f(f(f(f(f(elem!1))))))), introduced(assumption)).
% 0.86/1.09 tff(3751,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3750, 3749])).
% 0.86/1.09 tff(3752,plain,((~(f(f(f(f(f(f(elem!1)))))) = f(f(elem!1)))) | (f(elem!1) = f(f(f(f(f(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3753,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(elem!1)))))) = f(f(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3752, 3745])).
% 0.86/1.09 tff(3754,assumption,(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))), introduced(assumption)).
% 0.86/1.09 tff(3755,plain,
% 0.86/1.09 (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3754])).
% 0.86/1.09 tff(3756,plain,
% 0.86/1.09 (inj_0(f(f(f(f(f(f(f(elem!1)))))))) = inj_0(f(f(f(elem!1))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3755])).
% 0.86/1.09 tff(3757,plain,
% 0.86/1.09 (f(f(f(f(f(f(elem!1)))))) = f(f(elem!1))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1115, 3756, 69])).
% 0.86/1.09 tff(3758,assumption,(~(f(f(f(f(f(f(elem!1)))))) = f(f(elem!1)))), introduced(assumption)).
% 0.86/1.09 tff(3759,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3758, 3757])).
% 0.86/1.09 tff(3760,plain,((~(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(f(f(f(elem!1)))))) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3761,plain,
% 0.86/1.09 (~(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3760, 3753])).
% 0.86/1.09 tff(3762,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3761, 3742])).
% 0.86/1.09 tff(3763,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) <=> (f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.09 inference(commutativity,[status(thm)],[])).
% 0.86/1.09 tff(3764,plain,
% 0.86/1.09 ((f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3763])).
% 0.86/1.09 tff(3765,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3651])).
% 0.86/1.09 tff(3766,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3765, 3763])).
% 0.86/1.09 tff(3767,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3766, 3764])).
% 0.86/1.09 tff(3768,plain,
% 0.86/1.09 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3767])).
% 0.86/1.09 tff(3769,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1118, 3768])).
% 0.86/1.09 tff(3770,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))), introduced(assumption)).
% 0.86/1.09 tff(3771,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3652])).
% 0.86/1.09 tff(3772,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3771])).
% 0.86/1.09 tff(3773,plain,
% 0.86/1.09 ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) <=> (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3772])).
% 0.86/1.09 tff(3774,plain,
% 0.86/1.09 (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3015, 3773])).
% 0.86/1.09 tff(3775,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3652])).
% 0.86/1.09 tff(3776,plain,
% 0.86/1.09 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3775])).
% 0.86/1.09 tff(3777,plain,
% 0.86/1.09 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3776])).
% 0.86/1.09 tff(3778,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1118, 3777])).
% 0.86/1.09 tff(3779,plain,
% 0.86/1.09 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3657, 3650])).
% 0.86/1.09 tff(3780,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3781,plain,
% 0.86/1.09 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3782,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3781])).
% 0.86/1.09 tff(3783,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3782, 3780])).
% 0.86/1.09 tff(3784,plain,
% 0.86/1.09 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3785,plain,
% 0.86/1.09 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 0.86/1.09 tff(3786,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3785, 205, 805, 135, 3770, 3779])).
% 0.86/1.09 tff(3787,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3786, 3778, 3774])).
% 0.86/1.09 tff(3788,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1)) | (~(c = elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3789,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3788, 3770, 135, 3650, 805])).
% 0.86/1.09 tff(3790,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[2842, 3772])).
% 0.86/1.09 tff(3791,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))), introduced(assumption)).
% 0.86/1.09 tff(3792,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3791, 3790])).
% 0.86/1.09 tff(3793,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) | (~(c = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3794,plain,
% 0.86/1.09 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3793, 3789, 3650])).
% 0.86/1.09 tff(3795,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3796,plain,
% 0.86/1.09 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3797,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3796])).
% 0.86/1.09 tff(3798,plain,
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% 0.86/1.09 inference(transitivity,[status(thm)],[3797, 3795])).
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% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3800,plain,
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% 0.86/1.09 inference(modus_ponens,[status(thm)],[3799, 3798])).
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% 0.86/1.09 inference(rewrite,[status(thm)],[])).
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% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3804,plain,
% 0.86/1.09 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3803])).
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% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3804, 3802])).
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% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.10 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 0.86/1.10 tff(3808,plain,
% 0.86/1.10 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
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% 0.86/1.10 tff(3809,plain,
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% 0.86/1.10 tff(3811,plain,
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% 0.86/1.10 tff(3813,plain,
% 0.86/1.10 (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
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% 0.86/1.10 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(elem!1) = f(f(f(f(f(elem!1))))))),
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% 0.86/1.10 tff(3815,plain,
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% 0.86/1.10 inference(monotonicity,[status(thm)],[3814])).
% 0.86/1.10 tff(3816,plain,
% 0.86/1.10 (~(f(elem!1) = f(f(f(f(f(elem!1))))))),
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% 0.86/1.10 tff(3817,plain,
% 0.86/1.10 (~(f(f(f(f(f(f(elem!1)))))) = f(f(elem!1)))),
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% 0.86/1.10 (~(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))),
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% 0.86/1.10 tff(3820,plain,
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% 0.86/1.10 tff(3821,plain,
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% 0.86/1.10 tff(3826,plain,
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% 0.86/1.10 inference(unit_resolution,[status(thm)],[3834, 233, 964])).
% 0.86/1.10 tff(3836,plain,
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% 0.86/1.10 inference(unit_resolution,[status(thm)],[3835, 163])).
% 0.86/1.10 tff(3837,plain,
% 0.86/1.10 (~r(f(f(f(f(f(f(f(elem!1))))))), c)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3836, 3811, 3716, 3693])).
% 0.86/1.10 tff(3838,plain,
% 0.86/1.10 (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3837, 3828])).
% 0.86/1.10 tff(3839,assumption,(r(f(f(elem!1)), elem!1)), introduced(assumption)).
% 0.86/1.10 tff(3840,plain,
% 0.86/1.10 (~(f(f(elem!1)) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[62, 532])).
% 0.86/1.10 tff(3841,plain,
% 0.86/1.10 ((f(f(f(elem!1))) = c) <=> (f(f(f(elem!1))) = elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3650])).
% 0.86/1.10 tff(3842,plain,
% 0.86/1.10 ((f(f(f(elem!1))) = c) <=> (elem!1 = f(f(f(elem!1))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3841, 306])).
% 0.86/1.10 tff(3843,plain,
% 0.86/1.10 ((~(f(f(f(elem!1))) = c)) <=> (~(elem!1 = f(f(f(elem!1)))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3842])).
% 0.86/1.10 tff(3844,plain,
% 0.86/1.10 (~(elem!1 = f(f(f(elem!1))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[304, 3843])).
% 0.86/1.10 tff(3845,plain,
% 0.86/1.10 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[89, 3844])).
% 0.86/1.10 tff(3846,plain,
% 0.86/1.10 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3650])).
% 0.86/1.10 tff(3847,plain,
% 0.86/1.10 ((f(f(f(f(elem!1)))) = c) <=> (elem!1 = f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3846, 188])).
% 0.86/1.10 tff(3848,plain,
% 0.86/1.10 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(elem!1 = f(f(f(f(elem!1))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3847])).
% 0.86/1.10 tff(3849,plain,
% 0.86/1.10 (~(elem!1 = f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[97, 3848])).
% 0.86/1.10 tff(3850,plain,
% 0.86/1.10 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[814, 135, 91, 805, 806, 831])).
% 0.86/1.10 tff(3851,plain,
% 0.86/1.10 (r(elem!1, f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[249, 127, 806, 100, 93, 91])).
% 0.86/1.10 tff(3852,plain,
% 0.86/1.10 (r(elem!1, f(f(elem!1)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[221, 127, 135, 62, 100, 805])).
% 0.86/1.10 tff(3853,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3854,plain,
% 0.86/1.10 (((~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1)))))) <=> ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3855,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3854])).
% 0.86/1.10 tff(3856,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3855, 3853])).
% 0.86/1.10 tff(3857,plain,
% 0.86/1.10 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3858,plain,
% 0.86/1.10 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 0.86/1.10 tff(3859,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3858, 233, 3852, 62, 93, 3851, 831, 3850])).
% 0.86/1.10 tff(3860,plain,((elem!1 = f(elem!1)) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | r(elem!1, f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3861,plain,
% 0.86/1.10 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3860, 100, 62, 214, 172, 3845, 3849, 805])).
% 0.86/1.10 tff(3862,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3863,plain,
% 0.86/1.10 (((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3864,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3863])).
% 0.86/1.10 tff(3865,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3864, 3862])).
% 0.86/1.10 tff(3866,plain,
% 0.86/1.10 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3867,plain,
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% 0.86/1.10 inference(modus_ponens,[status(thm)],[3866, 3865])).
% 0.86/1.10 tff(3868,plain,
% 0.86/1.10 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3867, 233, 80, 3408, 3861, 3845, 666])).
% 0.86/1.10 tff(3869,plain,
% 0.86/1.10 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[467, 205, 666, 3868, 831, 427, 1470])).
% 0.86/1.10 tff(3870,plain,
% 0.86/1.10 ((elem!1 = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.10 inference(symmetry,[status(thm)],[188])).
% 0.86/1.10 tff(3871,plain,
% 0.86/1.10 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.10 inference(transitivity,[status(thm)],[3847, 3870])).
% 0.86/1.10 tff(3872,plain,
% 0.86/1.10 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(f(f(f(f(elem!1)))) = elem!1))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3871])).
% 0.86/1.10 tff(3873,plain,
% 0.86/1.10 (~(f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[97, 3872])).
% 0.86/1.10 tff(3874,assumption,(~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)), introduced(assumption)).
% 0.86/1.10 tff(3875,plain,
% 0.86/1.10 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[860, 3845])).
% 0.86/1.10 tff(3876,plain,
% 0.86/1.10 ((elem!1 = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.10 inference(symmetry,[status(thm)],[3685])).
% 0.86/1.10 tff(3877,plain,
% 0.86/1.10 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3650])).
% 0.86/1.10 tff(3878,plain,
% 0.86/1.10 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3877, 3685])).
% 0.86/1.10 tff(3879,plain,
% 0.86/1.10 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.10 inference(transitivity,[status(thm)],[3878, 3876])).
% 0.86/1.10 tff(3880,plain,
% 0.86/1.10 ((~(f(f(f(f(f(f(f(elem!1))))))) = c)) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3879])).
% 0.86/1.10 tff(3881,plain,
% 0.86/1.10 (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[964, 3880])).
% 0.86/1.10 tff(3882,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3883,plain,
% 0.86/1.10 ((r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(elem!1, f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)) <=> (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3884,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(elem!1, f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3883])).
% 0.86/1.10 tff(3885,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(elem!1, f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3884, 3882])).
% 0.86/1.10 tff(3886,plain,
% 0.86/1.10 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(elem!1, f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3887,plain,
% 0.86/1.10 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3886, 3885])).
% 0.86/1.10 tff(3888,plain,
% 0.86/1.10 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3887, 205, 100, 172, 3874, 3881, 3769])).
% 0.86/1.10 tff(3889,plain,
% 0.86/1.10 (~(f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2715, 3845])).
% 0.86/1.10 tff(3890,plain,
% 0.86/1.10 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | r(f(elem!1), f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | r(f(elem!1), f(f(f(f(elem!1))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3891,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | r(f(elem!1), f(f(f(f(elem!1))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3892,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(elem!1))) | r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 0.86/1.10 tff(3893,plain,
% 0.86/1.10 (r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3892, 180, 3861])).
% 0.86/1.10 tff(3894,plain,
% 0.86/1.10 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3895,plain,
% 0.86/1.11 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))) <=> ((~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3896,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3895])).
% 0.86/1.11 tff(3897,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3896, 3894])).
% 0.86/1.11 tff(3898,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3899,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 0.86/1.11 tff(3900,plain,
% 0.86/1.11 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3899, 233, 3893, 3889, 3875, 3888, 3769])).
% 0.86/1.11 tff(3901,plain,
% 0.86/1.11 (elem!1 = c),
% 0.86/1.11 inference(symmetry,[status(thm)],[3650])).
% 0.86/1.11 tff(3902,plain,
% 0.86/1.11 ((f(f(f(f(f(f(f(elem!1))))))) = elem!1) <=> (f(f(f(f(f(f(f(elem!1))))))) = c)),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3901])).
% 0.86/1.11 tff(3903,plain,
% 0.86/1.11 ((f(f(f(f(f(f(f(elem!1))))))) = c) <=> (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.11 inference(symmetry,[status(thm)],[3902])).
% 0.86/1.11 tff(3904,plain,
% 0.86/1.11 ((~(f(f(f(f(f(f(f(elem!1))))))) = c)) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3903])).
% 0.86/1.11 tff(3905,plain,
% 0.86/1.11 (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[964, 3904])).
% 0.86/1.11 tff(3906,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3907,plain,
% 0.86/1.11 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> (r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3908,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3907])).
% 0.86/1.11 tff(3909,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3908, 3906])).
% 0.86/1.11 tff(3910,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3911,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 0.86/1.11 tff(3912,plain,
% 0.86/1.11 (r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3911, 205, 171, 195, 897, 1381])).
% 0.86/1.11 tff(3913,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3912, 3905, 3874])).
% 0.86/1.11 tff(3914,plain,(r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(f(f(f(f(elem!1)))), elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (~(c = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3915,plain,
% 0.86/1.11 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3914, 3900, 3650, 3873, 3875, 3874])).
% 0.86/1.11 tff(3916,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3917,plain,
% 0.86/1.11 (((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(elem!1)) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> ((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3918,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(elem!1)) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3917])).
% 0.86/1.11 tff(3919,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(elem!1)) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3918, 3916])).
% 0.86/1.11 tff(3920,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(elem!1)) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3921,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3920, 3919])).
% 0.86/1.11 tff(3922,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3921, 233, 3915, 3873, 831, 3869, 3840, 3839])).
% 0.86/1.11 tff(3923,plain,(r(elem!1, f(elem!1)) | (~r(f(f(elem!1)), elem!1)) | (~(c = elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | r(f(f(f(elem!1))), f(f(elem!1))) | (~r(f(elem!1), f(f(f(elem!1))))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3924,plain,
% 0.86/1.11 (r(elem!1, f(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3923, 3711, 3686, 3838, 3826, 3739, 62, 3719])).
% 0.86/1.11 tff(3925,plain,
% 0.86/1.11 (~r(f(f(f(elem!1))), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[771, 3924, 2066, 3823, 62, 3715])).
% 0.86/1.11 tff(3926,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3927,plain,
% 0.86/1.11 ((r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1)) <=> (r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3928,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3927])).
% 0.86/1.11 tff(3929,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3928, 3926])).
% 0.86/1.11 tff(3930,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), elem!1) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3931,plain,
% 0.86/1.11 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(elem!1))), elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 0.86/1.11 tff(3932,plain,
% 0.86/1.11 (r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3931, 205, 3925, 3823, 3818, 3813, 3690])).
% 0.86/1.11 tff(3933,plain,
% 0.86/1.11 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3934,plain,
% 0.86/1.11 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3935,plain,
% 0.86/1.11 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3934, 3933])).
% 0.86/1.11 tff(3936,plain,
% 0.86/1.11 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3935, 180, 3932])).
% 0.86/1.11 tff(3937,plain,
% 0.86/1.11 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3818, 3742])).
% 0.86/1.11 tff(3938,plain,
% 0.86/1.11 ((~(f(f(f(elem!1))) = c)) <=> (~(elem!1 = f(f(f(elem!1)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3820])).
% 0.86/1.11 tff(3939,plain,
% 0.86/1.11 (~(elem!1 = f(f(f(elem!1))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[304, 3938])).
% 0.86/1.11 tff(3940,plain,
% 0.86/1.11 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[89, 3939])).
% 0.86/1.11 tff(3941,plain,
% 0.86/1.11 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[860, 3940])).
% 0.86/1.11 tff(3942,plain,
% 0.86/1.11 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3686])).
% 0.86/1.11 tff(3943,plain,
% 0.86/1.11 ((f(f(f(f(elem!1)))) = c) <=> (elem!1 = f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3942, 188])).
% 0.86/1.11 tff(3944,plain,
% 0.86/1.11 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.11 inference(transitivity,[status(thm)],[3943, 3870])).
% 0.86/1.11 tff(3945,plain,
% 0.86/1.11 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(f(f(f(f(elem!1)))) = elem!1))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3944])).
% 0.86/1.11 tff(3946,plain,
% 0.86/1.11 (~(f(f(f(f(elem!1)))) = elem!1)),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[97, 3945])).
% 0.86/1.11 tff(3947,plain,
% 0.86/1.11 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[681, 233, 610, 172, 91, 387, 195])).
% 0.86/1.11 tff(3948,plain,
% 0.86/1.11 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[393, 233, 373, 62, 387, 195, 831])).
% 0.86/1.11 tff(3949,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[814, 3948, 3947, 831, 214, 91, 805])).
% 0.86/1.11 tff(3950,plain,((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (f(f(f(f(elem!1)))) = elem!1) | (~r(elem!1, f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3951,plain,
% 0.86/1.11 (~r(f(f(f(f(elem!1)))), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3950, 3940, 3719, 3715, 62, 3946, 3924])).
% 0.86/1.11 tff(3952,plain,
% 0.86/1.11 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3914, 3951, 3686, 3946, 3941, 3838])).
% 0.86/1.11 tff(3953,plain,
% 0.86/1.11 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[380, 3951, 3823, 666, 3946, 3925])).
