%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA119-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 06:33:06 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.46s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA119-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:36:38 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.30/0.46 % SZS status Unsatisfiable
% 0.30/0.46 % SZS output start Proof
% 0.30/0.46 tff(r_type, type, (
% 0.30/0.46 r: ( $i * $i ) > $o)).
% 0.30/0.46 tff(f_type, type, (
% 0.30/0.46 f: $i > $i)).
% 0.30/0.46 tff(c_type, type, (
% 0.30/0.46 c: $i)).
% 0.30/0.46 tff(1,assumption,(f(f(f(f(f(c))))) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.46 tff(2,plain,
% 0.30/0.46 (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[1])).
% 0.30/0.46 tff(3,plain,
% 0.30/0.46 ((~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(4,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f64ck')).
% 0.30/0.46 tff(5,plain,
% 0.30/0.46 (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.30/0.46 tff(6,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.30/0.46 tff(7,plain,(~(f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(8,assumption,(f(f(f(f(c)))) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.46 tff(9,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[8])).
% 0.30/0.46 tff(10,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.46 inference(transitivity,[status(thm)],[9, 8])).
% 0.30/0.46 tff(11,assumption,(~(f(f(f(f(f(c))))) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.46 tff(12,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.30/0.46 tff(13,plain,((~(f(f(f(f(c)))) = f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(14,plain,
% 0.30/0.46 (~(f(f(f(f(c)))) = f(f(f(c))))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[13, 7])).
% 0.30/0.46 tff(15,assumption,(f(f(c)) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.46 tff(16,plain,
% 0.30/0.46 (f(f(f(c))) = f(f(f(f(f(f(c))))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[15])).
% 0.30/0.46 tff(17,plain,
% 0.30/0.46 (f(f(f(f(f(f(c)))))) = f(f(f(c)))),
% 0.30/0.46 inference(symmetry,[status(thm)],[16])).
% 0.30/0.46 tff(18,plain,
% 0.30/0.46 ((~(f(f(f(f(f(f(c)))))) = f(f(f(c))))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(f(c)))))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(19,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(f(c))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f63ck')).
% 0.30/0.46 tff(20,plain,
% 0.30/0.46 (~(f(f(f(f(f(f(c)))))) = f(f(f(c))))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.30/0.46 tff(21,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[20, 17])).
% 0.30/0.46 tff(22,plain,(~(f(f(c)) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(23,assumption,(f(f(f(f(c)))) = f(c)), introduced(assumption)).
% 0.30/0.46 tff(24,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(f(c))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[23])).
% 0.30/0.46 tff(25,plain,
% 0.30/0.46 (f(f(c)) = f(f(f(f(f(c)))))),
% 0.30/0.46 inference(symmetry,[status(thm)],[24])).
% 0.30/0.46 tff(26,assumption,(~(f(f(c)) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.46 tff(27,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.30/0.46 tff(28,plain,((~(f(f(f(f(c)))) = f(c))) | (f(f(c)) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(29,plain,
% 0.30/0.46 (~(f(f(f(f(c)))) = f(c))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.30/0.46 tff(30,assumption,(f(f(f(c))) = f(c)), introduced(assumption)).
% 0.30/0.46 tff(31,plain,
% 0.30/0.46 (f(f(f(f(c)))) = f(f(c))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[30])).
% 0.30/0.46 tff(32,assumption,(f(f(f(f(c)))) = f(f(c))), introduced(assumption)).
% 0.30/0.46 tff(33,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[32])).
% 0.30/0.46 tff(34,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[11, 33])).
% 0.30/0.46 tff(35,plain,((~(f(f(f(f(c)))) = f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(36,plain,
% 0.30/0.46 (~(f(f(f(f(c)))) = f(f(c)))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[35, 7])).
% 0.30/0.46 tff(37,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[36, 31])).
% 0.30/0.46 tff(38,plain,(~(f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(39,plain,
% 0.30/0.46 ((f(f(f(c))) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(f(c))))),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(40,plain,
% 0.30/0.46 ((f(f(f(f(f(c))))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.46 inference(symmetry,[status(thm)],[39])).
% 0.30/0.46 tff(41,plain,
% 0.30/0.46 ((~(f(f(f(f(f(c))))) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[40])).
% 0.30/0.46 tff(42,plain,
% 0.30/0.46 (~(f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[7, 41])).
% 0.30/0.46 tff(43,assumption,(~(f(f(f(c))) = f(c))), introduced(assumption)).
% 0.30/0.46 tff(44,plain,
% 0.30/0.46 ((f(c) = f(f(f(c)))) <=> (f(f(f(c))) = f(c))),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(45,assumption,(f(c) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.46 tff(46,plain,
% 0.30/0.46 (f(f(f(c))) = f(c)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.30/0.46 tff(47,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[43, 46])).
% 0.30/0.46 tff(48,plain,((~(f(c) = f(f(f(c))))) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(49,plain,
% 0.30/0.46 (~(f(c) = f(f(f(c))))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[48, 43])).
% 0.30/0.46 tff(50,assumption,(f(f(f(f(c)))) = c), introduced(assumption)).
% 0.30/0.46 tff(51,plain,
% 0.30/0.46 (c = f(f(f(f(c))))),
% 0.30/0.46 inference(symmetry,[status(thm)],[50])).
% 0.30/0.46 tff(52,assumption,(f(f(f(f(f(c))))) = f(c)), introduced(assumption)).