% 0.86/1.11 tff(3954,plain,
% 0.86/1.11 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(elem!1))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3955,plain,
% 0.86/1.11 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(elem!1))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3956,plain,
% 0.86/1.11 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 0.86/1.11 tff(3957,plain,
% 0.86/1.11 (r(f(f(f(elem!1))), f(f(f(f(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3956, 180, 3953])).
% 0.86/1.11 tff(3958,plain,
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% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3959,plain,
% 0.86/1.11 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3960,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3959])).
% 0.86/1.11 tff(3961,plain,
% 0.86/1.11 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3960, 3958])).
% 0.86/1.11 tff(3962,plain,
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% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(3963,plain,
% 0.86/1.12 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 0.86/1.12 tff(3964,plain,
% 0.86/1.12 (f(f(f(elem!1))) = f(f(f(f(elem!1))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3963, 233, 3957, 3941, 3952, 3937, 3936])).
% 0.86/1.12 tff(3965,plain,
% 0.86/1.12 (f(f(f(f(elem!1)))) = f(f(f(elem!1)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3964, 1020])).
% 0.86/1.12 tff(3966,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[666, 3965])).
% 0.86/1.12 tff(3967,plain,((elem!1 = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | (f(c) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(3968,plain,
% 0.86/1.12 (r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3967, 1588, 62, 3684])).
% 0.86/1.12 tff(3969,assumption,(f(f(f(c))) = f(f(f(elem!1)))), introduced(assumption)).
% 0.86/1.12 tff(3970,plain,
% 0.86/1.12 (r(f(f(f(c))), f(f(elem!1))) <=> r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3969])).
% 0.86/1.12 tff(3971,plain,
% 0.86/1.12 (r(f(f(f(elem!1))), f(f(elem!1))) <=> r(f(f(f(c))), f(f(elem!1)))),
% 0.86/1.12 inference(symmetry,[status(thm)],[3970])).
% 0.86/1.12 tff(3972,plain,
% 0.86/1.12 ((~r(f(f(f(elem!1))), f(f(elem!1)))) <=> (~r(f(f(f(c))), f(f(elem!1))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3971])).
% 0.86/1.12 tff(3973,plain,
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[1470, 3972])).
% 0.86/1.12 tff(3974,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3432, 3973])).
% 0.86/1.12 tff(3975,plain,((~(f(f(f(c))) = f(f(f(elem!1))))) | (~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(f(elem!1))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(3976,plain,
% 0.86/1.12 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3975, 3968, 3668])).
% 0.86/1.12 tff(3977,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[3649])).
% 0.86/1.12 tff(3978,plain,
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% 0.86/1.12 inference(transitivity,[status(thm)],[3977, 3685])).
% 0.86/1.12 tff(3979,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[3978])).
% 0.86/1.12 tff(3980,plain,
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[964, 3979])).
% 0.86/1.12 tff(3981,plain,
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% 0.86/1.12 tff(3982,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[3981])).
% 0.86/1.12 tff(3983,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[3649])).
% 0.86/1.12 tff(3984,plain,
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% 0.86/1.12 tff(3985,plain,
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% 0.86/1.12 tff(3986,plain,
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 0.86/1.12 tff(3987,assumption,(f(f(elem!1)) = f(f(f(f(elem!1))))), introduced(assumption)).
% 0.86/1.12 tff(3988,plain,
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[3987, 823])).
% 0.86/1.12 tff(3989,plain,
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% 0.86/1.12 inference(unit_resolution,[status(thm)],[194, 3988])).
% 0.86/1.12 tff(3990,plain,((~(f(f(elem!1)) = f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(3991,plain,
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% 0.86/1.12 tff(3992,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[3649])).
% 0.86/1.12 tff(3994,plain,
% 0.86/1.12 ((f(f(f(elem!1))) = c) <=> (elem!1 = f(f(f(elem!1))))),
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% 0.86/1.12 tff(3995,plain,
% 0.86/1.12 ((~(f(f(f(elem!1))) = c)) <=> (~(elem!1 = f(f(f(elem!1)))))),
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% 0.86/1.12 tff(3996,plain,
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% 0.86/1.12 tff(4004,plain,
% 0.86/1.12 (~r(elem!1, f(f(f(elem!1))))),
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% 0.86/1.12 tff(4005,plain,
% 0.86/1.12 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
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% 0.86/1.12 tff(4006,plain,
% 0.86/1.12 ((f(f(f(f(elem!1)))) = c) <=> (elem!1 = f(f(f(f(elem!1)))))),
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% 0.86/1.12 tff(4007,plain,
% 0.86/1.12 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(elem!1 = f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4006])).
% 0.86/1.12 tff(4008,plain,
% 0.86/1.12 (~(elem!1 = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[97, 4007])).
% 0.86/1.12 tff(4009,plain,
% 0.86/1.12 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3860, 100, 62, 214, 172, 3680, 4008, 805])).
% 0.86/1.12 tff(4010,plain,
% 0.86/1.12 (r(f(elem!1), f(f(f(elem!1))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[328, 4004, 80, 3996, 100, 172])).
% 0.86/1.12 tff(4011,plain,
% 0.86/1.12 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3867, 233, 80, 4010, 4009, 3680, 666])).
% 0.86/1.12 tff(4012,plain,
% 0.86/1.12 (r(elem!1, f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[412, 4011, 3996, 4008, 666, 4004])).
% 0.86/1.12 tff(4013,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4014,plain,
% 0.86/1.12 (((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = elem!1)) <=> ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4015,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4014])).
% 0.86/1.12 tff(4016,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4015, 4013])).
% 0.86/1.12 tff(4017,plain,
% 0.86/1.12 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = elem!1))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(4018,plain,
% 0.86/1.12 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[4017, 4016])).
% 0.86/1.12 tff(4019,plain,
% 0.86/1.12 (~r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4018, 233, 4008, 4012, 3840, 3992, 3991])).
% 0.86/1.12 tff(4020,plain,
% 0.86/1.12 (r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3892, 180, 4009])).
% 0.86/1.12 tff(4021,assumption,(~r(f(f(elem!1)), f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.86/1.12 tff(4022,plain,
% 0.86/1.12 ((f(f(f(f(elem!1)))) = f(elem!1)) <=> (f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(symmetry,[status(thm)],[2711])).
% 0.86/1.12 tff(4023,plain,
% 0.86/1.12 (f(f(c)) = f(f(elem!1))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3651])).
% 0.86/1.12 tff(4024,plain,
% 0.86/1.12 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4023])).
% 0.86/1.12 tff(4025,plain,
% 0.86/1.12 (f(f(f(f(c)))) = f(f(f(f(elem!1))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4024])).
% 0.86/1.12 tff(4026,plain,
% 0.86/1.12 ((f(c) = f(f(f(f(c))))) <=> (f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3651, 4025])).
% 0.86/1.12 tff(4027,plain,
% 0.86/1.12 ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4026, 2711])).
% 0.86/1.12 tff(4028,plain,
% 0.86/1.12 ((f(c) = f(f(f(f(c))))) <=> (f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4027, 4022])).
% 0.86/1.12 tff(4029,plain,
% 0.86/1.12 ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(elem!1) = f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4028])).
% 0.86/1.12 tff(4030,plain,
% 0.86/1.12 (~(f(elem!1) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3679, 4029])).
% 0.86/1.12 tff(4031,assumption,(r(f(elem!1), f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.86/1.12 tff(4032,assumption,(~(f(f(elem!1)) = f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.86/1.12 tff(4033,plain,
% 0.86/1.12 ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4027])).
% 0.86/1.12 tff(4034,plain,
% 0.86/1.12 (~(f(f(f(f(elem!1)))) = f(elem!1))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3679, 4033])).
% 0.86/1.12 tff(4035,plain,
% 0.86/1.12 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[860, 4034])).
% 0.86/1.12 tff(4036,assumption,(~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))), introduced(assumption)).
% 0.86/1.12 tff(4037,assumption,(r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))), introduced(assumption)).
% 0.86/1.12 tff(4038,assumption,(~(f(elem!1) = f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.86/1.12 tff(4039,plain,
% 0.86/1.12 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3899, 233, 4031, 4038, 4037])).
% 0.86/1.12 tff(4040,plain,
% 0.86/1.12 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4039, 897, 4036])).
% 0.86/1.12 tff(4041,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4042,plain,
% 0.86/1.12 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4043,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4042])).
% 0.86/1.12 tff(4044,plain,
% 0.86/1.12 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4043, 4041])).
% 0.86/1.12 tff(4045,plain,
% 0.86/1.12 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(4046,plain,
% 0.86/1.12 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 0.86/1.12 tff(4047,plain,
% 0.86/1.12 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4046, 205, 4021, 3770, 1681, 4032])).
% 0.86/1.12 tff(4048,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4047, 4040, 897])).
% 0.86/1.12 tff(4049,plain,((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(4050,plain,
% 0.86/1.12 (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4049, 3770, 4035, 3779, 4032, 3769, 4031, 4030, 4021])).
% 0.86/1.12 tff(4051,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3793, 4050, 3789, 3650])).
% 0.86/1.12 tff(4052,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (~(c = elem!1)) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(4053,plain,
% 0.86/1.12 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4052, 4020, 3991, 3649, 4019, 214, 805])).
% 0.86/1.12 tff(4054,plain,
% 0.86/1.12 (~r(c, f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1693, 4053, 3658, 3986])).
% 0.86/1.12 tff(4055,plain,
% 0.86/1.12 (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[4054, 3982])).
% 0.86/1.12 tff(4056,plain,
% 0.86/1.12 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(elem!1) = f(f(f(f(f(elem!1))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3660])).
% 0.86/1.12 tff(4057,plain,
% 0.86/1.12 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(elem!1) = f(f(f(f(f(elem!1)))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4056])).
% 0.86/1.12 tff(4058,plain,
% 0.86/1.12 (~(f(elem!1) = f(f(f(f(f(elem!1))))))),
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% 0.86/1.12 inference(monotonicity,[status(thm)],[4068])).
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% 0.86/1.12 inference(monotonicity,[status(thm)],[4071])).
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% 0.96/1.12 inference(rewrite,[status(thm)],[])).
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% 0.96/1.12 inference(monotonicity,[status(thm)],[4081])).
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% 0.96/1.12 inference(transitivity,[status(thm)],[4082, 4080])).
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% 0.96/1.12 inference(modus_ponens,[status(thm)],[4084, 4083])).
% 0.96/1.12 tff(4086,plain,
% 0.96/1.12 ($false),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4085, 233, 2066, 4079, 4060, 4078, 4070, 4065])).
% 0.96/1.12 tff(4087,plain,(r(elem!1, f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.12 tff(4088,plain,
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% 0.96/1.13 inference(monotonicity,[status(thm)],[3652])).
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% 0.96/1.13 ((f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) <=> (f(f(f(f(f(f(f(elem!1))))))) = f(c))),
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% 0.96/1.13 ((f(f(f(f(f(f(f(elem!1))))))) = f(c)) <=> (f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.13 inference(symmetry,[status(thm)],[4092])).
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% 0.96/1.13 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4093])).
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% 0.96/1.13 (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
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% 0.96/1.13 tff(4097,assumption,(~(f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
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% 0.96/1.13 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c)))) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
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% 0.96/1.13 ((f(f(f(c))) = f(f(elem!1))) <=> (f(f(f(elem!1))) = f(f(elem!1)))),
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% 0.96/1.13 ((~(f(f(f(elem!1))) = f(f(elem!1)))) <=> (~(f(f(f(c))) = f(f(elem!1))))),
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% 0.96/1.13 tff(4111,plain,
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% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4114,plain,
% 0.96/1.13 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c))))) <=> ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4115,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4114])).
% 0.96/1.13 tff(4116,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4115, 4113])).
% 0.96/1.13 tff(4117,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(c))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4118,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4117, 4116])).
% 0.96/1.13 tff(4119,plain,
% 0.96/1.13 ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(c)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4118, 233])).
% 0.96/1.13 tff(4120,plain,
% 0.96/1.13 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(c))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4119, 4112, 4111, 3779, 4107, 3432])).
% 0.96/1.13 tff(4121,plain,
% 0.96/1.13 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4120, 4102])).
% 0.96/1.13 tff(4122,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4123,plain,
% 0.96/1.13 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4124,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4123])).
% 0.96/1.13 tff(4125,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4124, 4122])).
% 0.96/1.13 tff(4126,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4127,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 0.96/1.13 tff(4128,plain,
% 0.96/1.13 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4127, 205, 552, 1834])).
% 0.96/1.13 tff(4129,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4128, 4121, 4098, 3774, 4096])).
% 0.96/1.13 tff(4130,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(c)) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (~(c = elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(elem!1)) | r(f(f(elem!1)), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(4131,plain,
% 0.96/1.13 (r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4130, 1834, 3650, 805, 3761, 3432, 4089, 552])).
% 0.96/1.13 tff(4132,plain,
% 0.96/1.13 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[3793, 4131, 3650])).
% 0.96/1.13 tff(4133,plain,
% 0.96/1.13 ((~(f(f(f(f(f(f(f(elem!1))))))) = c)) <=> (~(elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[3878])).
% 0.96/1.13 tff(4134,plain,
% 0.96/1.13 (~(elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[964, 4133])).
% 0.96/1.13 tff(4135,plain,
% 0.96/1.13 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[3766])).
% 0.96/1.13 tff(4136,plain,
% 0.96/1.13 (~(f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1118, 4135])).
% 0.96/1.13 tff(4137,plain,
% 0.96/1.13 ((~(elem!1 = f(f(f(f(f(f(f(elem!1))))))))) <=> (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[3876])).
% 0.96/1.13 tff(4138,assumption,(~(elem!1 = f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.13 tff(4139,plain,
% 0.96/1.13 (~(f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 0.96/1.13 tff(4140,assumption,(~(f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.13 tff(4141,plain,
% 0.96/1.13 (~(f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4140, 4090])).
% 0.96/1.13 tff(4142,assumption,(r(f(f(f(f(f(f(f(elem!1))))))), elem!1)), introduced(assumption)).
% 0.96/1.13 tff(4143,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4144,plain,
% 0.96/1.13 (((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)) <=> ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4145,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4144])).
% 0.96/1.13 tff(4146,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4145, 4143])).
% 0.96/1.13 tff(4147,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4148,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4147, 4146])).
% 0.96/1.13 tff(4149,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4148, 233, 610, 127, 4142, 4037, 4141, 4139])).
% 0.96/1.13 tff(4150,plain,((~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(4151,plain,
% 0.96/1.13 (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4150, 4132, 127, 4136, 4134, 610])).
% 0.96/1.13 tff(4152,plain,
% 0.96/1.13 (r(f(elem!1), elem!1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[2184, 180, 610])).
% 0.96/1.13 tff(4153,plain,
% 0.96/1.13 ((f(elem!1) = elem!1) <=> (elem!1 = f(elem!1))),
% 0.96/1.13 inference(commutativity,[status(thm)],[])).
% 0.96/1.13 tff(4154,plain,
% 0.96/1.13 ((elem!1 = f(elem!1)) <=> (f(elem!1) = elem!1)),
% 0.96/1.13 inference(symmetry,[status(thm)],[4153])).
% 0.96/1.13 tff(4155,plain,
% 0.96/1.13 ((~(elem!1 = f(elem!1))) <=> (~(f(elem!1) = elem!1))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4154])).
% 0.96/1.13 tff(4156,plain,
% 0.96/1.13 (~(f(elem!1) = elem!1)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[127, 4155])).
% 0.96/1.13 tff(4157,plain,
% 0.96/1.13 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[2166, 805, 1834, 135, 552])).
% 0.96/1.13 tff(4158,assumption,(r(f(f(elem!1)), f(f(f(f(elem!1)))))), introduced(assumption)).
% 0.96/1.13 tff(4159,plain,
% 0.96/1.13 (~(f(f(elem!1)) = f(f(f(elem!1))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[154, 2154])).
% 0.96/1.13 tff(4160,plain,
% 0.96/1.13 ((f(f(f(f(elem!1)))) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(f(f(elem!1)))))),
% 0.96/1.13 inference(symmetry,[status(thm)],[823])).
% 0.96/1.13 tff(4161,plain,
% 0.96/1.13 ((~(f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> (~(f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4160])).
% 0.96/1.13 tff(4162,plain,
% 0.96/1.13 (~(f(f(elem!1)) = f(f(f(f(elem!1)))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[194, 4161])).
% 0.96/1.13 tff(4163,plain,
% 0.96/1.13 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[674, 314, 91, 806, 1834, 552])).
% 0.96/1.13 tff(4164,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4165,plain,
% 0.96/1.13 (((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4166,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4165])).
% 0.96/1.13 tff(4167,plain,
% 0.96/1.13 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4166, 4164])).
% 0.96/1.13 tff(4168,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4169,plain,
% 0.96/1.13 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4168, 4167])).
% 0.96/1.13 tff(4170,plain,
% 0.96/1.13 ((f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4169, 233, 314, 4163, 1471, 4158])).
% 0.96/1.13 tff(4171,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4170, 4162, 4159])).
% 0.96/1.13 tff(4172,plain,((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(4173,plain,
% 0.96/1.13 (f(f(f(f(elem!1)))) = f(f(f(elem!1)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4172, 154, 4158, 194, 1471, 91, 806, 1834, 552])).
% 0.96/1.13 tff(4174,plain,
% 0.96/1.13 (f(f(f(elem!1))) = f(f(f(f(elem!1))))),
% 0.96/1.13 inference(symmetry,[status(thm)],[4173])).