% 0.30/0.46 tff(53,plain,
% 0.30/0.46 (f(f(f(f(f(f(c)))))) = f(f(c))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.30/0.46 tff(54,plain,
% 0.30/0.46 ((~(f(f(f(f(f(f(c)))))) = f(f(c)))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(55,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f62ck')).
% 0.30/0.46 tff(56,plain,
% 0.30/0.46 (~(f(f(f(f(f(f(c)))))) = f(f(c)))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.30/0.46 tff(57,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.30/0.46 tff(58,plain,(~(f(f(f(f(f(c))))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(59,assumption,(c = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.46 tff(60,plain,
% 0.30/0.46 (f(c) = f(f(f(f(f(c)))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[59])).
% 0.30/0.46 tff(61,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(c)),
% 0.30/0.46 inference(symmetry,[status(thm)],[60])).
% 0.30/0.46 tff(62,assumption,(~(f(f(f(f(f(c))))) = f(c))), introduced(assumption)).
% 0.30/0.46 tff(63,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.30/0.46 tff(64,plain,((~(c = f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(65,plain,
% 0.30/0.46 (~(c = f(f(f(f(c)))))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.30/0.46 tff(66,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[65, 51])).
% 0.30/0.46 tff(67,plain,(~(f(f(f(f(c)))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(68,assumption,(f(f(c)) = f(c)), introduced(assumption)).
% 0.30/0.46 tff(69,plain,
% 0.30/0.46 (f(f(f(c))) = f(f(c))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[68])).
% 0.30/0.46 tff(70,plain,
% 0.30/0.46 (f(f(f(c))) = f(c)),
% 0.30/0.46 inference(transitivity,[status(thm)],[69, 68])).
% 0.30/0.46 tff(71,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[43, 70])).
% 0.30/0.46 tff(72,plain,((~(f(f(c)) = f(c))) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(73,plain,
% 0.30/0.46 (~(f(f(c)) = f(c))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[72, 43])).
% 0.30/0.46 tff(74,plain,
% 0.30/0.46 ((f(c) = f(f(c))) <=> (f(f(c)) = f(c))),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(75,assumption,(f(c) = f(f(c))), introduced(assumption)).
% 0.30/0.46 tff(76,plain,
% 0.30/0.46 (f(f(c)) = f(c)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.30/0.46 tff(77,assumption,(~(f(f(c)) = f(c))), introduced(assumption)).
% 0.30/0.46 tff(78,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.30/0.46 tff(79,plain,((~(f(c) = f(f(c)))) | (f(f(c)) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(80,plain,
% 0.30/0.46 (~(f(c) = f(f(c)))),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.30/0.46 tff(81,assumption,(~r(f(f(f(c))), f(c))), introduced(assumption)).
% 0.30/0.46 tff(82,assumption,(f(f(f(f(c)))) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.46 tff(83,plain,
% 0.30/0.46 (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.30/0.46 inference(symmetry,[status(thm)],[82])).
% 0.30/0.46 tff(84,plain,
% 0.30/0.46 (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[83])).
% 0.30/0.46 tff(85,plain,
% 0.30/0.46 (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.30/0.46 inference(transitivity,[status(thm)],[84, 83])).
% 0.30/0.46 tff(86,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[5, 85])).
% 0.30/0.46 tff(87,plain,(~(f(f(f(f(c)))) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(88,assumption,(~r(f(f(c)), f(c))), introduced(assumption)).
% 0.30/0.46 tff(89,assumption,(~r(f(f(f(f(c)))), f(c))), introduced(assumption)).
% 0.30/0.46 tff(90,plain,
% 0.30/0.46 (^[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)))),
% 0.30/0.46 inference(bind,[status(th)],[])).
% 0.30/0.46 tff(91,plain,
% 0.30/0.46 (![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))),
% 0.30/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.30/0.46 tff(92,plain,
% 0.30/0.46 (![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))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(93,plain,
% 0.30/0.46 (^[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))))),
% 0.30/0.46 inference(bind,[status(th)],[])).
% 0.30/0.46 tff(94,plain,
% 0.30/0.46 (![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))),
% 0.30/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.30/0.46 tff(95,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')).
% 0.30/0.46 tff(96,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.30/0.46 tff(97,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.30/0.46 tff(98,plain,(
% 0.30/0.46 ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(skolemize,[status(sab)],[97])).
% 0.30/0.46 tff(99,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.30/0.46 tff(100,plain,
% 0.30/0.46 (((~![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(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(101,plain,
% 0.30/0.46 ((r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c)))) <=> ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(102,plain,
% 0.30/0.47 (((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = 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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.30/0.47 tff(103,plain,
% 0.30/0.47 (((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = 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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.47 inference(transitivity,[status(thm)],[102, 100])).
% 0.30/0.47 tff(104,plain,
% 0.30/0.47 ((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(105,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.30/0.47 tff(106,plain,
% 0.30/0.47 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.30/0.47 tff(107,plain,
% 0.30/0.47 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[106, 36])).
% 0.30/0.47 tff(108,plain,
% 0.30/0.47 (r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[107, 89, 73, 88, 29])).
% 0.30/0.47 tff(109,assumption,(f(f(c)) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.47 tff(110,plain,
% 0.30/0.47 (f(f(f(c))) = f(f(c))),
% 0.30/0.47 inference(symmetry,[status(thm)],[109])).
% 0.30/0.47 tff(111,plain,
% 0.30/0.47 (f(f(f(f(c)))) = f(f(f(c)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[110])).
% 0.30/0.47 tff(112,plain,
% 0.30/0.47 (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[111])).
% 0.30/0.47 tff(113,plain,
% 0.30/0.47 (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.47 inference(transitivity,[status(thm)],[112, 111])).