% 0.96/1.13 tff(4175,plain,
% 0.96/1.13 (inj_0(f(f(f(elem!1)))) = inj_0(f(f(f(f(elem!1)))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4174])).
% 0.96/1.13 tff(4176,plain,
% 0.96/1.13 (inj_0(f(f(f(f(elem!1))))) = inj_0(f(f(f(elem!1))))),
% 0.96/1.13 inference(symmetry,[status(thm)],[4175])).
% 0.96/1.13 tff(4177,plain,
% 0.96/1.13 (f(f(f(elem!1))) = f(f(elem!1))),
% 0.96/1.13 inference(transitivity,[status(thm)],[152, 4176, 69])).
% 0.96/1.13 tff(4178,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[154, 4177])).
% 0.96/1.13 tff(4179,plain,((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(4180,plain,
% 0.96/1.13 (~r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4179, 194, 1528, 552, 91, 806, 1834, 4157])).
% 0.96/1.14 tff(4181,plain,
% 0.96/1.14 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[814, 194, 805, 135, 91, 806])).
% 0.96/1.14 tff(4182,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(elem!1))))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4183,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(elem!1))))))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4184,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4183, 4182])).
% 0.96/1.14 tff(4185,plain,
% 0.96/1.14 ($false),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4184, 180, 4181, 4180])).
% 0.96/1.14 tff(4186,plain,((f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | r(f(f(elem!1)), f(elem!1)) | (f(f(elem!1)) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(4187,plain,
% 0.96/1.14 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4186, 1834, 194, 805, 4034, 552, 4089])).
% 0.96/1.14 tff(4188,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4189,plain,
% 0.96/1.14 (((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(elem!1))) <=> ((~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4190,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4189])).
% 0.96/1.14 tff(4191,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4190, 4188])).
% 0.96/1.14 tff(4192,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4193,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(elem!1) = elem!1) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 0.96/1.14 tff(4194,plain,
% 0.96/1.14 (~r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4193, 233, 4187, 4034, 3873, 4156, 4152])).
% 0.96/1.14 tff(4195,plain,
% 0.96/1.14 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3914, 4194, 3650, 3873, 4035, 4151])).
% 0.96/1.14 tff(4196,plain,
% 0.96/1.14 (r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3892, 180, 4187])).
% 0.96/1.14 tff(4197,plain,
% 0.96/1.14 ($false),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3899, 233, 4196, 4030, 4035, 4195, 4132, 3769])).
% 0.96/1.14 tff(4198,plain,(r(f(f(f(elem!1))), f(elem!1)) | (~(c = elem!1)) | (elem!1 = f(elem!1)) | (~r(elem!1, f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(c))), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(4199,plain,
% 0.96/1.14 (r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4198, 4088, 172, 3649, 831, 3666, 2066, 3968])).
% 0.96/1.14 tff(4200,plain,
% 0.96/1.14 (r(f(elem!1), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[2184, 180, 4088])).
% 0.96/1.14 tff(4201,plain,
% 0.96/1.14 (~(f(elem!1) = elem!1)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[172, 4155])).
% 0.96/1.14 tff(4202,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4203,plain,
% 0.96/1.14 (((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(elem!1))) <=> ((~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4204,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1)))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4203])).
% 0.96/1.14 tff(4205,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4204, 4202])).
% 0.96/1.14 tff(4206,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(elem!1), elem!1)) | (~r(f(f(f(elem!1))), elem!1)) | (f(elem!1) = elem!1) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(elem!1)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4207,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(elem!1) = elem!1)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4206, 4205])).
% 0.96/1.14 tff(4208,plain,
% 0.96/1.14 (~r(f(f(f(elem!1))), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4207, 233, 2066, 4199, 4063, 4201, 4200])).
% 0.96/1.14 tff(4209,plain,
% 0.96/1.14 ((f(f(f(f(elem!1)))) = c) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.96/1.14 inference(transitivity,[status(thm)],[4006, 3870])).
% 0.96/1.14 tff(4210,plain,
% 0.96/1.14 ((~(f(f(f(f(elem!1)))) = c)) <=> (~(f(f(f(f(elem!1)))) = elem!1))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4209])).
% 0.96/1.14 tff(4211,plain,
% 0.96/1.14 (~(f(f(f(f(elem!1)))) = elem!1)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[97, 4210])).
% 0.96/1.14 tff(4212,plain,
% 0.96/1.14 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[368, 3976])).
% 0.96/1.14 tff(4213,plain,
% 0.96/1.14 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4060, 3742])).
% 0.96/1.14 tff(4214,plain,
% 0.96/1.14 (~r(f(f(elem!1)), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3714, 180, 187])).
% 0.96/1.14 tff(4215,plain,
% 0.96/1.14 (r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3788, 3770, 4089, 3650, 805])).
% 0.96/1.14 tff(4216,plain,
% 0.96/1.14 (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[3793, 4215, 3650])).
% 0.96/1.14 tff(4217,plain,
% 0.96/1.14 (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4150, 4216, 127, 4136, 4134, 610])).
% 0.96/1.14 tff(4218,assumption,(~(f(f(elem!1)) = elem!1)), introduced(assumption)).
% 0.96/1.14 tff(4219,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4220,plain,
% 0.96/1.14 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(elem!1)) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4221,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(elem!1)) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4220])).
% 0.96/1.14 tff(4222,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(elem!1)) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4221, 4219])).
% 0.96/1.14 tff(4223,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(elem!1)) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4224,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 0.96/1.14 tff(4225,plain,
% 0.96/1.14 ($false),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4224, 205, 4218, 3707, 3770, 3779, 4217, 3881])).
% 0.96/1.14 tff(4226,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | (elem!1 = f(elem!1)) | (~r(elem!1, f(elem!1))) | (~(c = elem!1)) | r(f(f(elem!1)), f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(4227,plain,
% 0.96/1.14 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4226, 4214, 3840, 172, 610, 3649, 805])).
% 0.96/1.14 tff(4228,plain,
% 0.96/1.14 (~(f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[860, 3680])).
% 0.96/1.14 tff(4229,plain,
% 0.96/1.14 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[720, 187, 4063, 4211, 831, 62, 316])).
% 0.96/1.14 tff(4230,plain,
% 0.96/1.14 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[681, 233, 610, 172, 3680, 4229, 4211])).
% 0.96/1.14 tff(4231,plain,
% 0.96/1.14 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[814, 4230, 831, 214, 3680, 805])).
% 0.96/1.14 tff(4232,plain,
% 0.96/1.14 (r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4184, 180, 4231])).
% 0.96/1.14 tff(4233,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4234,plain,
% 0.96/1.14 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4235,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4234])).
% 0.96/1.14 tff(4236,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4235, 4233])).
% 0.96/1.14 tff(4237,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4238,plain,
% 0.96/1.14 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4237, 4236])).
% 0.96/1.14 tff(4239,plain,
% 0.96/1.14 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4238, 233, 4232, 4228, 4227, 3658, 3991])).
% 0.96/1.14 tff(4240,plain,
% 0.96/1.14 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[718, 233, 666, 831, 4231, 1471, 710])).
% 0.96/1.14 tff(4241,plain,
% 0.96/1.14 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4242,plain,
% 0.96/1.14 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4243,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4242])).
% 0.96/1.15 tff(4244,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4243, 4241])).
% 0.96/1.15 tff(4245,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4246,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4245, 4244])).
% 0.96/1.15 tff(4247,plain,
% 0.96/1.15 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4246, 205, 666, 4240, 4228, 4239, 4213])).
% 0.96/1.15 tff(4248,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4249,plain,
% 0.96/1.15 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4250,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4249])).
% 0.96/1.15 tff(4251,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4250, 4248])).
% 0.96/1.15 tff(4252,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4253,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4252, 4251])).
% 0.96/1.15 tff(4254,plain,
% 0.96/1.15 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4253, 233, 1471, 710, 4227, 3658])).
% 0.96/1.15 tff(4255,plain,
% 0.96/1.15 ($false),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4254, 4247, 4213])).
% 0.96/1.15 tff(4256,plain,(r(elem!1, f(f(elem!1))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(elem!1, f(elem!1))) | r(f(f(elem!1)), f(elem!1)) | (elem!1 = f(f(elem!1))) | r(f(f(f(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(4257,plain,
% 0.96/1.15 (r(elem!1, f(f(elem!1)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4256, 4212, 4088, 3666, 62, 4208])).
% 0.96/1.15 tff(4258,plain,
% 0.96/1.15 (~r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[3950, 4257, 3680, 3666, 62, 4211, 4088])).
% 0.96/1.15 tff(4259,plain,
% 0.96/1.15 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[380, 4258, 4063, 666, 4211, 4208])).
% 0.96/1.15 tff(4260,plain,
% 0.96/1.15 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[559, 233, 3680, 666, 4259, 2066, 4199])).
% 0.96/1.15 tff(4261,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4262,plain,
% 0.96/1.15 (((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4263,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4262])).
% 0.96/1.15 tff(4264,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4263, 4261])).
% 0.96/1.15 tff(4265,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4266,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(elem!1))), f(f(elem!1))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 0.96/1.15 tff(4267,plain,
% 0.96/1.15 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4266, 233, 666, 4259, 831, 427, 3976])).
% 0.96/1.15 tff(4268,plain,
% 0.96/1.15 ($false),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[814, 4267, 4260, 831, 214, 3680, 3666])).
% 0.96/1.15 tff(4269,plain,(r(f(c), f(f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(4270,plain,
% 0.96/1.15 (r(f(c), f(f(elem!1)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4269, 62])).
% 0.96/1.15 tff(4271,plain,
% 0.96/1.15 (r(f(elem!1), f(f(elem!1)))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4270, 3663])).
% 0.96/1.15 tff(4272,plain,
% 0.96/1.15 (r(f(f(f(f(f(f(f(elem!1))))))), f(c)) <=> r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[3660])).
% 0.96/1.15 tff(4273,plain,
% 0.96/1.15 ((~r(f(f(f(f(f(f(f(elem!1))))))), f(c))) <=> (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4272])).
% 0.96/1.15 tff(4274,plain,
% 0.96/1.15 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[3807, 205, 363, 710, 3770, 3658])).
% 0.96/1.15 tff(4275,plain,
% 0.96/1.15 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4274, 4213])).
% 0.96/1.15 tff(4276,plain,
% 0.96/1.15 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(elem!1)))) | r(f(f(elem!1)), f(elem!1)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(elem!1)))) | r(f(f(elem!1)), f(elem!1)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4277,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(elem!1)))) | r(f(f(elem!1)), f(elem!1)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4278,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(elem!1)))) | r(f(f(elem!1)), f(elem!1))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 0.96/1.15 tff(4279,plain,
% 0.96/1.15 (r(f(f(elem!1)), f(elem!1))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4278, 180, 4271])).
% 0.96/1.15 tff(4280,plain,
% 0.96/1.15 ((f(c) = f(f(f(f(c))))) <=> (f(elem!1) = f(f(f(f(elem!1)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[3671, 4022])).
% 0.96/1.15 tff(4281,plain,
% 0.96/1.15 ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(elem!1) = f(f(f(f(elem!1))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4280])).
% 0.96/1.15 tff(4282,plain,
% 0.96/1.15 (~(f(elem!1) = f(f(f(f(elem!1)))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[3679, 4281])).
% 0.96/1.15 tff(4283,plain,
% 0.96/1.15 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4284,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4285,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 0.96/1.15 tff(4286,plain,
% 0.96/1.15 (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4285, 180, 3770])).
% 0.96/1.15 tff(4287,plain,
% 0.96/1.15 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4288,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4289,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4288, 4287])).
% 0.96/1.15 tff(4290,plain,
% 0.96/1.15 (r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4289, 180, 4275])).
% 0.96/1.15 tff(4291,assumption,(r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.15 tff(4292,assumption,(~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.15 tff(4293,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4294,plain,
% 0.96/1.15 ((r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(elem!1)))) <=> (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4295,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4294])).
% 0.96/1.15 tff(4296,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4295, 4293])).
% 0.96/1.15 tff(4297,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(elem!1))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4298,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(elem!1))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4297, 4296])).
% 0.96/1.15 tff(4299,plain,
% 0.96/1.15 (r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4298, 205, 187, 62, 3980, 4292, 3659])).
% 0.96/1.15 tff(4300,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4301,plain,
% 0.96/1.15 ((r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1)))) <=> (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4302,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4301])).
% 0.96/1.15 tff(4303,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4302, 4300])).
% 0.96/1.15 tff(4304,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (elem!1 = f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4305,plain,
% 0.96/1.15 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(f(elem!1))) | (elem!1 = f(f(f(elem!1)))) | r(elem!1, f(f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 0.96/1.15 tff(4306,plain,
% 0.96/1.15 (r(elem!1, f(f(f(elem!1))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4305, 205, 187, 62, 3996, 363, 710])).
% 0.96/1.15 tff(4307,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4308,plain,
% 0.96/1.15 (((~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(elem!1))))) <=> ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4309,plain,
% 0.96/1.15 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4308])).
% 0.96/1.16 tff(4310,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4309, 4307])).
% 0.96/1.16 tff(4311,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(elem!1)))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4312,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 0.96/1.16 tff(4313,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4312, 233, 3996, 4306, 4060, 4299, 3980, 4291])).
% 0.96/1.16 tff(4314,plain,(r(elem!1, f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(elem!1)), f(f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(4315,plain,
% 0.96/1.16 (r(elem!1, f(f(elem!1)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4314, 4290, 62, 4286, 363])).
% 0.96/1.16 tff(4316,plain,
% 0.96/1.16 (r(f(f(elem!1)), elem!1)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[528, 180, 4315])).
% 0.96/1.16 tff(4317,plain,
% 0.96/1.16 (~r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4018, 233, 4008, 173, 3840, 4316, 3991])).
% 0.96/1.16 tff(4318,plain,
% 0.96/1.16 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4046, 205, 4317, 4228, 3770, 3658, 3991])).
% 0.96/1.16 tff(4319,plain,
% 0.96/1.16 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[185, 173])).
% 0.96/1.16 tff(4320,plain,
% 0.96/1.16 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[393, 233, 4315, 62, 4319, 4211, 831])).
% 0.96/1.16 tff(4321,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4322,plain,
% 0.96/1.16 ((r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1)))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4323,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4322])).
% 0.96/1.16 tff(4324,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1)))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4323, 4321])).
% 0.96/1.16 tff(4325,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4326,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(elem!1)))), f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(elem!1))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4325, 4324])).
% 0.96/1.16 tff(4327,plain,
% 0.96/1.16 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4326, 205, 666, 831, 4320, 363, 710])).
% 0.96/1.16 tff(4328,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4329,plain,
% 0.96/1.16 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4330,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4329])).
% 0.96/1.16 tff(4331,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4330, 4328])).
% 0.96/1.16 tff(4332,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4333,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(elem!1)))) = f(f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4332, 4331])).
% 0.96/1.16 tff(4334,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4333, 233, 666, 4327, 4228, 4318, 4213, 4275])).
% 0.96/1.16 tff(4335,plain,((~r(elem!1, f(f(f(f(elem!1)))))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(4336,plain,
% 0.96/1.16 (~r(elem!1, f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4335, 3770, 363, 62])).
% 0.96/1.16 tff(4337,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4338,plain,
% 0.96/1.16 ((r(f(elem!1), elem!1) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1)) <=> (r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4339,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1)))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4338])).
% 0.96/1.16 tff(4340,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4339, 4337])).
% 0.96/1.16 tff(4341,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4342,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (elem!1 = f(f(f(f(elem!1))))) | r(elem!1, f(f(f(f(elem!1))))) | r(f(elem!1), f(f(f(f(elem!1))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(elem!1) = elem!1)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4341, 4340])).
% 0.96/1.16 tff(4343,plain,
% 0.96/1.16 (r(f(elem!1), f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4342, 205, 4008, 4336, 4282, 4201, 1175])).
% 0.96/1.16 tff(4344,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4345,plain,
% 0.96/1.16 (((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1))) <=> ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4346,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4345])).
% 0.96/1.16 tff(4347,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4346, 4344])).
% 0.96/1.16 tff(4348,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(elem!1)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4349,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(elem!1), f(f(f(f(elem!1)))))) | (f(elem!1) = f(f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4348, 4347])).
% 0.96/1.16 tff(4350,plain,
% 0.96/1.16 (~r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4349, 233, 4343, 4282, 4279, 214, 3991])).
% 0.96/1.16 tff(4351,plain,
% 0.96/1.16 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4046, 205, 4350, 4228, 3770, 3658, 3991])).
% 0.96/1.16 tff(4352,plain,
% 0.96/1.16 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[249, 4336, 3680, 172, 4008, 100])).
% 0.96/1.16 tff(4353,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4354,plain,
% 0.96/1.16 (((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1))) <=> ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4355,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4354])).
% 0.96/1.16 tff(4356,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4355, 4353])).
% 0.96/1.16 tff(4357,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(elem!1)))), f(elem!1))) | (~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4358,plain,
% 0.96/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(elem!1)))) = f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), f(f(elem!1)))) | (~r(f(f(f(f(elem!1)))), f(elem!1)))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4357, 4356])).
% 0.96/1.16 tff(4359,plain,
% 0.96/1.16 (~r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4358, 233, 4271, 426, 4352, 3680, 831])).
% 0.96/1.16 tff(4360,plain,
% 0.96/1.16 (r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4326, 205, 666, 831, 4359, 363, 710])).
% 0.96/1.16 tff(4361,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4333, 233, 666, 4360, 4228, 4351, 4213, 4275])).