% 0.30/0.47 tff(114,plain,
% 0.30/0.47 ($false),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[11, 113])).
% 0.30/0.47 tff(115,plain,((~(f(f(c)) = f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47 tff(116,plain,
% 0.30/0.47 (~(f(f(c)) = f(f(f(c))))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[115, 7])).
% 0.30/0.47 tff(117,plain,
% 0.30/0.47 (((~![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(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(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)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(118,plain,
% 0.30/0.47 ((r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(c))))) <=> ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(119,plain,
% 0.30/0.47 (((~![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))), f(c)) | r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | (f(f(c)) = 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)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c))))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[118])).
% 0.30/0.47 tff(120,plain,
% 0.30/0.47 (((~![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))), f(c)) | r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | (f(f(c)) = 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)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.47 inference(transitivity,[status(thm)],[119, 117])).
% 0.30/0.47 tff(121,plain,
% 0.30/0.47 ((~![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))), f(c)) | r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(122,plain,
% 0.30/0.47 ((~![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(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c))))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.30/0.47 tff(123,plain,
% 0.30/0.47 ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c))))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[122, 99])).
% 0.30/0.47 tff(124,plain,
% 0.30/0.47 ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), f(f(f(c))))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[123, 116])).
% 0.30/0.47 tff(125,plain,
% 0.30/0.47 (r(f(f(c)), f(f(f(c))))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[124, 81, 73, 88, 43])).
% 0.30/0.47 tff(126,plain,
% 0.30/0.47 (^[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)))),
% 0.30/0.47 inference(bind,[status(th)],[])).
% 0.30/0.47 tff(127,plain,
% 0.30/0.47 (![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))),
% 0.30/0.47 inference(quant_intro,[status(thm)],[126])).
% 0.30/0.47 tff(128,plain,
% 0.30/0.47 (![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))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(129,plain,
% 0.30/0.47 (^[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))))),
% 0.30/0.47 inference(bind,[status(th)],[])).
% 0.30/0.47 tff(130,plain,
% 0.30/0.47 (![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))),
% 0.30/0.47 inference(quant_intro,[status(thm)],[129])).
% 0.30/0.47 tff(131,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')).
% 0.30/0.47 tff(132,plain,
% 0.30/0.47 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.30/0.47 tff(133,plain,
% 0.30/0.47 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.30/0.47 tff(134,plain,(
% 0.30/0.47 ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(skolemize,[status(sab)],[133])).
% 0.30/0.47 tff(135,plain,
% 0.30/0.47 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.30/0.47 tff(136,plain,
% 0.30/0.47 (((~![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(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(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(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(f(c))))))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(137,plain,
% 0.30/0.47 (((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(c)))) <=> ((f(f(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(f(c))))))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(138,plain,
% 0.30/0.47 (((~![Z: $i, 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(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(f(c)))))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[137])).
% 0.30/0.47 tff(139,plain,
% 0.30/0.47 (((~![Z: $i, 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(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(f(c))))))),
% 0.30/0.47 inference(transitivity,[status(thm)],[138, 136])).
% 0.30/0.47 tff(140,plain,
% 0.30/0.47 ((~![Z: $i, 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(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(c))))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(141,plain,
% 0.30/0.47 ((~![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(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (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(f(c)))))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.30/0.48 tff(142,plain,
% 0.30/0.48 (~r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[141, 135, 125, 116, 36, 108, 14])).
% 0.30/0.48 tff(143,plain,
% 0.30/0.48 (((~![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)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(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(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(144,plain,
% 0.30/0.48 ((r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(c))))) <=> ((f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(145,plain,
% 0.30/0.48 (((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(c)))) = 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(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.30/0.48 tff(146,plain,
% 0.30/0.48 (((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(c)))) = 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(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.30/0.48 tff(147,plain,
% 0.30/0.48 ((~![Z: $i, 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(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(148,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.30/0.48 tff(149,plain,
% 0.30/0.48 ($false),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[148, 99, 43, 81, 89, 29, 14, 142])).
% 0.30/0.48 tff(150,plain,(r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48 tff(151,plain,
% 0.30/0.48 (r(f(f(f(f(c)))), f(c))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[150, 88, 43, 81])).
% 0.30/0.48 tff(152,plain,
% 0.30/0.48 ((f(f(f(f(f(c))))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(f(c))))))),
% 0.30/0.48 inference(commutativity,[status(thm)],[])).
% 0.30/0.48 tff(153,plain,
% 0.30/0.48 ((f(f(c)) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.48 inference(symmetry,[status(thm)],[152])).
% 0.30/0.48 tff(154,plain,
% 0.30/0.48 ((~(f(f(c)) = f(f(f(f(f(c))))))) <=> (~(f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.30/0.48 tff(155,plain,
% 0.30/0.48 (~(f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[22, 154])).
% 0.30/0.48 tff(156,plain,
% 0.30/0.48 ((f(f(c)) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(c)))),
% 0.30/0.48 inference(commutativity,[status(thm)],[])).
% 0.30/0.48 tff(157,plain,
% 0.30/0.48 ((f(f(f(c))) = f(f(c))) <=> (f(f(c)) = f(f(f(c))))),
% 0.30/0.48 inference(symmetry,[status(thm)],[156])).
% 0.30/0.48 tff(158,assumption,(f(f(f(c))) = f(f(c))), introduced(assumption)).