% 0.96/1.16 tff(4362,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(4363,plain,
% 0.96/1.16 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4362, 363, 100, 62])).
% 0.96/1.16 tff(4364,plain,
% 0.96/1.16 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1753, 4363, 3684, 3658, 4270])).
% 0.96/1.16 tff(4365,plain,
% 0.96/1.16 (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4364, 4273])).
% 0.96/1.16 tff(4366,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4367,plain,
% 0.96/1.16 ((r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(elem!1) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))) <=> (r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4368,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(elem!1) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4367])).
% 0.96/1.16 tff(4369,plain,
% 0.96/1.16 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(elem!1) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4368, 4366])).
% 0.96/1.17 tff(4370,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(elem!1) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4371,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(elem!1), elem!1) | (f(elem!1) = elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4370, 4369])).
% 0.96/1.17 tff(4372,plain,
% 0.96/1.17 (r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4371, 205, 4201, 1175, 4365, 4073, 4070])).
% 0.96/1.17 tff(4373,plain,
% 0.96/1.17 (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[2900, 4363, 3684, 3658, 4270])).
% 0.96/1.17 tff(4374,plain,
% 0.96/1.17 (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4373, 3662])).
% 0.96/1.17 tff(4375,plain,
% 0.96/1.17 ((~(f(f(f(f(f(f(f(elem!1))))))) = f(c))) <=> (~(f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4067])).
% 0.96/1.17 tff(4376,plain,
% 0.96/1.17 (~(f(elem!1) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[1118, 4375])).
% 0.96/1.17 tff(4377,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4378,plain,
% 0.96/1.17 ((r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(elem!1))) <=> (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4379,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4378])).
% 0.96/1.17 tff(4380,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4379, 4377])).
% 0.96/1.17 tff(4381,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(elem!1, f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(elem!1)))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4382,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4381, 4380])).
% 0.96/1.17 tff(4383,plain,
% 0.96/1.17 (r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4382, 205, 100, 172, 4376, 4374, 3980])).
% 0.96/1.17 tff(4384,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4385,plain,
% 0.96/1.17 (((~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1))))))))) <=> ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4386,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4385])).
% 0.96/1.17 tff(4387,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4386, 4384])).
% 0.96/1.17 tff(4388,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (~r(elem!1, f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4389,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(elem!1, f(f(elem!1)))) | (elem!1 = f(f(elem!1))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 0.96/1.17 tff(4390,plain,
% 0.96/1.17 (~r(elem!1, f(f(elem!1)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4389, 233, 62, 4363, 3658, 4383, 3980])).
% 0.96/1.17 tff(4391,plain,
% 0.96/1.17 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[251, 4390, 831, 3680, 100, 62, 4008])).
% 0.96/1.17 tff(4392,plain,
% 0.96/1.17 (r(elem!1, f(f(f(f(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[605, 180, 4391])).
% 0.96/1.17 tff(4393,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4394,plain,
% 0.96/1.17 (((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1)) <=> ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4395,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4394])).
% 0.96/1.17 tff(4396,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4395, 4393])).
% 0.96/1.17 tff(4397,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(elem!1, f(f(f(f(elem!1)))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (elem!1 = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4398,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(f(elem!1))))) | (~r(elem!1, f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 0.96/1.17 tff(4399,plain,
% 0.96/1.17 (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4398, 233, 4008, 4392, 4228, 4372, 4073])).
% 0.96/1.17 tff(4400,plain,
% 0.96/1.17 (r(f(f(f(elem!1))), elem!1)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[370, 4390, 80, 4063, 100])).
% 0.96/1.17 tff(4401,plain,
% 0.96/1.17 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[596, 4391, 4063, 666, 4211, 4400])).
% 0.96/1.17 tff(4402,plain,
% 0.96/1.17 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[467, 205, 666, 4401, 831, 427, 3409])).
% 0.96/1.17 tff(4403,plain,
% 0.96/1.17 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[239, 233, 3680, 4279, 214, 831, 4402])).
% 0.96/1.17 tff(4404,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4405,plain,
% 0.96/1.17 ((r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4406,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4405])).
% 0.96/1.17 tff(4407,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4406, 4404])).
% 0.96/1.17 tff(4408,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(elem!1)))), f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4409,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(elem!1)))), f(elem!1)) | (f(f(f(f(elem!1)))) = f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 0.96/1.17 tff(4410,plain,
% 0.96/1.17 ($false),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4409, 205, 4403, 3680, 4228, 4399, 4365, 4070])).
% 0.96/1.17 tff(4411,plain,(r(f(f(elem!1)), f(f(f(elem!1)))) | r(elem!1, f(elem!1)) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.17 tff(4412,plain,
% 0.96/1.17 (r(f(f(elem!1)), f(f(f(elem!1))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4411, 100, 62])).
% 0.96/1.17 tff(4413,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4414,plain,
% 0.96/1.17 (((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1)))) <=> ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4415,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[4414])).
% 0.96/1.17 tff(4416,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[4415, 4413])).
% 0.96/1.17 tff(4417,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(elem!1), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4418,plain,
% 0.96/1.17 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(elem!1), f(f(elem!1)))) | (f(elem!1) = f(f(elem!1))) | (f(elem!1) = f(f(f(elem!1)))) | (~r(f(elem!1), f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4417, 4416])).
% 0.96/1.17 tff(4419,plain,
% 0.96/1.17 (~r(f(elem!1), f(f(f(elem!1))))),
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% 0.96/1.17 tff(4420,plain,
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% 0.96/1.17 tff(4421,plain,
% 0.96/1.17 (~r(elem!1, f(f(elem!1)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[517, 4420, 3996, 62, 4412, 710])).
% 0.96/1.17 tff(4422,plain,
% 0.96/1.17 (r(f(f(f(elem!1))), elem!1)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[370, 4421, 80, 4063, 100])).
% 0.96/1.17 tff(4423,plain,
% 0.96/1.17 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[251, 4421, 831, 3680, 100, 62, 4008])).
% 0.96/1.17 tff(4424,plain,
% 0.96/1.17 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[596, 4423, 4063, 666, 4211, 4422])).
% 0.96/1.17 tff(4425,plain,
% 0.96/1.17 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4426,plain,
% 0.96/1.17 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(elem!1))), f(elem!1))) | r(f(elem!1), f(f(f(elem!1)))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4427,plain,
% 0.96/1.17 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(elem!1))), f(elem!1))) | r(f(elem!1), f(f(f(elem!1))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 0.96/1.17 tff(4428,plain,
% 0.96/1.17 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[4427, 180, 4419])).
% 0.96/1.17 tff(4429,plain,
% 0.96/1.17 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[674, 4428, 2066, 3680, 666, 4424])).
% 0.96/1.17 tff(4430,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[4358, 233, 4271, 426, 4429, 3680, 831])).
% 0.96/1.17 tff(4431,plain,
% 0.96/1.17 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(4432,plain,
% 0.96/1.17 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(elem!1))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(4433,plain,
% 0.96/1.17 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(f(f(elem!1)))))) | r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[4432, 4431])).
% 0.96/1.17 tff(4434,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[4433, 180, 4430])).
% 0.96/1.17 tff(4435,plain,
% 0.96/1.17 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4436,plain,
% 0.96/1.18 (((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1)) <=> ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4437,plain,
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% 0.96/1.18 inference(monotonicity,[status(thm)],[4436])).
% 0.96/1.18 tff(4438,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[4437, 4435])).
% 0.96/1.18 tff(4439,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(elem!1)), elem!1)) | (~r(elem!1, f(f(f(elem!1))))) | (~r(f(f(elem!1)), f(f(f(elem!1))))) | (elem!1 = f(f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4440,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 0.96/1.18 tff(4441,plain,
% 0.96/1.18 ((elem!1 = f(f(f(elem!1)))) | (~r(elem!1, f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(elem!1)))) | (f(f(elem!1)) = elem!1) | (~r(f(f(elem!1)), elem!1)) | (~r(f(f(elem!1)), f(f(f(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4440, 233])).
% 0.96/1.18 tff(4442,plain,
% 0.96/1.18 (~r(f(f(elem!1)), elem!1)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4441, 4420, 3996, 710, 3840, 4412])).
% 0.96/1.18 tff(4443,assumption,(~(f(f(f(f(f(f(f(elem!1))))))) = elem!1)), introduced(assumption)).
% 0.96/1.18 tff(4444,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[4224, 205, 4218, 3707, 3770, 1681, 4443])).
% 0.96/1.18 tff(4445,plain,
% 0.96/1.18 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4046, 205, 4021, 897, 3770, 1681, 4032])).
% 0.96/1.18 tff(4446,plain,
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% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4447,plain,
% 0.96/1.18 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1)))))) <=> ((~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
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% 0.96/1.18 inference(monotonicity,[status(thm)],[4447])).
% 0.96/1.18 tff(4449,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)))),
% 0.96/1.18 inference(transitivity,[status(thm)],[4448, 4446])).
% 0.96/1.18 tff(4450,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4451,plain,
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% 0.96/1.18 inference(modus_ponens,[status(thm)],[4450, 4449])).
% 0.96/1.18 tff(4452,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4451, 233, 387, 195, 897, 4445, 4444, 4443])).
% 0.96/1.18 tff(4453,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (~r(f(f(f(f(elem!1)))), elem!1)) | (f(f(f(f(elem!1)))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(f(elem!1))))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(elem!1)) = elem!1) | r(f(f(elem!1)), elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(elem!1))))) | (f(f(elem!1)) = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4454,plain,
% 0.96/1.18 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4453, 4423, 4211, 4228, 4073, 3840, 4442, 3658, 4434, 3991])).
% 0.96/1.18 tff(4455,plain,
% 0.96/1.18 (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
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% 0.96/1.18 tff(4456,plain,
% 0.96/1.18 (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4455, 3662])).
% 0.96/1.18 tff(4457,assumption,(~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.18 tff(4458,assumption,(r(elem!1, f(f(f(f(f(f(f(elem!1))))))))), introduced(assumption)).
% 0.96/1.18 tff(4459,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4460,plain,
% 0.96/1.18 (((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1)) <=> ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4461,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[4460])).
% 0.96/1.18 tff(4462,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[4461, 4459])).
% 0.96/1.18 tff(4463,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = elem!1))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4464,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 0.96/1.18 tff(4465,plain,
% 0.96/1.18 ((f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4464, 233, 425, 310, 4458, 4138])).
% 0.96/1.18 tff(4466,plain,
% 0.96/1.18 (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4465, 4097])).
% 0.96/1.18 tff(4467,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4468,plain,
% 0.96/1.18 ((r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(elem!1))) <=> ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4469,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[4468])).
% 0.96/1.18 tff(4470,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[4469, 4467])).
% 0.96/1.18 tff(4471,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(elem!1))), f(elem!1)) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(elem!1)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4472,plain,
% 0.96/1.18 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 0.96/1.18 tff(4473,plain,
% 0.96/1.18 ((f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4472, 205, 552, 1834, 4140, 4457])).
% 0.96/1.18 tff(4474,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4473, 4466, 4097])).
% 0.96/1.18 tff(4475,plain,((f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(elem!1)) | r(f(f(f(elem!1))), f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4476,plain,
% 0.96/1.18 (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4475, 4457, 4097, 4140, 4138, 425, 310, 1834, 552])).
% 0.96/1.18 tff(4477,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4382, 205, 100, 127, 4140, 4457, 4476, 4138])).
% 0.96/1.18 tff(4478,plain,(r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | r(elem!1, f(elem!1)) | (elem!1 = f(elem!1)) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | r(f(f(f(elem!1))), f(elem!1)) | (f(f(f(elem!1))) = f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4479,plain,
% 0.96/1.18 (r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4478, 4428, 172, 2066, 3980, 4376, 4060, 4063, 4422, 100])).
% 0.96/1.18 tff(4480,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4479, 4456])).
% 0.96/1.18 tff(4481,plain,(r(elem!1, f(elem!1)) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4482,plain,
% 0.96/1.18 (r(elem!1, f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4481, 62])).
% 0.96/1.18 tff(4483,plain,
% 0.96/1.18 (~r(elem!1, f(f(elem!1)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[739, 4482, 62, 426, 172, 4271])).
% 0.96/1.18 tff(4484,plain,
% 0.96/1.18 (~r(f(f(elem!1)), elem!1)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[3714, 180, 4483])).
% 0.96/1.18 tff(4485,plain,
% 0.96/1.18 (r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4224, 205, 3840, 4484, 3770, 3658, 4073])).
% 0.96/1.18 tff(4486,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4487,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4488,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 0.96/1.18 tff(4489,plain,
% 0.96/1.18 (r(elem!1, f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4488, 180, 4485])).
% 0.96/1.18 tff(4490,plain,
% 0.96/1.18 (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4150, 4485, 172, 4376, 3980, 4482])).
% 0.96/1.18 tff(4491,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4492,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(4493,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 0.96/1.18 tff(4494,plain,
% 0.96/1.18 (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4493, 180, 4490])).
% 0.96/1.18 tff(4495,plain,
% 0.96/1.18 (r(elem!1, f(f(f(elem!1))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[2611, 1470, 62, 3996, 4271, 426, 172, 4482])).
% 0.96/1.18 tff(4496,plain,
% 0.96/1.18 (r(f(f(f(elem!1))), elem!1)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[320, 180, 4495])).
% 0.96/1.18 tff(4497,plain,
% 0.96/1.18 (r(c, f(elem!1)) <=> r(elem!1, f(elem!1))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[3649])).
% 0.96/1.18 tff(4498,plain,
% 0.96/1.18 (r(elem!1, f(elem!1)) <=> r(c, f(elem!1))),
% 0.96/1.18 inference(symmetry,[status(thm)],[4497])).
% 0.96/1.18 tff(4499,plain,
% 0.96/1.18 (r(c, f(elem!1))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[4482, 4498])).
% 0.96/1.18 tff(4500,plain,
% 0.96/1.18 (~r(f(elem!1), f(f(f(elem!1))))),
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% 0.96/1.18 tff(4501,plain,
% 0.96/1.18 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4427, 180, 4500])).
% 0.96/1.18 tff(4502,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[4475, 4501, 4496, 3980, 4376, 4060, 4457, 4063, 4458, 2066])).
% 0.96/1.18 tff(4503,plain,(r(f(f(f(elem!1))), f(f(elem!1))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1))))))))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4504,plain,
% 0.96/1.18 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4503, 4494, 4489, 62])).
% 0.96/1.18 tff(4505,plain,
% 0.96/1.18 (r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4475, 425, 4138, 4140, 4097, 4457, 310, 4458, 552])).
% 0.96/1.18 tff(4506,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[664, 233, 610, 127, 552, 4505, 425, 310])).
% 0.96/1.18 tff(4507,plain,((~r(f(f(f(elem!1))), elem!1)) | (~r(elem!1, f(elem!1))) | (elem!1 = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = elem!1) | (elem!1 = f(f(f(f(f(f(f(elem!1)))))))) | (f(elem!1) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | r(f(elem!1), f(f(f(f(f(f(f(elem!1)))))))) | (~r(elem!1, f(f(f(f(f(f(f(elem!1)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(4508,plain,
% 0.96/1.18 (~r(f(f(f(elem!1))), elem!1)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4507, 4494, 172, 2066, 4063, 3980, 4376, 4060, 4482, 4489])).
% 0.96/1.18 tff(4509,plain,
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% 0.96/1.18 tff(4511,plain,
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% 0.96/1.18 tff(4512,plain,
% 0.96/1.18 (~r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[681, 233, 4482, 172, 3680, 4509, 4211])).
% 0.96/1.18 tff(4513,plain,
% 0.96/1.18 (r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[4179, 4512, 2066, 427, 3680, 831, 4511, 4510])).
% 0.96/1.18 tff(4514,plain,
% 0.96/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(4515,plain,
% 0.96/1.18 (((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1)))) <=> ((f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4516,plain,
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% 0.96/1.19 inference(monotonicity,[status(thm)],[4515])).
% 0.96/1.19 tff(4517,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4516, 4514])).
% 0.96/1.19 tff(4518,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(elem!1))) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (f(f(f(elem!1))) = f(elem!1)) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4519,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(elem!1)) | (~r(f(f(f(elem!1))), f(elem!1))) | (f(f(elem!1)) = f(elem!1)) | (~r(f(f(elem!1)), f(elem!1))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4518, 4517])).
% 0.96/1.19 tff(4520,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[4519, 233, 2066, 4513, 4279, 214, 427, 4504])).
% 0.96/1.19 tff(4521,plain,(r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4522,plain,
% 0.96/1.19 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4521, 62])).
% 0.96/1.19 tff(4523,plain,
% 0.96/1.19 (~r(f(c), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2900, 4522, 3684, 3658, 4270])).
% 0.96/1.19 tff(4524,plain,
% 0.96/1.19 (~r(f(elem!1), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4523, 3662])).
% 0.96/1.19 tff(4525,plain,
% 0.96/1.19 (~r(f(f(f(f(f(f(f(elem!1))))))), f(c))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1753, 4522, 3684, 3658, 4270])).
% 0.96/1.19 tff(4526,plain,
% 0.96/1.19 (~r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4525, 4273])).
% 0.96/1.19 tff(4527,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4528,plain,
% 0.96/1.19 ((r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1))) <=> ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4529,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4528])).
% 0.96/1.19 tff(4530,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4529, 4527])).