% 0.30/0.48 tff(159,plain,
% 0.30/0.48 (f(f(c)) = f(f(f(c)))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.30/0.48 tff(160,assumption,(~(f(f(c)) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.48 tff(161,plain,
% 0.30/0.48 ($false),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.30/0.48 tff(162,plain,((~(f(f(f(c))) = f(f(c)))) | (f(f(c)) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48 tff(163,plain,
% 0.30/0.48 (~(f(f(f(c))) = f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[162, 116])).
% 0.30/0.48 tff(164,plain,
% 0.30/0.48 (((~![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(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(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))) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(165,plain,
% 0.30/0.48 ((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)))) <=> ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(166,plain,
% 0.30/0.48 (((~![Z: $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))) | ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[165])).
% 0.30/0.48 tff(167,plain,
% 0.30/0.48 (((~![Z: $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))) | (f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.30/0.48 inference(transitivity,[status(thm)],[166, 164])).
% 0.30/0.48 tff(168,plain,
% 0.30/0.48 ((~![Z: $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))))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(169,plain,
% 0.30/0.48 ((~![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(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.30/0.48 tff(170,plain,
% 0.30/0.48 ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[169, 99])).
% 0.30/0.48 tff(171,plain,
% 0.30/0.48 ((f(f(c)) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(c)), f(c)) | r(f(f(f(c))), f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[170, 163])).
% 0.30/0.48 tff(172,plain,
% 0.30/0.48 (r(f(f(f(c))), f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[171, 81, 73, 88, 43])).
% 0.30/0.48 tff(173,assumption,(~r(f(f(f(f(f(c))))), f(c))), introduced(assumption)).
% 0.30/0.48 tff(174,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(175,plain,
% 0.30/0.48 ((r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(176,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c))))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[175])).
% 0.30/0.48 tff(177,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.48 inference(transitivity,[status(thm)],[176, 174])).
% 0.30/0.48 tff(178,plain,
% 0.30/0.48 ((~![Z: $i, 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(c))))), f(f(f(c)))) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(179,plain,
% 0.30/0.48 ((~![Z: $i, 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(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c))))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.30/0.48 tff(180,plain,
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% 0.30/0.48 inference(unit_resolution,[status(thm)],[179, 99])).
% 0.30/0.48 tff(181,plain,
% 0.30/0.48 (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[180, 7])).
% 0.30/0.48 tff(182,plain,
% 0.30/0.48 (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[181, 173, 43, 81, 58])).
% 0.30/0.48 tff(183,plain,
% 0.30/0.48 (((~![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(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(184,plain,
% 0.30/0.48 ((r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(c)))) <=> ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(185,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[184])).
% 0.30/0.48 tff(186,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.48 inference(transitivity,[status(thm)],[185, 183])).
% 0.30/0.48 tff(187,plain,
% 0.30/0.48 ((~![Z: $i, 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(c))))), f(f(c))) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(188,plain,
% 0.30/0.48 ((~![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(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.30/0.48 tff(189,plain,
% 0.30/0.48 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[188, 99])).
% 0.30/0.48 tff(190,plain,
% 0.30/0.48 (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[189, 173, 88, 58, 155, 73])).
% 0.30/0.48 tff(191,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(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))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(192,plain,
% 0.30/0.48 (((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(f(c))))) <=> ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(193,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[192])).
% 0.30/0.48 tff(194,plain,
% 0.30/0.48 (((~![Z: $i, 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(c))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.30/0.49 inference(transitivity,[status(thm)],[193, 191])).
% 0.30/0.49 tff(195,plain,
% 0.30/0.49 ((~![Z: $i, 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(c))))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(196,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.30/0.49 tff(197,plain,
% 0.30/0.49 ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[196, 135])).
% 0.30/0.49 tff(198,plain,
% 0.30/0.49 ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[197, 163, 7])).
% 0.30/0.49 tff(199,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[198, 190, 182, 172, 155])).
% 0.30/0.49 tff(200,plain,(r(f(f(f(f(f(c))))), f(c)) | r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(201,plain,
% 0.30/0.49 (r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[200, 88, 43, 81])).
% 0.30/0.49 tff(202,plain,
% 0.30/0.49 (^[Y: $i, X: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.30/0.49 inference(bind,[status(th)],[])).
% 0.30/0.49 tff(203,plain,
% 0.30/0.49 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.49 inference(quant_intro,[status(thm)],[202])).
% 0.30/0.49 tff(204,plain,
% 0.30/0.49 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(205,axiom,(![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rsym')).
% 0.30/0.49 tff(206,plain,
% 0.30/0.49 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.30/0.49 tff(207,plain,(
% 0.30/0.49 ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.49 inference(skolemize,[status(sab)],[206])).
% 0.30/0.49 tff(208,plain,
% 0.30/0.49 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.30/0.49 tff(209,plain,
% 0.30/0.49 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(c))) | r(f(c), f(f(f(f(f(c)))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(c))) | r(f(c), f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(210,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(c))) | r(f(c), f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(211,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(c))) | r(f(c), f(f(f(f(f(c))))))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.30/0.49 tff(212,plain,
% 0.30/0.49 (r(f(c), f(f(f(f(f(c))))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[211, 208, 201])).
% 0.30/0.49 tff(213,plain,
% 0.30/0.49 ((f(c) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(c))),
% 0.30/0.49 inference(commutativity,[status(thm)],[])).
% 0.30/0.49 tff(214,plain,
% 0.30/0.49 ((f(f(f(f(f(c))))) = f(c)) <=> (f(c) = f(f(f(f(f(c))))))),
% 0.30/0.49 inference(symmetry,[status(thm)],[213])).
% 0.30/0.49 tff(215,plain,
% 0.30/0.49 ((~(f(f(f(f(f(c))))) = f(c))) <=> (~(f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[214])).