% 0.96/1.19 tff(4531,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | r(f(elem!1), f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))) | (f(elem!1) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4532,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(elem!1) = f(f(f(elem!1)))) | r(f(elem!1), f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(elem!1)) | (f(f(f(f(f(f(f(elem!1))))))) = f(elem!1)) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4531, 4530])).
% 0.96/1.19 tff(4533,plain,
% 0.96/1.19 ((f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4532, 205, 80, 4500, 4526, 4070])).
% 0.96/1.19 tff(4534,plain,
% 0.96/1.19 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4533, 4213])).
% 0.96/1.19 tff(4535,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4536,plain,
% 0.96/1.19 (((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1))))) <=> ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4537,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4536])).
% 0.96/1.19 tff(4538,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4537, 4535])).
% 0.96/1.19 tff(4539,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1))))) | (~r(f(f(f(elem!1))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4540,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(elem!1))), elem!1)) | (f(f(f(elem!1))) = elem!1) | (f(f(f(f(f(f(f(elem!1))))))) = f(f(f(elem!1)))) | (f(f(f(f(f(f(f(elem!1))))))) = elem!1) | (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(elem!1)))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4539, 4538])).
% 0.96/1.19 tff(4541,plain,
% 0.96/1.19 (~r(f(f(f(f(f(f(f(elem!1))))))), elem!1)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4540, 233, 4496, 4063, 4073, 4213, 4534])).
% 0.96/1.19 tff(4542,plain,
% 0.96/1.19 (r(f(f(f(f(f(f(f(elem!1))))))), f(f(f(f(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[3914, 171, 3649, 4211, 4228, 3874])).
% 0.96/1.19 tff(4543,plain,
% 0.96/1.19 (r(f(f(f(f(elem!1)))), f(f(elem!1)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[212, 171, 4211, 62, 831, 4483])).
% 0.96/1.19 tff(4544,plain,
% 0.96/1.19 (r(f(f(elem!1)), f(f(f(f(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4184, 180, 4543])).
% 0.96/1.19 tff(4545,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4238, 233, 4544, 4228, 4542, 4522, 3658, 3991])).
% 0.96/1.19 tff(4546,plain,(r(f(f(f(f(elem!1)))), elem!1) | r(f(f(f(f(f(f(f(elem!1))))))), elem!1) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4547,plain,
% 0.96/1.19 (r(f(f(f(f(elem!1)))), elem!1)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4546, 4541, 62])).
% 0.96/1.19 tff(4548,plain,
% 0.96/1.19 (~r(f(f(f(f(elem!1)))), f(f(f(elem!1))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[596, 4547, 4063, 666, 4211, 4496])).
% 0.96/1.19 tff(4549,plain,
% 0.96/1.19 (r(f(f(f(f(elem!1)))), f(elem!1))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[674, 4548, 2066, 3680, 666, 4501])).
% 0.96/1.19 tff(4550,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[681, 233, 4482, 172, 4549, 3680, 4547, 4211])).
% 0.96/1.19 tff(4551,plain,(r(f(f(f(elem!1))), f(f(elem!1))) | (elem!1 = f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4552,plain,
% 0.96/1.19 (r(f(f(f(elem!1))), f(f(elem!1)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4551, 62])).
% 0.96/1.19 tff(4553,plain,
% 0.96/1.19 (~r(f(f(f(elem!1))), f(elem!1))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4519, 233, 2066, 4279, 214, 427, 4552])).
% 0.96/1.19 tff(4554,plain,
% 0.96/1.19 (r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4472, 205, 2066, 4553, 4060, 4376, 4524])).
% 0.96/1.19 tff(4555,plain,
% 0.96/1.19 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4556,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4557,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(f(elem!1))))))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 0.96/1.19 tff(4558,plain,
% 0.96/1.19 (r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4557, 180, 4522])).
% 0.96/1.19 tff(4559,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4560,plain,
% 0.96/1.19 (((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(elem!1)))) <=> ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4561,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4560])).
% 0.96/1.19 tff(4562,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4561, 4559])).
% 0.96/1.19 tff(4563,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(elem!1))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (f(f(f(elem!1))) = f(f(elem!1))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4564,plain,
% 0.96/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(elem!1))) = f(f(elem!1))) | (~r(f(f(f(elem!1))), f(f(elem!1)))) | (f(f(f(elem!1))) = f(f(f(f(f(f(f(elem!1)))))))) | (~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (~r(f(f(elem!1)), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 0.96/1.19 tff(4565,plain,
% 0.96/1.19 ((~r(f(f(f(elem!1))), f(f(f(f(f(f(f(elem!1))))))))) | (f(f(elem!1)) = f(f(f(f(f(f(f(elem!1))))))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4564, 233, 427, 4552, 4060, 4558])).
% 0.96/1.19 tff(4566,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4565, 4554, 3659])).
% 0.96/1.19 tff(4567,plain,(elem!1 = f(f(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4568,plain,
% 0.96/1.19 (f(elem!1) = f(f(f(elem!1)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[109, 4567])).
% 0.96/1.19 tff(4569,assumption,(f(f(elem!1)) = f(f(f(f(c))))), introduced(assumption)).
% 0.96/1.19 tff(4570,plain,
% 0.96/1.19 (f(f(f(f(c)))) = f(f(elem!1))),
% 0.96/1.19 inference(symmetry,[status(thm)],[4569])).
% 0.96/1.19 tff(4571,plain,
% 0.96/1.19 (inj_0(f(f(f(f(c))))) = inj_0(f(f(elem!1)))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4570])).
% 0.96/1.19 tff(4572,plain,
% 0.96/1.19 (f(f(f(c))) = f(f(f(elem!1)))),
% 0.96/1.19 inference(transitivity,[status(thm)],[3676, 4571, 122, 4568])).
% 0.96/1.19 tff(4573,plain,
% 0.96/1.19 (elem!1 = f(f(elem!1))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[79, 70])).
% 0.96/1.19 tff(4574,plain,
% 0.96/1.19 (f(f(elem!1)) = elem!1),
% 0.96/1.19 inference(symmetry,[status(thm)],[4573])).
% 0.96/1.19 tff(4575,plain,
% 0.96/1.19 ((f(f(f(f(elem!1)))) = f(f(elem!1))) <=> (f(f(f(f(elem!1)))) = elem!1)),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4574])).
% 0.96/1.19 tff(4576,plain,
% 0.96/1.19 ((f(f(f(f(elem!1)))) = f(f(elem!1))) <=> (elem!1 = f(f(f(f(elem!1)))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4575, 188])).
% 0.96/1.19 tff(4577,plain,
% 0.96/1.19 ((elem!1 = f(f(f(f(elem!1))))) <=> (f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.96/1.19 inference(symmetry,[status(thm)],[4576])).
% 0.96/1.19 tff(4578,plain,
% 0.96/1.19 ((~(elem!1 = f(f(f(f(elem!1)))))) <=> (~(f(f(f(f(elem!1)))) = f(f(elem!1))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4577])).
% 0.96/1.19 tff(4579,plain,
% 0.96/1.19 (~(f(f(f(f(elem!1)))) = f(f(elem!1)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[93, 4578])).
% 0.96/1.19 tff(4580,plain,
% 0.96/1.19 (f(f(f(f(elem!1)))) = f(f(elem!1))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[71])).
% 0.96/1.19 tff(4581,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4580, 4579])).
% 0.96/1.19 tff(4582,plain,((~(f(elem!1) = f(f(f(elem!1))))) | (elem!1 = f(f(f(f(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4583,plain,
% 0.96/1.19 (elem!1 = f(f(f(f(elem!1))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4582, 4568])).
% 0.96/1.19 tff(4584,plain,
% 0.96/1.19 (f(f(f(f(elem!1)))) = elem!1),
% 0.96/1.19 inference(symmetry,[status(thm)],[4583])).
% 0.96/1.19 tff(4585,plain,
% 0.96/1.19 (f(f(f(f(elem!1)))) = f(f(elem!1))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4584, 4567])).
% 0.96/1.19 tff(4586,plain,
% 0.96/1.19 (f(f(f(f(f(elem!1))))) = f(f(f(elem!1)))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4585])).
% 0.96/1.19 tff(4587,plain,
% 0.96/1.19 ((f(f(f(f(f(elem!1))))) = f(f(f(c)))) <=> (f(f(f(elem!1))) = f(f(f(c))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4586])).
% 0.96/1.19 tff(4588,plain,
% 0.96/1.19 ((f(f(f(f(f(elem!1))))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(elem!1))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[4587, 2034])).
% 0.96/1.19 tff(4589,plain,
% 0.96/1.19 ((~(f(f(f(f(f(elem!1))))) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(elem!1)))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4588])).
% 0.96/1.19 tff(4590,plain,
% 0.96/1.19 (~(f(f(f(f(f(elem!1))))) = f(f(f(c))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2757, 4583])).
% 0.96/1.19 tff(4591,plain,
% 0.96/1.19 (~(f(f(f(c))) = f(f(f(elem!1))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 0.96/1.19 tff(4592,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4591, 4572])).
% 0.96/1.19 tff(4593,plain,(~(f(f(elem!1)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4594,plain,
% 0.96/1.19 (~(f(f(f(f(c)))) = f(f(elem!1)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4593, 58])).
% 0.96/1.19 tff(4595,assumption,(r(f(f(elem!1)), f(f(f(f(c)))))), introduced(assumption)).
% 0.96/1.19 tff(4596,plain,
% 0.96/1.19 ((c = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = c)),
% 0.96/1.19 inference(commutativity,[status(thm)],[])).
% 0.96/1.19 tff(4597,plain,
% 0.96/1.19 ((f(f(f(f(c)))) = c) <=> (c = f(f(f(f(c)))))),
% 0.96/1.19 inference(symmetry,[status(thm)],[4596])).
% 0.96/1.19 tff(4598,plain,
% 0.96/1.19 ((~(f(f(f(f(c)))) = c)) <=> (~(c = f(f(f(f(c))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4597])).
% 0.96/1.19 tff(4599,plain,
% 0.96/1.19 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(c)))) = c))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(4600,plain,
% 0.96/1.19 (~(f(f(f(f(c)))) = c)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4599, 28])).
% 0.96/1.19 tff(4601,plain,
% 0.96/1.19 (~(c = f(f(f(f(c)))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4600, 4598])).
% 0.96/1.19 tff(4602,plain,
% 0.96/1.19 ((c = f(f(c))) <=> (f(f(c)) = c)),
% 0.96/1.19 inference(commutativity,[status(thm)],[])).
% 0.96/1.19 tff(4603,plain,
% 0.96/1.19 ((f(f(c)) = c) <=> (c = f(f(c)))),
% 0.96/1.19 inference(symmetry,[status(thm)],[4602])).
% 0.96/1.19 tff(4604,plain,
% 0.96/1.19 ((~(f(f(c)) = c)) <=> (~(c = f(f(c))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4603])).
% 0.96/1.19 tff(4605,plain,
% 0.96/1.19 (~(c = f(f(c)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[50, 4604])).
% 0.96/1.19 tff(4606,assumption,(f(f(elem!1)) = f(f(f(c)))), introduced(assumption)).
% 0.96/1.19 tff(4607,plain,
% 0.96/1.19 (f(f(f(c))) = f(f(elem!1))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[4606, 2725])).
% 0.96/1.19 tff(4608,plain,
% 0.96/1.19 (~(f(c) = elem!1)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[966, 4583])).
% 0.96/1.19 tff(4609,plain,
% 0.96/1.19 (~(f(f(f(c))) = f(f(elem!1)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1609, 4608])).
% 0.96/1.19 tff(4610,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[4609, 4607])).
% 0.96/1.19 tff(4611,plain,(~(f(f(elem!1)) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(4612,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4613,plain,
% 0.96/1.19 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(elem!1)))) <=> (r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(4614,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[4613])).
% 0.96/1.19 tff(4615,plain,
% 0.96/1.19 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[4614, 4612])).
% 0.96/1.20 tff(4616,plain,
% 0.96/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(elem!1))))),
% 0.96/1.20 inference(quant_inst,[status(thm)],[])).
% 0.96/1.20 tff(4617,plain,
% 0.96/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(f(f(c)))) | r(f(f(elem!1)), f(f(f(c)))) | (f(f(elem!1)) = f(f(f(c))))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 0.96/1.20 tff(4618,plain,
% 0.96/1.20 (r(c, f(f(f(c))))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[4617, 205, 4611, 3728, 163, 3495, 3130])).
% 0.96/1.20 tff(4619,plain,
% 0.96/1.20 ((f(f(f(c))) = f(f(c))) <=> (f(f(c)) = f(f(f(c))))),
% 0.96/1.20 inference(commutativity,[status(thm)],[])).
% 0.96/1.20 tff(4620,plain,
% 0.96/1.20 ((f(f(c)) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(c)))),
% 0.96/1.20 inference(symmetry,[status(thm)],[4619])).
% 0.96/1.20 tff(4621,plain,
% 0.96/1.20 ((~(f(f(c)) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(c))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[4620])).
% 0.96/1.20 tff(4622,assumption,(f(f(c)) = f(f(f(c)))), introduced(assumption)).
% 0.96/1.20 tff(4623,plain,
% 0.96/1.20 (inj_0(f(f(c))) = inj_0(f(f(f(c))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[4622])).
% 0.96/1.20 tff(4624,plain,
% 0.96/1.20 (f(c) = f(f(f(c)))),
% 0.96/1.20 inference(transitivity,[status(thm)],[20, 4623, 46, 4622])).
% 0.96/1.20 tff(4625,plain,
% 0.96/1.20 ($false),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[52, 4624])).
% 0.96/1.20 tff(4626,plain,(~(f(f(c)) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.20 tff(4627,plain,
% 0.96/1.20 (~(f(f(f(c))) = f(f(c)))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[4626, 4621])).
% 0.96/1.20 tff(4628,assumption,(~r(f(f(elem!1)), f(f(c)))), introduced(assumption)).
% 0.96/1.20 tff(4629,assumption,(f(f(elem!1)) = f(f(c))), introduced(assumption)).
% 0.96/1.20 tff(4630,plain,
% 0.96/1.20 (f(f(c)) = f(f(elem!1))),
% 0.96/1.20 inference(symmetry,[status(thm)],[4629])).
% 0.96/1.20 tff(4631,plain,
% 0.96/1.20 (inj_0(f(f(c))) = inj_0(f(f(elem!1)))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[4630])).
% 0.96/1.20 tff(4632,plain,
% 0.96/1.20 (f(c) = f(f(f(elem!1)))),
% 0.96/1.20 inference(transitivity,[status(thm)],[20, 4631, 122, 4568])).
% 0.96/1.20 tff(4633,plain,
% 0.96/1.20 ((f(c) = f(f(f(f(f(elem!1)))))) <=> (f(c) = f(f(f(elem!1))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[4586])).
% 0.96/1.20 tff(4634,plain,
% 0.96/1.20 ((~(f(c) = f(f(f(f(f(elem!1))))))) <=> (~(f(c) = f(f(f(elem!1)))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[4633])).
% 0.96/1.20 tff(4635,plain,
% 0.96/1.20 (~(f(c) = f(f(f(elem!1))))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[981, 4634])).
% 0.96/1.20 tff(4636,plain,
% 0.96/1.20 ($false),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[4635, 4632])).
% 0.96/1.20 tff(4637,plain,(~(f(f(elem!1)) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.20 tff(4638,plain,
% 0.96/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(4639,plain,
% 0.96/1.20 ((r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1)))) <=> (r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(4640,plain,
% 0.96/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4639])).
% 1.04/1.20 tff(4641,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4640, 4638])).
% 1.04/1.20 tff(4642,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4643,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4642, 4641])).
% 1.04/1.20 tff(4644,plain,
% 1.04/1.20 (r(f(f(f(c))), f(f(c)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4643, 205, 1638, 4609, 4637, 4628, 4627])).
% 1.04/1.20 tff(4645,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4646,plain,
% 1.04/1.20 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4647,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4646])).
% 1.04/1.20 tff(4648,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4647, 4645])).
% 1.04/1.20 tff(4649,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4650,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(c, f(f(c))) | (c = f(f(c)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4649, 4648])).
% 1.04/1.20 tff(4651,plain,
% 1.04/1.20 (r(c, f(f(c)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4650, 205, 163, 3495, 4637, 4628, 4605])).
% 1.04/1.20 tff(4652,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4653,plain,
% 1.04/1.20 (((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(c))))) <=> ((c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4654,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4653])).
% 1.04/1.20 tff(4655,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4654, 4652])).
% 1.04/1.20 tff(4656,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(c)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4657,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 1.04/1.20 tff(4658,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4657, 233, 3130, 4618, 4651, 4605, 4627, 4644])).
% 1.04/1.20 tff(4659,plain,(r(f(f(elem!1)), f(f(c))) | r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4660,plain,
% 1.04/1.20 (r(f(f(elem!1)), f(f(c)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4659, 3495, 1638])).
% 1.04/1.20 tff(4661,assumption,(~(f(f(elem!1)) = f(f(f(f(c)))))), introduced(assumption)).
% 1.04/1.20 tff(4662,plain,
% 1.04/1.20 ((f(f(f(c))) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(f(c))))),
% 1.04/1.20 inference(commutativity,[status(thm)],[])).
% 1.04/1.20 tff(4663,plain,
% 1.04/1.20 ((f(f(f(f(c)))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(f(c)))))),
% 1.04/1.20 inference(symmetry,[status(thm)],[4662])).
% 1.04/1.20 tff(4664,plain,
% 1.04/1.20 ((~(f(f(f(f(c)))) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(f(c))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4663])).
% 1.04/1.20 tff(4665,assumption,(f(f(f(f(c)))) = f(f(f(c)))), introduced(assumption)).