% 0.30/0.49 tff(216,plain,
% 0.30/0.49 (~(f(c) = f(f(f(f(f(c))))))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[58, 215])).
% 0.30/0.49 tff(217,plain,
% 0.30/0.49 (((~![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(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(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(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
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% 0.30/0.49 (((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c))) <=> ((f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(219,plain,
% 0.30/0.49 (((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[218])).
% 0.30/0.49 tff(220,plain,
% 0.30/0.49 (((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.49 inference(transitivity,[status(thm)],[219, 217])).
% 0.30/0.49 tff(221,plain,
% 0.30/0.49 ((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(222,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.30/0.49 tff(223,plain,
% 0.30/0.49 (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[222, 135, 216, 212, 151, 29, 87])).
% 0.30/0.49 tff(224,plain,
% 0.30/0.49 ((f(f(f(f(c)))) = c) <=> (c = f(f(f(f(c)))))),
% 0.30/0.49 inference(commutativity,[status(thm)],[])).
% 0.30/0.49 tff(225,plain,
% 0.30/0.49 ((c = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = c)),
% 0.30/0.49 inference(symmetry,[status(thm)],[224])).
% 0.30/0.49 tff(226,plain,
% 0.30/0.49 ((~(c = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = c))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[225])).
% 0.30/0.49 tff(227,plain,
% 0.30/0.49 (~(f(f(f(f(c)))) = c)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[65, 226])).
% 0.30/0.49 tff(228,assumption,(c = f(c)), introduced(assumption)).
% 0.30/0.49 tff(229,plain,
% 0.30/0.49 (f(c) = c),
% 0.30/0.49 inference(symmetry,[status(thm)],[228])).
% 0.30/0.49 tff(230,plain,
% 0.30/0.49 (f(f(c)) = f(c)),
% 0.30/0.49 inference(monotonicity,[status(thm)],[229])).
% 0.30/0.49 tff(231,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[77, 230])).
% 0.30/0.49 tff(232,plain,((~(c = f(c))) | (f(f(c)) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(233,plain,
% 0.30/0.49 (~(c = f(c))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[232, 73])).
% 0.30/0.49 tff(234,assumption,(c = f(f(f(c)))), introduced(assumption)).
% 0.30/0.49 tff(235,plain,
% 0.30/0.49 (f(c) = f(f(f(f(c))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[234])).
% 0.30/0.49 tff(236,plain,
% 0.30/0.49 (f(f(c)) = f(f(f(f(f(c)))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.30/0.49 tff(237,plain,
% 0.30/0.49 (f(f(f(f(f(c))))) = f(f(c))),
% 0.30/0.49 inference(symmetry,[status(thm)],[236])).
% 0.30/0.49 tff(238,plain,
% 0.30/0.49 (f(f(f(f(f(f(c)))))) = f(f(f(c)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[237])).
% 0.30/0.49 tff(239,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[20, 238])).
% 0.30/0.49 tff(240,plain,(~(c = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(241,assumption,(~r(c, f(c))), introduced(assumption)).
% 0.30/0.49 tff(242,assumption,(~(c = f(c))), introduced(assumption)).
% 0.30/0.49 tff(243,plain,
% 0.30/0.49 (((~![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)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(244,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(245,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.30/0.49 tff(246,plain,
% 0.30/0.49 (~r(f(c), f(f(f(c))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[245, 208, 81])).
% 0.30/0.49 tff(247,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(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(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(248,plain,
% 0.30/0.49 ((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))) <=> ((c = f(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(249,plain,
% 0.30/0.49 (((~![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))) | ((c = f(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[248])).
% 0.30/0.49 tff(250,plain,
% 0.30/0.49 (((~![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))) | (c = f(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.49 inference(transitivity,[status(thm)],[249, 247])).
% 0.30/0.49 tff(251,plain,
% 0.30/0.49 ((~![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)))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(252,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | r(c, f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.30/0.49 tff(253,plain,
% 0.30/0.49 (r(c, f(f(f(c))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[252, 99, 246, 49, 242, 241, 240])).
% 0.30/0.49 tff(254,plain,
% 0.30/0.49 ((c = f(c)) <=> (f(c) = c)),
% 0.30/0.49 inference(commutativity,[status(thm)],[])).
% 0.30/0.49 tff(255,plain,
% 0.30/0.49 ((f(c) = c) <=> (c = f(c))),
% 0.30/0.49 inference(symmetry,[status(thm)],[254])).
% 0.30/0.49 tff(256,assumption,(f(c) = c), introduced(assumption)).
% 0.30/0.49 tff(257,plain,
% 0.30/0.49 (c = f(c)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.30/0.49 tff(258,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[242, 257])).
% 0.30/0.49 tff(259,plain,((~(f(c) = c)) | (c = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(260,plain,
% 0.30/0.49 (~(f(c) = c)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[259, 242])).
% 0.30/0.49 tff(261,assumption,(r(f(c), c)), introduced(assumption)).
% 0.30/0.49 tff(262,plain,
% 0.30/0.49 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), c)) | r(c, f(c)))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), c)) | r(c, f(c)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(263,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), c)) | r(c, f(c)))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(264,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), c)) | r(c, f(c))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.30/0.49 tff(265,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[264, 208, 261, 241])).
% 0.30/0.49 tff(266,plain,((~r(f(c), c)) | r(c, f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(267,plain,
% 0.30/0.49 (~r(f(c), c)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[266, 241])).
% 0.30/0.49 tff(268,assumption,(~(c = f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.49 tff(269,assumption,(~(f(f(f(f(c)))) = f(c))), introduced(assumption)).
% 0.30/0.49 tff(270,plain,
% 0.30/0.49 (r(f(f(c)), f(f(f(c))))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[124, 88, 73, 81, 43])).
% 0.30/0.49 tff(271,assumption,(c = f(f(c))), introduced(assumption)).
% 0.30/0.49 tff(272,plain,
% 0.30/0.49 (f(c) = f(f(f(c)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.30/0.49 tff(273,plain,
% 0.30/0.49 (f(f(f(c))) = f(c)),
% 0.30/0.49 inference(symmetry,[status(thm)],[272])).
% 0.30/0.49 tff(274,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[43, 273])).
% 0.30/0.49 tff(275,plain,((~(c = f(f(c)))) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(276,plain,
% 0.30/0.49 (~(c = f(f(c)))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[275, 43])).
% 0.30/0.49 tff(277,plain,
% 0.30/0.49 (((~![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(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(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)) = f(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(278,plain,
% 0.30/0.49 ((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)))) <=> ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c))))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(279,plain,
% 0.30/0.49 (((~![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))) | ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c)))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[278])).
% 0.30/0.49 tff(280,plain,
% 0.30/0.49 (((~![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))) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c))))),
% 0.30/0.49 inference(transitivity,[status(thm)],[279, 277])).
% 0.30/0.49 tff(281,plain,
% 0.30/0.49 ((~![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))))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(282,plain,
% 0.30/0.49 ((~![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(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c)))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.30/0.49 tff(283,plain,
% 0.30/0.49 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(c))) | r(c, f(f(c)))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[282, 99])).
% 0.30/0.49 tff(284,plain,
% 0.30/0.49 (r(c, f(f(c)))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[283, 88, 73, 242, 241, 276])).
% 0.30/0.50 tff(285,assumption,(~(c = f(f(f(c))))), introduced(assumption)).
% 0.30/0.50 tff(286,assumption,(r(c, f(f(c)))), introduced(assumption)).
% 0.30/0.50 tff(287,assumption,(r(f(f(c)), f(f(f(c))))), introduced(assumption)).
% 0.30/0.50 tff(288,plain,
% 0.30/0.50 (((~![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(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, 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))) | (f(f(c)) = f(f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(c))))))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(289,plain,
% 0.30/0.50 (((~r(c, f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(c)))) <=> ((f(f(c)) = f(f(f(c)))) | (c = f(f(c))) | (~r(f(f(c)), f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(c))))))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(290,plain,
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% 0.30/0.50 inference(monotonicity,[status(thm)],[289])).
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% 0.30/0.50 inference(unit_resolution,[status(thm)],[294, 285])).
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% 0.30/0.50 inference(unit_resolution,[status(thm)],[301, 99, 43, 81, 242, 241, 295, 285])).
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% 0.30/0.50 (r(f(f(c)), f(c))),
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% 0.30/0.50 tff(309,assumption,(r(f(f(c)), f(c))), introduced(assumption)).
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% 0.30/0.50 inference(unit_resolution,[status(thm)],[312, 208, 309, 308])).
% 0.30/0.50 tff(314,plain,((~r(f(f(c)), f(c))) | r(f(c), f(f(c)))), inference(lemma,lemma(discharge,[]))).
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% 0.30/0.50 inference(unit_resolution,[status(thm)],[314, 307])).
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% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(318,axiom,(~(f(f(f(f(f(f(c)))))) = f(c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f6ck')).
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% 0.30/0.50 inference(modus_ponens,[status(thm)],[318, 317])).
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% 0.30/0.50 (((~![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(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(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(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))))),
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% 0.30/0.50 ((f(f(f(f(c)))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(f(c)))))),
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% 0.30/0.51 inference(commutativity,[status(thm)],[])).
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% 0.30/0.51 inference(symmetry,[status(thm)],[340])).
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% 0.30/0.51 ((~(c = f(f(f(c))))) <=> (~(f(f(f(c))) = c))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[341])).
% 0.30/0.51 tff(343,plain,
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% 0.30/0.51 inference(modus_ponens,[status(thm)],[240, 342])).
% 0.30/0.51 tff(344,plain,
% 0.30/0.51 (((~![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))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (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(c) = c) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(345,plain,
% 0.30/0.51 ((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))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(346,plain,
% 0.30/0.51 (((~![Z: $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))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (f(f(f(c))) = c) | r(f(f(f(c))), c)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[345])).
% 0.30/0.51 tff(347,plain,
% 0.30/0.51 (((~![Z: $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))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.51 inference(transitivity,[status(thm)],[346, 344])).
% 0.30/0.51 tff(348,plain,
% 0.30/0.51 ((~![Z: $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)))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(349,plain,
% 0.30/0.51 ((~![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))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(c), c) | (f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.30/0.51 tff(350,plain,
% 0.30/0.51 ((f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[349, 99, 260, 267, 43, 81])).
% 0.30/0.51 tff(351,plain,
% 0.30/0.51 (r(f(f(f(c))), c)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[350, 343])).
% 0.30/0.51 tff(352,plain,
% 0.30/0.51 (((~![Z: $i, 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)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(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))) | r(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(353,plain,
% 0.30/0.51 ((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(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(354,plain,
% 0.30/0.51 (((~![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(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[353])).
% 0.30/0.51 tff(355,plain,
% 0.30/0.51 (((~![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(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[354, 352])).