% 1.04/1.20 tff(4666,plain,
% 1.04/1.20 (f(f(f(c))) = f(f(f(f(c))))),
% 1.04/1.20 inference(symmetry,[status(thm)],[4665])).
% 1.04/1.20 tff(4667,plain,
% 1.04/1.20 (inj_0(f(f(f(c)))) = inj_0(f(f(f(f(c)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4666])).
% 1.04/1.20 tff(4668,plain,
% 1.04/1.20 (f(f(c)) = f(f(f(c)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[47, 4667, 38])).
% 1.04/1.20 tff(4669,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4626, 4668])).
% 1.04/1.20 tff(4670,plain,(~(f(f(f(f(c)))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4671,plain,
% 1.04/1.20 (~(f(f(f(c))) = f(f(f(f(c)))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4670, 4664])).
% 1.04/1.20 tff(4672,plain,
% 1.04/1.20 (f(f(elem!1)) = elem!1),
% 1.04/1.20 inference(symmetry,[status(thm)],[4567])).
% 1.04/1.20 tff(4673,plain,
% 1.04/1.20 ((f(c) = f(f(elem!1))) <=> (f(c) = elem!1)),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4672])).
% 1.04/1.20 tff(4674,plain,
% 1.04/1.20 ((f(c) = elem!1) <=> (f(c) = f(f(elem!1)))),
% 1.04/1.20 inference(symmetry,[status(thm)],[4673])).
% 1.04/1.20 tff(4675,plain,
% 1.04/1.20 ((~(f(c) = elem!1)) <=> (~(f(c) = f(f(elem!1))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4674])).
% 1.04/1.20 tff(4676,plain,
% 1.04/1.20 (~(f(c) = f(f(elem!1)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4608, 4675])).
% 1.04/1.20 tff(4677,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4678,plain,
% 1.04/1.20 ((r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4679,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4678])).
% 1.04/1.20 tff(4680,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4679, 4677])).
% 1.04/1.20 tff(4681,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4682,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 1.04/1.20 tff(4683,plain,
% 1.04/1.20 (r(f(c), f(f(c)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4682, 205, 4676, 1588, 4637, 4628, 33])).
% 1.04/1.20 tff(4684,assumption,(~r(c, f(c))), introduced(assumption)).
% 1.04/1.20 tff(4685,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4686,plain,
% 1.04/1.20 ((r(c, f(c)) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c))) <=> (r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4687,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4686])).
% 1.04/1.20 tff(4688,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4687, 4685])).
% 1.04/1.20 tff(4689,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | (c = f(f(elem!1))) | (c = f(c)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4690,plain,
% 1.04/1.20 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(elem!1))) | (f(c) = f(f(elem!1))) | r(c, f(c)) | (c = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (c = f(c))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 1.04/1.20 tff(4691,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4690, 205, 4684, 1582, 1588, 163, 3495, 1352])).
% 1.04/1.20 tff(4692,plain,(r(c, f(c)) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4693,plain,
% 1.04/1.20 (r(c, f(c)) | r(f(c), f(f(elem!1))) | r(c, f(f(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4692, 4676])).
% 1.04/1.20 tff(4694,plain,
% 1.04/1.20 (r(c, f(c))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4693, 1588, 3495])).
% 1.04/1.20 tff(4695,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4696,plain,
% 1.04/1.20 (((~r(c, f(c))) | (~r(f(c), f(f(c)))) | (~r(c, f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c))) <=> ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4697,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(c)))) | (~r(c, f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4696])).
% 1.04/1.20 tff(4698,plain,
% 1.04/1.20 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(c)))) | (~r(c, f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4697, 4695])).
% 1.04/1.21 tff(4699,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(c)))) | (~r(c, f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4700,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (c = f(f(c)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 1.04/1.21 tff(4701,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4700, 233, 4694, 1352, 4651, 4605, 4683, 33])).
% 1.04/1.21 tff(4702,plain,(r(f(f(elem!1)), f(f(c))) | r(c, f(f(elem!1))) | r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(4703,plain,
% 1.04/1.21 (r(f(f(elem!1)), f(f(c)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4702, 3495, 1588])).
% 1.04/1.21 tff(4704,plain,
% 1.04/1.21 (r(f(c), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), c)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1868, 4609, 4676])).
% 1.04/1.21 tff(4705,plain,
% 1.04/1.21 (r(f(f(f(c))), f(f(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4704, 3497, 1588])).
% 1.04/1.21 tff(4706,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4707,plain,
% 1.04/1.21 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4708,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4707])).
% 1.04/1.21 tff(4709,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4708, 4706])).
% 1.04/1.21 tff(4710,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4711,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 1.04/1.21 tff(4712,plain,
% 1.04/1.21 ((f(f(elem!1)) = f(f(c))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4711, 233, 4609])).
% 1.04/1.21 tff(4713,plain,
% 1.04/1.21 ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4712, 4627, 4637])).
% 1.04/1.21 tff(4714,plain,
% 1.04/1.21 (~r(f(f(f(c))), f(f(c)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4713, 4705, 4703])).
% 1.04/1.21 tff(4715,plain,
% 1.04/1.21 (r(c, f(c))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4693, 3495, 1588])).
% 1.04/1.21 tff(4716,assumption,(~r(f(f(c)), f(c))), introduced(assumption)).
% 1.04/1.21 tff(4717,plain,
% 1.04/1.21 ((f(f(c)) = f(f(elem!1))) <=> (f(f(elem!1)) = f(f(c)))),
% 1.04/1.21 inference(commutativity,[status(thm)],[])).
% 1.04/1.21 tff(4718,plain,
% 1.04/1.21 ((f(f(elem!1)) = f(f(c))) <=> (f(f(c)) = f(f(elem!1)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[4717])).
% 1.04/1.21 tff(4719,plain,
% 1.04/1.21 ((~(f(f(elem!1)) = f(f(c)))) <=> (~(f(f(c)) = f(f(elem!1))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4718])).
% 1.04/1.21 tff(4720,plain,
% 1.04/1.21 (~(f(f(c)) = f(f(elem!1)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4637, 4719])).
% 1.04/1.21 tff(4721,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4722,plain,
% 1.04/1.21 ((r(f(f(c)), f(c)) | r(f(c), f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(c))) <=> ((f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4723,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4722])).
% 1.04/1.21 tff(4724,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4723, 4721])).
% 1.04/1.21 tff(4725,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(c) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(c)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4726,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(f(elem!1)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 1.04/1.21 tff(4727,plain,
% 1.04/1.21 (r(f(f(c)), f(f(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4726, 205, 4676, 1588, 4716, 32, 4720])).
% 1.04/1.21 tff(4728,assumption,(r(f(f(c)), f(f(elem!1)))), introduced(assumption)).
% 1.04/1.21 tff(4729,assumption,(~r(f(c), f(f(f(f(c)))))), introduced(assumption)).
% 1.04/1.21 tff(4730,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4731,plain,
% 1.04/1.21 ((r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c))) <=> (r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4732,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4731])).
% 1.04/1.21 tff(4733,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4732, 4730])).
% 1.04/1.21 tff(4734,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4735,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 1.04/1.21 tff(4736,plain,
% 1.04/1.21 (r(f(f(c)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c))))) | (f(f(c)) = f(c))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4735, 205])).
% 1.04/1.21 tff(4737,plain,
% 1.04/1.21 (r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(c)) | r(f(c), f(f(f(f(c)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4736, 3679, 32, 54])).
% 1.04/1.21 tff(4738,plain,
% 1.04/1.21 (r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4737, 4729, 4716])).
% 1.04/1.21 tff(4739,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4740,plain,
% 1.04/1.21 (((~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(elem!1)))) <=> ((f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4741,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4740])).
% 1.04/1.21 tff(4742,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4741, 4739])).
% 1.04/1.21 tff(4743,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(elem!1))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4744,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(elem!1))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4743, 4742])).
% 1.04/1.21 tff(4745,plain,
% 1.04/1.21 ((f(f(c)) = f(f(elem!1))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4744, 233, 54])).
% 1.04/1.21 tff(4746,plain,
% 1.04/1.21 (~r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4745, 4738, 4720, 4661, 4728])).
% 1.04/1.21 tff(4747,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4748,plain,
% 1.04/1.21 ((r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4749,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4748])).
% 1.04/1.21 tff(4750,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4749, 4747])).
% 1.04/1.21 tff(4751,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4752,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4751, 4750])).
% 1.04/1.21 tff(4753,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4752, 205, 4676, 1588, 3679, 4729, 4661, 4746])).
% 1.04/1.21 tff(4754,plain,(r(f(c), f(f(f(f(c))))) | r(f(c), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(c)), f(f(elem!1)))) | r(f(f(c)), f(c))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(4755,plain,
% 1.04/1.21 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4754, 4727, 4661, 4716, 1588])).
% 1.04/1.21 tff(4756,assumption,(~r(f(f(f(c))), f(f(c)))), introduced(assumption)).
% 1.04/1.21 tff(4757,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4758,plain,
% 1.04/1.21 ((r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c)))) <=> (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4759,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4758])).
% 1.04/1.21 tff(4760,plain,
% 1.04/1.21 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4759, 4757])).
% 1.04/1.21 tff(4761,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4762,plain,
% 1.04/1.21 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 1.04/1.22 tff(4763,plain,
% 1.04/1.22 (r(f(f(f(c))), f(c))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4762, 205, 1718, 4716, 32, 4627, 4756])).
% 1.04/1.22 tff(4764,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4765,plain,
% 1.04/1.22 (((~r(f(f(f(c))), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c))) <=> ((f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4766,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4765])).
% 1.04/1.22 tff(4767,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[4766, 4764])).
% 1.04/1.22 tff(4768,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4769,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4768, 4767])).
% 1.04/1.22 tff(4770,plain,
% 1.04/1.22 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4769, 233, 1718, 4763, 3679, 4755, 4671])).
% 1.04/1.22 tff(4771,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4772,plain,
% 1.04/1.22 (((~r(c, f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c))) <=> ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4773,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4772])).
% 1.04/1.22 tff(4774,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[4773, 4771])).
% 1.04/1.22 tff(4775,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4776,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 1.04/1.22 tff(4777,plain,
% 1.04/1.22 (~r(c, f(f(f(f(c)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4776, 233, 3299, 1352, 3679, 4755, 4601])).
% 1.04/1.22 tff(4778,plain,
% 1.04/1.22 (r(f(c), c)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1713, 180, 3299])).
% 1.04/1.22 tff(4779,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4780,plain,
% 1.04/1.22 (((~r(f(f(f(c))), f(c))) | (~r(f(c), c)) | (~r(f(f(f(c))), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c))) <=> ((~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4781,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), c)) | (~r(f(f(f(c))), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4780])).
% 1.04/1.22 tff(4782,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), c)) | (~r(f(f(f(c))), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[4781, 4779])).
% 1.04/1.22 tff(4783,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(c))) | (~r(f(c), c)) | (~r(f(f(f(c))), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4784,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4783, 4782])).
% 1.04/1.22 tff(4785,plain,
% 1.04/1.22 (~r(f(f(f(c))), c)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4784, 233, 30, 1669, 4778, 1718, 4763])).
% 1.04/1.22 tff(4786,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4787,plain,
% 1.04/1.22 ((r(f(f(f(c))), c) | r(c, f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c)) <=> ((f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4788,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4787])).
% 1.04/1.22 tff(4789,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[4788, 4786])).
% 1.04/1.22 tff(4790,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(c, f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4791,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 1.04/1.22 tff(4792,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4791, 205, 1669, 4785, 4777, 4601, 4671, 4770])).
% 1.04/1.22 tff(4793,plain,(r(f(f(c)), f(c)) | (~r(c, f(c))) | (f(f(elem!1)) = f(f(f(f(c))))) | r(f(c), f(f(elem!1))) | r(f(f(f(c))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(4794,plain,
% 1.04/1.22 (r(f(f(c)), f(c))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4793, 4715, 4661, 1588, 4714])).
% 1.04/1.22 tff(4795,plain,
% 1.04/1.22 (r(f(c), c)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1713, 180, 4715])).
% 1.04/1.22 tff(4796,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4797,plain,
% 1.04/1.22 (((~r(f(f(c)), f(c))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c))) <=> ((~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4798,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4797])).
% 1.04/1.22 tff(4799,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[4798, 4796])).
% 1.04/1.22 tff(4800,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4801,plain,
% 1.04/1.22 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (f(c) = c) | (f(f(c)) = c) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), c))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 1.04/1.22 tff(4802,plain,
% 1.04/1.22 (~r(f(f(c)), c)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4801, 233, 30, 50, 4795, 4794, 32])).
% 1.04/1.22 tff(4803,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(c)))) | r(f(f(c)), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(c)))) | r(f(f(c)), c))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4804,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(c)))) | r(f(f(c)), c))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(4805,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(c)))) | r(f(f(c)), c)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 1.04/1.22 tff(4806,plain,
% 1.04/1.22 (~r(c, f(f(c)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4805, 180, 4802])).
% 1.04/1.22 tff(4807,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4808,plain,
% 1.04/1.22 ((r(f(f(f(c))), f(f(c))) | r(f(f(c)), c) | r(f(f(f(c))), c) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c)))) <=> ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(4809,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), c) | r(f(f(f(c))), c) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4808])).
% 1.04/1.22 tff(4810,plain,
% 1.04/1.22 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), c) | r(f(f(f(c))), c) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4809, 4807])).
% 1.04/1.23 tff(4811,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), c) | r(f(f(f(c))), c) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4812,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4811, 4810])).
% 1.04/1.23 tff(4813,plain,
% 1.04/1.23 (r(f(f(f(c))), c)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4812, 205, 50, 1669, 4627, 4714, 4802])).
% 1.04/1.23 tff(4814,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4815,plain,
% 1.04/1.23 (((~r(f(f(f(c))), c)) | (~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c)) <=> ((~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4816,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4815])).
% 1.04/1.23 tff(4817,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4816, 4814])).
% 1.04/1.23 tff(4818,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4819,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(c))) | (c = f(c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 1.04/1.23 tff(4820,plain,
% 1.04/1.23 (~r(f(f(f(c))), f(c))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4819, 233, 1669, 4715, 4813, 1718, 1352])).
% 1.04/1.23 tff(4821,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4822,plain,
% 1.04/1.23 ((r(f(f(f(c))), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c))) <=> (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4823,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4822])).
% 1.04/1.23 tff(4824,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4823, 4821])).
% 1.04/1.23 tff(4825,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(c)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4826,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.04/1.23 tff(4827,plain,
% 1.04/1.23 (r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4826, 205, 1718, 1929, 3679, 4729, 4671])).
% 1.04/1.23 tff(4828,assumption,(f(f(elem!1)) = f(c)), introduced(assumption)).
% 1.04/1.23 tff(4829,plain,
% 1.04/1.23 (f(c) = f(f(elem!1))),
% 1.04/1.23 inference(symmetry,[status(thm)],[4828])).
% 1.04/1.23 tff(4830,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4676, 4829])).
% 1.04/1.23 tff(4831,plain,(~(f(f(elem!1)) = f(c))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(4832,assumption,(~r(f(f(elem!1)), f(c))), introduced(assumption)).
% 1.04/1.23 tff(4833,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4834,plain,
% 1.04/1.23 ((r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(c))) <=> (r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4835,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4834])).
% 1.04/1.23 tff(4836,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4835, 4833])).
% 1.04/1.23 tff(4837,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(c)) | r(f(c), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(c)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4838,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(elem!1)) = f(c)) | r(f(f(elem!1)), f(c)) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 1.04/1.23 tff(4839,plain,
% 1.04/1.23 (r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4838, 205, 4832, 3679, 4729, 4661, 4831])).
% 1.04/1.23 tff(4840,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4841,plain,
% 1.04/1.23 (((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1)))) <=> ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4842,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4841])).
% 1.04/1.23 tff(4843,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4842, 4840])).
% 1.04/1.23 tff(4844,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4845,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(elem!1))) | (~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 1.04/1.23 tff(4846,plain,
% 1.04/1.23 ((~r(f(f(f(c))), f(f(elem!1)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4845, 233, 4609])).
% 1.04/1.23 tff(4847,plain,
% 1.04/1.23 ((~r(f(f(f(c))), f(f(elem!1)))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4846, 4671])).
% 1.04/1.23 tff(4848,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4847, 4839, 4827, 4661, 3432])).
% 1.04/1.23 tff(4849,plain,(r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(c)) | r(f(f(f(c))), f(c))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(4850,plain,
% 1.04/1.23 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4849, 4705, 4661, 1592, 4820])).
% 1.04/1.23 tff(4851,plain,
% 1.04/1.23 (~r(c, f(f(f(f(c)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4776, 233, 4715, 1352, 3679, 4850, 4601])).
% 1.04/1.23 tff(4852,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4853,plain,
% 1.04/1.23 (((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c))) <=> ((f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4854,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4853])).
% 1.04/1.23 tff(4855,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4854, 4852])).
% 1.04/1.23 tff(4856,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4857,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4856, 4855])).
% 1.04/1.23 tff(4858,plain,
% 1.04/1.23 ((~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4857, 233, 3679, 54, 32])).
% 1.04/1.23 tff(4859,plain,
% 1.04/1.23 (~r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4858, 4850, 4794])).
% 1.04/1.23 tff(4860,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4861,plain,
% 1.04/1.23 ((r(c, f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c)))) <=> (r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(4862,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c)))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[4861])).
% 1.04/1.23 tff(4863,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[4862, 4860])).