% 0.30/0.51 tff(356,plain,
% 0.30/0.51 ((~![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))))))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(357,plain,
% 0.30/0.51 ((~![Z: $i, 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)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.30/0.51 tff(358,plain,
% 0.30/0.51 (r(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[357, 99])).
% 0.30/0.51 tff(359,plain,
% 0.30/0.51 (r(c, f(f(f(f(c)))))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[358, 269, 268, 241, 242, 89])).
% 0.30/0.51 tff(360,plain,
% 0.30/0.51 (((~![Z: $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)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(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))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(361,plain,
% 0.30/0.51 (((~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)) <=> ((~r(f(f(f(c))), f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(362,plain,
% 0.30/0.51 (((~![Z: $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))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[361])).
% 0.30/0.51 tff(363,plain,
% 0.30/0.51 (((~![Z: $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))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.51 inference(transitivity,[status(thm)],[362, 360])).
% 0.30/0.51 tff(364,plain,
% 0.30/0.51 ((~![Z: $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))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(365,plain,
% 0.30/0.51 ((~![Z: $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)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.30/0.51 tff(366,plain,
% 0.30/0.51 ((~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[365, 135, 268, 359, 351, 343])).
% 0.30/0.51 tff(367,plain,
% 0.30/0.51 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[366, 339])).
% 0.30/0.51 tff(368,plain,
% 0.30/0.51 (((~![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))))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(369,plain,
% 0.30/0.51 ((~![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))))))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(370,plain,
% 0.30/0.51 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.30/0.51 tff(371,plain,
% 0.30/0.51 (~r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[370, 208, 367])).
% 0.30/0.51 tff(372,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[148, 99, 43, 81, 89, 269, 338, 371])).
% 0.30/0.51 tff(373,plain,((f(f(f(f(c)))) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(c)))) | (c = f(f(f(f(c))))) | r(c, f(c)) | (c = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(374,plain,
% 0.30/0.51 (r(f(f(f(f(c)))), f(c))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[373, 334, 81, 43, 269, 268, 241, 242])).
% 0.30/0.51 tff(375,plain,
% 0.30/0.51 (((~![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(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(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))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(376,plain,
% 0.30/0.51 (((~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))) <=> ((~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(377,plain,
% 0.30/0.51 (((~![Z: $i, 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))) | ((~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c)))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[376])).
% 0.30/0.51 tff(378,plain,
% 0.30/0.51 (((~![Z: $i, 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))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))))),
% 0.30/0.51 inference(transitivity,[status(thm)],[377, 375])).
% 0.30/0.51 tff(379,plain,
% 0.30/0.51 ((~![Z: $i, 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)))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(380,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c)))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.30/0.51 tff(381,plain,
% 0.30/0.51 ((f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[380, 135, 374, 269, 333, 332])).
% 0.30/0.51 tff(382,plain,
% 0.30/0.51 (~r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[381, 331])).
% 0.30/0.51 tff(383,plain,
% 0.30/0.51 ((f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.30/0.51 inference(commutativity,[status(thm)],[])).
% 0.30/0.51 tff(384,plain,
% 0.30/0.51 ((f(f(f(f(f(f(c)))))) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.30/0.51 inference(symmetry,[status(thm)],[383])).
% 0.30/0.51 tff(385,plain,
% 0.30/0.51 ((~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(f(f(f(f(f(c))))))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[384])).
% 0.30/0.51 tff(386,plain,
% 0.30/0.51 (~(f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[5, 385])).
% 0.30/0.51 tff(387,assumption,(r(f(c), f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.30/0.51 tff(388,assumption,(f(c) = f(f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.51 tff(389,plain,
% 0.30/0.51 (f(f(f(f(f(f(c)))))) = f(c)),
% 0.30/0.51 inference(symmetry,[status(thm)],[388])).
% 0.30/0.51 tff(390,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[319, 389])).
% 0.30/0.51 tff(391,plain,(~(f(c) = f(f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(392,plain,
% 0.30/0.51 (((~![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(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(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)))) = f(c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(393,plain,
% 0.30/0.51 (((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c))) <=> ((f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(394,plain,
% 0.30/0.51 (((~![Z: $i, 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(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(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(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(f(c))))))))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[393])).
% 0.30/0.51 tff(395,plain,
% 0.30/0.51 (((~![Z: $i, 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(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(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(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.30/0.52 inference(transitivity,[status(thm)],[394, 392])).
% 0.30/0.52 tff(396,plain,
% 0.30/0.52 ((~![Z: $i, 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(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(397,plain,
% 0.30/0.52 ((~![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(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(f(c))))))))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.30/0.52 tff(398,plain,
% 0.30/0.52 ((~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[397, 135, 374, 269, 391, 387])).
% 0.30/0.52 tff(399,plain,
% 0.30/0.52 (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[398, 386])).
% 0.30/0.52 tff(400,assumption,(~r(f(f(f(f(f(f(c)))))), f(f(c)))), introduced(assumption)).
% 0.30/0.52 tff(401,plain,
% 0.30/0.52 (((~![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(c)))))) = f(f(c))) | (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(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(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(f(f(c)))))) = f(f(c))) | (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(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(402,plain,
% 0.30/0.52 ((r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))) <=> ((f(f(f(f(f(f(c)))))) = f(f(c))) | (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(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(403,plain,
% 0.30/0.52 (((~![Z: $i, 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(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(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(f(f(c)))))) = f(f(c))) | (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(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c)))))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[402])).
% 0.30/0.52 tff(404,plain,
% 0.30/0.52 (((~![Z: $i, 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(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(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(f(f(c)))))) = f(f(c))) | (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(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))))),
% 0.30/0.52 inference(transitivity,[status(thm)],[403, 401])).