% 1.04/1.23 tff(4864,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(4865,plain,
% 1.04/1.23 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 1.04/1.23 tff(4866,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4865, 205, 4859, 54, 4851, 4601, 4806, 4605])).
% 1.04/1.23 tff(4867,plain,(r(c, f(f(elem!1))) | (f(f(elem!1)) = f(f(f(f(c))))) | r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(4868,plain,
% 1.04/1.23 (r(c, f(f(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4867, 4661, 1588])).
% 1.04/1.23 tff(4869,plain,
% 1.04/1.23 (r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1646, 4676, 4609])).
% 1.04/1.23 tff(4870,plain,
% 1.04/1.23 (r(f(c), f(f(f(c))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4869, 1638, 1588])).
% 1.04/1.23 tff(4871,plain,
% 1.04/1.23 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4872,plain,
% 1.04/1.24 (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c))))) <=> ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4873,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4872])).
% 1.04/1.24 tff(4874,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4873, 4871])).
% 1.04/1.24 tff(4875,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4876,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4875, 4874])).
% 1.04/1.24 tff(4877,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4876, 233, 4870, 52, 4627, 4644, 4683, 33])).
% 1.04/1.24 tff(4878,plain,(r(f(f(elem!1)), f(f(c))) | r(f(c), f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(4879,plain,
% 1.04/1.24 (r(f(f(elem!1)), f(f(c)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4878, 1638, 1588])).
% 1.04/1.24 tff(4880,plain,
% 1.04/1.24 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(c)))) | r(f(f(c)), f(f(elem!1))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(c)))) | r(f(f(c)), f(f(elem!1))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4881,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(elem!1)), f(f(c)))) | r(f(f(c)), f(f(elem!1))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4882,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(elem!1)), f(f(c)))) | r(f(f(c)), f(f(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 1.04/1.24 tff(4883,plain,
% 1.04/1.24 (r(f(f(c)), f(f(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4882, 180, 4879])).
% 1.04/1.24 tff(4884,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4885,plain,
% 1.04/1.24 (((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4886,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4885])).
% 1.04/1.24 tff(4887,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4886, 4884])).
% 1.04/1.24 tff(4888,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(c))) | (c = f(f(elem!1))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4889,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4888, 4887])).
% 1.04/1.24 tff(4890,plain,
% 1.04/1.24 ((f(f(elem!1)) = f(f(c))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4889, 233, 163])).
% 1.04/1.24 tff(4891,plain,
% 1.04/1.24 ((~r(c, f(f(elem!1)))) | (~r(c, f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4890, 4637, 4605])).
% 1.04/1.24 tff(4892,plain,
% 1.04/1.24 (~r(c, f(f(c)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4891, 4879, 4868])).
% 1.04/1.24 tff(4893,plain,
% 1.04/1.24 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4894,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4895,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 1.04/1.24 tff(4896,plain,
% 1.04/1.24 (~r(f(f(c)), c)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4895, 180, 4892])).
% 1.04/1.24 tff(4897,assumption,(~r(f(f(c)), c)), introduced(assumption)).
% 1.04/1.24 tff(4898,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4899,plain,
% 1.04/1.24 (((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1)))) <=> ((c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4900,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4899])).
% 1.04/1.24 tff(4901,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4900, 4898])).
% 1.04/1.24 tff(4902,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4903,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(elem!1))) | (~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 1.04/1.24 tff(4904,plain,
% 1.04/1.24 ((~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4903, 233, 163])).
% 1.04/1.24 tff(4905,plain,
% 1.04/1.24 ((~r(c, f(f(elem!1)))) | (~r(c, f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4904, 4601])).
% 1.04/1.24 tff(4906,plain,
% 1.04/1.24 (~r(c, f(f(f(f(c)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4905, 4595, 4661, 3435])).
% 1.04/1.24 tff(4907,plain,
% 1.04/1.24 ((f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4745, 4720])).
% 1.04/1.24 tff(4908,plain,
% 1.04/1.24 (~r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4907, 4595, 4661, 4728])).
% 1.04/1.24 tff(4909,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4910,plain,
% 1.04/1.24 ((r(f(f(c)), c) | r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c)) <=> ((f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4911,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c)))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4910])).
% 1.04/1.24 tff(4912,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4911, 4909])).
% 1.04/1.24 tff(4913,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4914,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4913, 4912])).
% 1.04/1.24 tff(4915,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4914, 205, 50, 4908, 54, 4906, 4601, 4897])).
% 1.04/1.24 tff(4916,plain,((~r(f(f(elem!1)), f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(c)), f(f(elem!1)))) | (~r(c, f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(4917,plain,
% 1.04/1.24 (~r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4916, 4896, 4661, 4883, 4868])).
% 1.04/1.24 tff(4918,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4919,plain,
% 1.04/1.24 ((r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1)))) <=> (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4920,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4919])).
% 1.04/1.24 tff(4921,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4920, 4918])).
% 1.04/1.24 tff(4922,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4923,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(f(c))) = f(f(elem!1))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4922, 4921])).
% 1.04/1.24 tff(4924,plain,
% 1.04/1.24 (r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4923, 205, 1638, 4609, 4661, 4917, 4671])).
% 1.04/1.24 tff(4925,plain,
% 1.04/1.24 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4752, 205, 4676, 1588, 3679, 4661, 4917])).
% 1.04/1.24 tff(4926,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4927,plain,
% 1.04/1.24 (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c))))) <=> ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(4928,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4927])).
% 1.04/1.24 tff(4929,plain,
% 1.04/1.24 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[4928, 4926])).
% 1.04/1.24 tff(4930,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(4931,plain,
% 1.04/1.24 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 1.04/1.24 tff(4932,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4931, 233, 4870, 52, 3679, 4925, 4671, 4924])).
% 1.04/1.24 tff(4933,plain,(r(f(f(f(c))), f(f(elem!1))) | r(f(c), f(f(elem!1))) | (f(f(elem!1)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(4934,plain,
% 1.04/1.24 (r(f(f(f(c))), f(f(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4933, 4661, 1588])).
% 1.04/1.25 tff(4935,plain,
% 1.04/1.25 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4847, 4839, 4661, 3432])).
% 1.04/1.25 tff(4936,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4937,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4938,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 1.04/1.25 tff(4939,plain,
% 1.04/1.25 (~r(f(f(f(f(c)))), f(f(f(c))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4938, 180, 4935])).
% 1.04/1.25 tff(4940,plain,
% 1.04/1.25 (~r(c, f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4905, 4839, 4661, 3435])).
% 1.04/1.25 tff(4941,plain,
% 1.04/1.25 (r(f(f(f(c))), f(c))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4849, 4729, 4661, 4832, 3432])).
% 1.04/1.25 tff(4942,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4943,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4944,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4943, 4942])).
% 1.04/1.25 tff(4945,plain,
% 1.04/1.25 (r(f(c), f(f(f(c))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4944, 180, 4941])).
% 1.04/1.25 tff(4946,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4947,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4948,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4947, 4946])).
% 1.04/1.25 tff(4949,plain,
% 1.04/1.25 (~r(f(f(f(f(c)))), f(c))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4948, 180, 4729])).
% 1.04/1.25 tff(4950,plain,
% 1.04/1.25 ((f(f(f(f(c)))) = f(c)) <=> (f(c) = f(f(f(f(c)))))),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(4951,plain,
% 1.04/1.25 ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(c))),
% 1.04/1.25 inference(symmetry,[status(thm)],[4950])).
% 1.04/1.25 tff(4952,plain,
% 1.04/1.25 ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(c)))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[4951])).
% 1.04/1.25 tff(4953,plain,
% 1.04/1.25 (~(f(f(f(f(c)))) = f(c))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[3679, 4952])).
% 1.04/1.25 tff(4954,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4955,plain,
% 1.04/1.25 ((r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c)))))) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4956,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[4955])).
% 1.04/1.25 tff(4957,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[4956, 4954])).
% 1.04/1.25 tff(4958,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4959,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 1.04/1.25 tff(4960,plain,
% 1.04/1.25 (r(c, f(c))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4959, 205, 1352, 4940, 4601, 4953, 4949])).
% 1.04/1.25 tff(4961,plain,
% 1.04/1.25 (~r(c, f(f(f(c))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3305, 233, 4960, 4945, 52, 3130, 1352])).
% 1.04/1.25 tff(4962,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4963,plain,
% 1.04/1.25 ((r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(c)))))) <=> (r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4964,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[4963])).
% 1.04/1.25 tff(4965,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[4964, 4962])).
% 1.04/1.25 tff(4966,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(c))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4967,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4966, 4965])).
% 1.04/1.25 tff(4968,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4967, 205, 3130, 4961, 4940, 4601, 4670, 4939])).
% 1.04/1.25 tff(4969,plain,(r(f(c), f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | r(f(f(elem!1)), f(c))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(4970,plain,
% 1.04/1.25 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4969, 4934, 4868, 4661, 1592])).
% 1.04/1.25 tff(4971,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(c)))) | r(f(f(c)), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(c)))) | r(f(f(c)), f(c)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4972,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(c)))) | r(f(f(c)), f(c)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4973,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(c)))) | r(f(f(c)), f(c))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4972, 4971])).
% 1.04/1.25 tff(4974,plain,
% 1.04/1.25 (r(f(f(c)), f(c))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4973, 180, 4683])).
% 1.04/1.25 tff(4975,plain,
% 1.04/1.25 (~r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4858, 4974, 4970])).
% 1.04/1.25 tff(4976,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4977,plain,
% 1.04/1.25 ((r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(c)))) <=> ((f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4978,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[4977])).
% 1.04/1.25 tff(4979,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[4978, 4976])).
% 1.04/1.25 tff(4980,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(c))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4981,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(f(f(elem!1)), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 1.04/1.25 tff(4982,plain,
% 1.04/1.25 (r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4981, 205, 4637, 4628, 4975, 54, 4661])).
% 1.04/1.25 tff(4983,plain,
% 1.04/1.25 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4847, 4982, 4661, 4934])).
% 1.04/1.25 tff(4984,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[439, 180, 3435, 1776])).
% 1.04/1.25 tff(4985,plain,(r(f(f(elem!1)), c) | (~r(c, f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(4986,plain,
% 1.04/1.25 (r(f(f(elem!1)), c)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4985, 4868])).
% 1.04/1.25 tff(4987,assumption,(~(f(f(f(f(c)))) = f(f(elem!1)))), introduced(assumption)).
% 1.04/1.25 tff(4988,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4989,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4990,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4989, 4988])).
% 1.04/1.25 tff(4991,plain,
% 1.04/1.25 (r(f(f(f(f(c)))), f(c))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4990, 180, 4970])).
% 1.04/1.25 tff(4992,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4993,plain,
% 1.04/1.25 (((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c))) <=> ((f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(4994,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[4993])).
% 1.04/1.25 tff(4995,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[4994, 4992])).
% 1.04/1.25 tff(4996,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(4997,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 1.04/1.25 tff(4998,plain,
% 1.04/1.25 (~r(f(f(f(f(c)))), f(f(c)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4997, 233, 4953, 4991, 55, 4683, 33])).
% 1.04/1.25 tff(4999,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(elem!1)))) | r(f(f(elem!1)), f(f(c))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(elem!1)))) | r(f(f(elem!1)), f(f(c))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5000,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(elem!1)))) | r(f(f(elem!1)), f(f(c))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5001,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(elem!1)))) | r(f(f(elem!1)), f(f(c)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 1.04/1.25 tff(5002,plain,
% 1.04/1.25 (~r(f(f(c)), f(f(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5001, 180, 4628])).
% 1.04/1.25 tff(5003,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5004,plain,
% 1.04/1.25 ((r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(elem!1))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c)))) <=> (r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5005,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(elem!1))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5004])).
% 1.04/1.25 tff(5006,plain,
% 1.04/1.25 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(elem!1))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5005, 5003])).
% 1.04/1.25 tff(5007,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(elem!1))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5008,plain,
% 1.04/1.25 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(c)) = f(f(elem!1))) | r(f(f(c)), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 1.04/1.25 tff(5009,plain,
% 1.04/1.25 (r(f(f(f(f(c)))), f(f(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5008, 205, 4720, 5002, 4987, 4998, 55])).
% 1.04/1.26 tff(5010,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5011,plain,
% 1.04/1.26 (((~r(f(f(f(f(c)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5012,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5011])).
% 1.04/1.26 tff(5013,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c)))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.04/1.26 tff(5014,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(elem!1)))) | (~r(f(f(elem!1)), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(elem!1)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(elem!1))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5015,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = c) | (~r(f(f(elem!1)), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.04/1.26 tff(5016,plain,
% 1.04/1.26 ((~r(f(f(elem!1)), c)) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | (f(f(f(f(c)))) = f(f(elem!1))) | (~r(f(f(f(f(c)))), c))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5015, 233, 162, 4600])).
% 1.04/1.26 tff(5017,plain,
% 1.04/1.26 (~r(f(f(f(f(c)))), c)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5016, 5009, 4987, 4986])).
% 1.04/1.26 tff(5018,plain,
% 1.04/1.26 (~r(f(f(f(c))), c)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1675, 233, 162, 1669, 4934, 4609, 4986])).
% 1.04/1.26 tff(5019,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5020,plain,
% 1.04/1.26 ((r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c)))))) <=> ((f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5021,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c)))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5020])).
% 1.04/1.26 tff(5022,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5021, 5019])).
% 1.04/1.26 tff(5023,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5024,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 1.04/1.26 tff(5025,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5024, 205, 1669, 4600, 5018, 5017, 4671, 4983])).
% 1.04/1.26 tff(5026,plain,(r(f(f(elem!1)), f(f(c))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(elem!1))) | r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5027,plain,
% 1.04/1.26 (r(f(f(elem!1)), f(f(c)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5026, 1588, 4593, 4594])).
% 1.04/1.26 tff(5028,plain,
% 1.04/1.26 (r(c, f(f(elem!1)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4867, 1588, 4593])).
% 1.04/1.26 tff(5029,plain,
% 1.04/1.26 (~r(c, f(f(c)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4891, 5028, 5027])).
% 1.04/1.26 tff(5030,plain,
% 1.04/1.26 (~r(f(f(c)), c)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4895, 180, 5029])).
% 1.04/1.26 tff(5031,plain,
% 1.04/1.26 (r(f(f(f(c))), f(f(elem!1)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4933, 1588, 4593])).
% 1.04/1.26 tff(5032,plain,
% 1.04/1.26 (~r(f(f(f(c))), f(f(c)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4713, 5031, 5027])).
% 1.04/1.26 tff(5033,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(c))))) | r(f(f(f(c))), f(f(c))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(c))))) | r(f(f(f(c))), f(f(c))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5034,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(c))))) | r(f(f(f(c))), f(f(c))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5035,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(c))))) | r(f(f(f(c))), f(f(c)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5034, 5033])).
% 1.04/1.26 tff(5036,plain,
% 1.04/1.26 (~r(f(f(c)), f(f(f(c))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5035, 180, 5032])).
% 1.04/1.26 tff(5037,plain,
% 1.04/1.26 (r(f(f(elem!1)), c)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4985, 5028])).
% 1.04/1.26 tff(5038,plain,
% 1.04/1.26 (~r(f(f(f(c))), c)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1675, 233, 162, 1669, 5031, 4609, 5037])).
% 1.04/1.26 tff(5039,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5040,plain,
% 1.04/1.26 ((r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), c) | r(f(f(c)), c) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c))))) <=> ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5041,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), c) | r(f(f(c)), c) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5040])).
% 1.04/1.26 tff(5042,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), c) | r(f(f(c)), c) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5041, 5039])).
% 1.04/1.26 tff(5043,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), c) | r(f(f(c)), c) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5044,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (f(f(f(c))) = c) | r(f(f(f(c))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5043, 5042])).
% 1.04/1.26 tff(5045,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5044, 205, 50, 1669, 5038, 4626, 5036, 5030])).
% 1.04/1.26 tff(5046,plain,(r(f(c), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5047,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5048,plain,
% 1.04/1.26 (((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5049,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5048])).
% 1.04/1.26 tff(5050,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c)))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5049, 5047])).
% 1.04/1.26 tff(5051,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(c)))) | (~r(f(c), f(f(c)))) | (f(f(elem!1)) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(elem!1))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5052,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 1.04/1.26 tff(5053,plain,
% 1.04/1.26 (~r(f(c), f(f(c)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5052, 233, 4676, 5046, 4637, 4660, 33])).
% 1.04/1.26 tff(5054,plain,
% 1.04/1.26 (r(f(f(c)), f(f(elem!1)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4882, 180, 4660])).
% 1.04/1.26 tff(5055,assumption,(~r(f(c), f(f(c)))), introduced(assumption)).
% 1.04/1.26 tff(5056,assumption,(r(f(f(c)), f(c))), introduced(assumption)).
% 1.04/1.26 tff(5057,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(c))) | r(f(c), f(f(c))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(c))) | r(f(c), f(f(c))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5058,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(c))) | r(f(c), f(f(c))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5059,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(c))) | r(f(c), f(f(c)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5058, 5057])).
% 1.04/1.26 tff(5060,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5059, 180, 5056, 5055])).
% 1.04/1.26 tff(5061,plain,((~r(f(f(c)), f(c))) | r(f(c), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5062,plain,
% 1.04/1.26 (~r(f(f(c)), f(c))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5061, 5055])).
% 1.04/1.26 tff(5063,plain,
% 1.04/1.26 (r(f(f(f(c))), f(c))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4762, 205, 1718, 5062, 32, 4627, 4756])).
% 1.04/1.26 tff(5064,plain,
% 1.04/1.26 (~r(c, f(c))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3352, 233, 1718, 5063, 3130, 3591, 1352])).
% 1.04/1.26 tff(5065,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5066,plain,
% 1.04/1.26 ((r(c, f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c))) <=> (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5067,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5066])).
% 1.04/1.26 tff(5068,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5067, 5065])).
% 1.04/1.26 tff(5069,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5070,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5069, 5068])).
% 1.04/1.26 tff(5071,plain,
% 1.04/1.26 (r(c, f(f(c)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5070, 205, 5064, 1352, 4605, 5055, 33])).
% 1.04/1.26 tff(5072,assumption,(r(f(f(c)), f(f(f(f(c)))))), introduced(assumption)).
% 1.04/1.26 tff(5073,plain,
% 1.04/1.26 (~r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4907, 5072, 4593, 4728])).
% 1.04/1.26 tff(5074,assumption,(r(c, f(f(c)))), introduced(assumption)).
% 1.04/1.26 tff(5075,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5076,plain,
% 1.04/1.26 (((~r(c, f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c)))) <=> ((~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5077,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5076])).
% 1.04/1.26 tff(5078,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5077, 5075])).
% 1.04/1.26 tff(5079,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5080,plain,
% 1.04/1.26 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5079, 5078])).
% 1.04/1.26 tff(5081,plain,
% 1.04/1.26 (~r(c, f(f(f(f(c)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5080, 233, 5072, 54, 4601, 5074, 4605])).
% 1.04/1.26 tff(5082,plain,
% 1.04/1.26 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5083,plain,
% 1.04/1.27 ((r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1)))) <=> (r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5084,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5083])).
% 1.04/1.27 tff(5085,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.04/1.27 tff(5086,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(elem!1))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5087,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(elem!1)), f(f(f(f(c))))) | r(c, f(f(elem!1))) | (c = f(f(elem!1))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.04/1.27 tff(5088,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5087, 205, 163, 3495, 5081, 4593, 5073, 4601])).
% 1.04/1.27 tff(5089,plain,((~r(f(f(c)), f(f(f(f(c)))))) | r(c, f(f(elem!1))) | (~r(c, f(f(c)))) | (~r(f(f(c)), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5090,plain,
% 1.04/1.27 (~r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5089, 5071, 3495, 4728])).
% 1.04/1.27 tff(5091,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5092,plain,
% 1.04/1.27 ((r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c)))) <=> (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5093,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5092])).
% 1.04/1.27 tff(5094,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5093, 5091])).
% 1.04/1.27 tff(5095,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5096,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 1.04/1.27 tff(5097,plain,
% 1.04/1.27 (r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5096, 205, 5090, 54, 4627, 4756, 4671])).
% 1.04/1.27 tff(5098,plain,
% 1.04/1.27 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4737, 5090, 5062])).
% 1.04/1.27 tff(5099,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4769, 233, 1718, 5063, 3679, 5098, 4671, 5097])).
% 1.04/1.27 tff(5100,plain,(r(f(f(f(c))), f(f(c))) | r(c, f(f(elem!1))) | (~r(f(f(c)), f(f(elem!1)))) | r(f(c), f(f(c))) | (~r(c, f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5101,plain,
% 1.04/1.27 (r(f(f(f(c))), f(f(c)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5100, 3495, 5054, 5053, 4618])).
% 1.04/1.27 tff(5102,plain,
% 1.04/1.27 (~r(c, f(f(c)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4657, 233, 3130, 4618, 4605, 4627, 5101])).
% 1.04/1.27 tff(5103,assumption,(r(f(f(f(c))), f(f(c)))), introduced(assumption)).
% 1.04/1.27 tff(5104,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5105,plain,
% 1.04/1.27 (((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c)))) <=> ((f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5106,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5105])).
% 1.04/1.27 tff(5107,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5106, 5104])).
% 1.04/1.27 tff(5108,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5109,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5108, 5107])).
% 1.04/1.27 tff(5110,plain,
% 1.04/1.27 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5109, 233, 5072, 54, 4627, 5103, 4671])).
% 1.04/1.27 tff(5111,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4923, 205, 1638, 4609, 4593, 5073, 4671, 5110])).
% 1.04/1.27 tff(5112,plain,((~r(f(f(c)), f(f(f(f(c)))))) | r(f(f(f(c))), f(f(elem!1))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5113,plain,
% 1.04/1.27 (~r(f(f(c)), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5112, 5101, 1638, 5054])).
% 1.04/1.27 tff(5114,plain,
% 1.04/1.27 (r(c, f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4865, 205, 5113, 54, 4601, 5102, 4605])).
% 1.04/1.27 tff(5115,plain,
% 1.04/1.27 (~r(f(f(c)), f(c))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5061, 5053])).
% 1.04/1.27 tff(5116,plain,
% 1.04/1.27 (r(f(c), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4737, 5113, 5115])).
% 1.04/1.27 tff(5117,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5118,plain,
% 1.04/1.27 ((r(c, f(f(c))) | r(f(f(c)), f(c)) | r(c, f(c)) | (f(f(c)) = f(c)) | (c = f(c)) | (c = f(f(c)))) <=> (r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5119,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(c)) | r(c, f(c)) | (f(f(c)) = f(c)) | (c = f(c)) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5118])).
% 1.04/1.27 tff(5120,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(c)) | r(c, f(c)) | (f(f(c)) = f(c)) | (c = f(c)) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5119, 5117])).
% 1.04/1.27 tff(5121,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(c)), f(c)) | r(c, f(c)) | (f(f(c)) = f(c)) | (c = f(c)) | (c = f(f(c))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5122,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(f(c)), f(c)) | (f(f(c)) = f(c)) | r(c, f(f(c))) | (c = f(f(c)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5121, 5120])).
% 1.04/1.27 tff(5123,plain,
% 1.04/1.27 (r(c, f(c))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5122, 205, 1352, 5115, 32, 5102, 4605])).
% 1.04/1.27 tff(5124,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4776, 233, 5123, 1352, 3679, 5116, 5114, 4601])).
% 1.04/1.27 tff(5125,plain,(r(c, f(f(elem!1))) | r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5126,plain,
% 1.04/1.27 (r(c, f(f(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5125, 1638])).
% 1.04/1.27 tff(5127,plain,
% 1.04/1.27 (~r(c, f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4905, 4595, 4593, 3435])).
% 1.04/1.27 tff(5128,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5129,plain,
% 1.04/1.27 (((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1)))) <=> ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5130,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5129])).
% 1.04/1.27 tff(5131,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5130, 5128])).
% 1.04/1.27 tff(5132,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(elem!1)))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5133,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(elem!1)))) | (f(c) = f(f(elem!1))) | (f(c) = f(f(f(f(c))))) | (f(f(elem!1)) = f(f(f(f(c))))) | (~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5132, 5131])).
% 1.04/1.27 tff(5134,plain,
% 1.04/1.27 (~r(f(c), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5133, 233, 4676, 5046, 3679, 4593, 4595])).
% 1.04/1.27 tff(5135,plain,
% 1.04/1.27 ((~r(f(c), c)) | (~r(f(c), f(f(elem!1)))) | (~r(c, f(f(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1938, 4676])).
% 1.04/1.27 tff(5136,plain,
% 1.04/1.27 (~r(f(c), c)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5135, 3435, 5046])).
% 1.04/1.27 tff(5137,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5138,plain,
% 1.04/1.27 ((r(f(c), c) | r(c, f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = c)) <=> ((f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5139,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5138])).
% 1.04/1.27 tff(5140,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5139, 5137])).
% 1.04/1.27 tff(5141,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = c))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5142,plain,
% 1.04/1.27 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5141, 5140])).
% 1.04/1.27 tff(5143,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5142, 205, 30, 5136, 3679, 5134, 5127, 4601])).
% 1.04/1.27 tff(5144,plain,((~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(c, f(f(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5145,plain,
% 1.04/1.27 (~r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5144, 5126])).
% 1.04/1.27 tff(5146,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(c))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(c))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5147,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(c))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5148,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(elem!1)))) | r(f(f(elem!1)), f(f(f(f(c)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5147, 5146])).
% 1.04/1.27 tff(5149,plain,
% 1.04/1.27 (~r(f(f(f(f(c)))), f(f(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5148, 180, 5145])).
% 1.04/1.27 tff(5150,plain,
% 1.04/1.27 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5151,plain,
% 1.04/1.28 ((r(f(f(f(f(c)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(elem!1)))) <=> ((f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5152,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5151])).
% 1.04/1.28 tff(5153,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(elem!1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5152, 5150])).
% 1.04/1.28 tff(5154,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(elem!1))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(elem!1)) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5155,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(elem!1)) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(elem!1)), f(f(c))) | r(f(f(f(f(c)))), f(f(elem!1))) | (f(f(f(f(c)))) = f(f(elem!1))) | (f(f(f(f(c)))) = f(f(c)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 1.04/1.28 tff(5156,plain,
% 1.04/1.28 (r(f(f(f(f(c)))), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5155, 205, 4637, 4628, 5149, 4594, 55])).
% 1.04/1.28 tff(5157,plain,
% 1.04/1.28 (r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4923, 205, 1638, 4609, 4593, 5145, 4671])).
% 1.04/1.28 tff(5158,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5159,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5160,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5159, 5158])).
% 1.04/1.28 tff(5161,plain,
% 1.04/1.28 (r(f(f(f(f(c)))), f(f(f(c))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5160, 180, 5157])).
% 1.04/1.28 tff(5162,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5163,plain,
% 1.04/1.28 (((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c))))) <=> ((f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5164,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5163])).
% 1.04/1.28 tff(5165,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5164, 5162])).
% 1.04/1.28 tff(5166,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5167,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 1.04/1.28 tff(5168,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5167, 233, 4670, 5161, 4627, 4644, 5156, 55])).
% 1.04/1.28 tff(5169,plain,(r(f(f(elem!1)), f(f(c))) | r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(5170,plain,
% 1.04/1.28 (r(f(f(elem!1)), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5169, 1638])).
% 1.04/1.28 tff(5171,plain,
% 1.04/1.28 (~r(f(c), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5052, 233, 4676, 5046, 4637, 5170, 33])).
% 1.04/1.28 tff(5172,plain,
% 1.04/1.28 (~r(c, f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4891, 5170, 5126])).
% 1.04/1.28 tff(5173,plain,
% 1.04/1.28 (~r(f(c), c)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5135, 5126, 5046])).
% 1.04/1.28 tff(5174,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5175,plain,
% 1.04/1.28 ((r(f(c), c) | r(c, f(f(c))) | r(f(c), f(f(c))) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c)) <=> ((f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5176,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(c))) | r(f(c), f(f(c))) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5175])).
% 1.04/1.28 tff(5177,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(c))) | r(f(c), f(f(c))) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5176, 5174])).
% 1.04/1.28 tff(5178,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(c, f(f(c))) | r(f(c), f(f(c))) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5179,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(c))) | r(c, f(f(c))) | (f(c) = f(f(c))) | (c = f(f(c)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5178, 5177])).
% 1.04/1.28 tff(5180,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5179, 205, 30, 5173, 5172, 4605, 5171, 33])).
% 1.04/1.28 tff(5181,plain,(r(f(f(f(c))), f(f(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(5182,plain,
% 1.04/1.28 ((~r(f(f(elem!1)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4847, 4593, 5181])).
% 1.04/1.28 tff(5183,plain,
% 1.04/1.28 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5182, 4595])).
% 1.04/1.28 tff(5184,plain,
% 1.04/1.28 (r(f(c), elem!1) <=> r(f(c), f(f(elem!1)))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[4567])).
% 1.04/1.28 tff(5185,plain,
% 1.04/1.28 (r(f(c), f(f(elem!1))) <=> r(f(c), elem!1)),
% 1.04/1.28 inference(symmetry,[status(thm)],[5184])).
% 1.04/1.28 tff(5186,plain,
% 1.04/1.28 (r(f(c), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5046, 5185])).
% 1.04/1.28 tff(5187,plain,
% 1.04/1.28 (r(f(f(f(c))), elem!1) <=> r(f(f(f(c))), f(f(elem!1)))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[4567])).
% 1.04/1.28 tff(5188,plain,
% 1.04/1.28 (r(f(f(f(c))), f(f(elem!1))) <=> r(f(f(f(c))), elem!1)),
% 1.04/1.28 inference(symmetry,[status(thm)],[5187])).
% 1.04/1.28 tff(5189,plain,
% 1.04/1.28 (r(f(f(f(c))), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5181, 5188])).
% 1.04/1.28 tff(5190,plain,
% 1.04/1.28 ((elem!1 = f(f(f(c)))) <=> (f(f(elem!1)) = f(f(f(c))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[4567])).
% 1.04/1.28 tff(5191,plain,
% 1.04/1.28 ((elem!1 = f(f(f(c)))) <=> (f(f(f(c))) = f(f(elem!1)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5190, 2725])).
% 1.04/1.28 tff(5192,plain,
% 1.04/1.28 ((f(f(f(c))) = f(f(elem!1))) <=> (elem!1 = f(f(f(c))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5191])).
% 1.04/1.28 tff(5193,plain,
% 1.04/1.28 ((f(f(f(c))) = f(f(elem!1))) <=> (f(f(f(c))) = elem!1)),
% 1.04/1.28 inference(transitivity,[status(thm)],[5192, 1612])).
% 1.04/1.28 tff(5194,plain,
% 1.04/1.28 ((~(f(f(f(c))) = f(f(elem!1)))) <=> (~(f(f(f(c))) = elem!1))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5193])).
% 1.04/1.28 tff(5195,plain,
% 1.04/1.28 (~(f(f(f(c))) = elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[4609, 5194])).
% 1.04/1.28 tff(5196,plain,
% 1.04/1.28 ((~r(f(c), elem!1)) | (~r(f(f(f(c))), elem!1)) | (~r(f(c), f(f(f(c)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1654, 4608, 5195])).
% 1.04/1.28 tff(5197,plain,
% 1.04/1.28 (~r(f(c), f(f(f(c))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5196, 5189, 5186])).
% 1.04/1.28 tff(5198,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5199,plain,
% 1.04/1.28 ((r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c))))) <=> (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5200,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5199])).
% 1.04/1.28 tff(5201,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5200, 5198])).
% 1.04/1.28 tff(5202,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(c)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5203,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5202, 5201])).
% 1.04/1.28 tff(5204,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5203, 205, 5197, 52, 3679, 5134, 4671, 5183])).
% 1.04/1.28 tff(5205,plain,(~r(f(f(elem!1)), f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(5206,plain,
% 1.04/1.28 (~r(f(f(f(f(c)))), f(f(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5148, 180, 5205])).
% 1.04/1.28 tff(5207,plain,
% 1.04/1.28 (r(f(f(f(f(c)))), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5155, 205, 4637, 4628, 5206, 4594, 55])).
% 1.04/1.28 tff(5208,plain,
% 1.04/1.28 ((~r(c, f(f(elem!1)))) | (~r(f(f(f(c))), f(f(elem!1)))) | (~r(f(c), f(f(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[3445, 4609, 4676])).
% 1.04/1.28 tff(5209,plain,
% 1.04/1.28 (~r(c, f(f(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5208, 5181, 5046])).
% 1.04/1.28 tff(5210,plain,
% 1.04/1.28 (r(c, f(f(f(f(c)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5087, 205, 163, 5209, 4593, 5205, 4601])).
% 1.04/1.28 tff(5211,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5212,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5213,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5212, 5211])).
% 1.04/1.28 tff(5214,plain,
% 1.04/1.28 (r(f(f(f(f(c)))), c)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5213, 180, 5210])).
% 1.04/1.28 tff(5215,plain,
% 1.04/1.28 (r(c, f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4650, 205, 163, 5209, 4637, 4628, 4605])).
% 1.04/1.28 tff(5216,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5217,plain,
% 1.04/1.28 (((~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c)) <=> ((f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5218,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5217])).
% 1.04/1.28 tff(5219,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5218, 5216])).
% 1.04/1.28 tff(5220,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5221,plain,
% 1.04/1.28 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5220, 5219])).
% 1.04/1.28 tff(5222,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5221, 233, 4600, 5215, 4605, 5214, 5207, 55])).
% 1.04/1.28 tff(5223,plain,(r(f(f(elem!1)), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(5224,plain,
% 1.04/1.28 (~r(f(c), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5052, 233, 4676, 5046, 4637, 5223, 33])).
% 1.04/1.28 tff(5225,plain,
% 1.04/1.28 ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(elem!1)), f(f(c))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4713, 5181])).
% 1.04/1.28 tff(5226,plain,
% 1.04/1.28 (~r(f(f(f(c))), f(f(c)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5225, 5223])).
% 1.04/1.28 tff(5227,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5228,plain,
% 1.04/1.28 ((r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(c))) | r(f(c), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c))))) <=> (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5229,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(c))) | r(f(c), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5228])).
% 1.04/1.28 tff(5230,plain,
% 1.04/1.28 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(c))) | r(f(c), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[5229, 5227])).
% 1.04/1.29 tff(5231,plain,
% 1.04/1.29 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(f(f(f(c))), f(f(c))) | r(f(c), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(5232,plain,
% 1.04/1.29 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[5231, 5230])).
% 1.04/1.29 tff(5233,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5232, 205, 5197, 52, 4627, 5226, 5224, 33])).
% 1.04/1.29 % SZS output end Proof
% 1.04/1.29 % E exiting
%------------------------------------------------------------------------------