% 0.30/0.52 tff(405,plain,
% 0.30/0.52 ((~![Z: $i, 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(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(406,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(c)))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.30/0.52 tff(407,plain,
% 0.30/0.52 ((f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[406, 99, 56, 400, 399, 386])).
% 0.30/0.52 tff(408,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[407, 382, 331])).
% 0.30/0.52 tff(409,plain,((f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (c = f(f(f(f(c))))) | r(c, f(c)) | (c = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(410,plain,
% 0.30/0.52 (r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (c = f(f(f(f(c))))) | r(c, f(c)) | (c = f(c))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[409, 7])).
% 0.30/0.52 tff(411,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[410, 330, 326, 242, 80, 315, 81, 43, 269, 241, 268])).
% 0.30/0.52 tff(412,plain,((~r(f(f(f(f(f(f(c)))))), f(c))) | (c = f(c)) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(c)) | (c = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(413,plain,
% 0.30/0.52 (~r(f(f(f(f(f(f(c)))))), f(c))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[412, 242, 29, 65, 43, 81, 241])).
% 0.30/0.52 tff(414,assumption,(~(f(f(f(f(f(f(c)))))) = c)), introduced(assumption)).
% 0.30/0.52 tff(415,assumption,(~(f(c) = c)), introduced(assumption)).
% 0.30/0.52 tff(416,assumption,(~r(f(c), c)), introduced(assumption)).
% 0.30/0.52 tff(417,assumption,(~(f(c) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.52 tff(418,assumption,(~r(f(c), f(f(f(c))))), introduced(assumption)).
% 0.30/0.52 tff(419,assumption,(~r(f(f(f(c))), c)), introduced(assumption)).
% 0.30/0.52 tff(420,plain,
% 0.30/0.52 (((~![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) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (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(c) = c) | r(f(c), c) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(421,plain,
% 0.30/0.52 ((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))))) <=> ((f(c) = c) | r(f(c), c) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(422,plain,
% 0.30/0.52 (((~![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))) | ((f(c) = c) | r(f(c), c) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[421])).
% 0.30/0.52 tff(423,plain,
% 0.30/0.52 (((~![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))) | (f(c) = c) | r(f(c), c) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c))),
% 0.30/0.52 inference(transitivity,[status(thm)],[422, 420])).
% 0.30/0.52 tff(424,plain,
% 0.30/0.52 ((~![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)))))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(425,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.30/0.52 tff(426,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[425, 99, 415, 416, 418, 417, 419, 343])).
% 0.30/0.52 tff(427,plain,(r(f(f(f(c))), c) | (f(c) = c) | r(f(c), c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(428,plain,
% 0.30/0.52 (r(f(f(f(c))), c)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[427, 415, 416, 418, 417])).
% 0.30/0.52 tff(429,assumption,(~r(f(f(f(f(f(f(c)))))), f(c))), introduced(assumption)).
% 0.30/0.52 tff(430,plain,
% 0.30/0.52 (((~![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(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(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(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(431,plain,
% 0.30/0.52 ((r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(c))) <=> ((f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(432,plain,
% 0.30/0.52 (((~![Z: $i, 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(c)))))), f(c)) | r(f(c), c) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(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(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[431])).
% 0.30/0.52 tff(433,plain,
% 0.30/0.52 (((~![Z: $i, 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(c)))))), f(c)) | r(f(c), c) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(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(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c))),
% 0.30/0.52 inference(transitivity,[status(thm)],[432, 430])).
% 0.30/0.52 tff(434,plain,
% 0.30/0.52 ((~![Z: $i, 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(c)))))), f(c)) | r(f(c), c) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(c)))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(435,plain,
% 0.30/0.52 ((~![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(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.30/0.52 tff(436,plain,
% 0.30/0.52 (r(f(f(f(f(f(f(c)))))), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), c) | (f(f(f(f(f(f(c)))))) = c)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[435, 99, 319])).
% 0.30/0.52 tff(437,plain,
% 0.30/0.52 (r(f(f(f(f(f(f(c)))))), c)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[436, 414, 416, 415, 429])).
% 0.30/0.52 tff(438,assumption,(r(f(f(f(c))), c)), introduced(assumption)).
% 0.30/0.52 tff(439,assumption,(r(f(f(f(f(f(f(c)))))), f(f(f(c))))), introduced(assumption)).
% 0.30/0.52 tff(440,plain,
% 0.30/0.52 (((~![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(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(c)))))), c)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(441,plain,
% 0.30/0.53 (((~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(f(c)))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(c))))) <=> ((f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(c)))))), c)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(442,plain,
% 0.30/0.53 (((~![Z: $i, 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(c)))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(f(c)))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(c)))))), c))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[441])).
% 0.30/0.53 tff(443,plain,
% 0.30/0.53 (((~![Z: $i, 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(c)))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(f(c)))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(c)))))), c)))),
% 0.30/0.53 inference(transitivity,[status(thm)],[442, 440])).
% 0.30/0.53 tff(444,plain,
% 0.30/0.53 ((~![Z: $i, 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(c)))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(f(c)))))), c)) | (f(f(f(c))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(445,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(f(f(f(c)))))), c))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.30/0.53 tff(446,plain,
% 0.30/0.53 ((f(f(f(f(f(f(c)))))) = c) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(f(c)))))), c))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[445, 135, 20, 439, 438])).
% 0.30/0.53 tff(447,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[446, 437, 414, 343])).
% 0.30/0.53 tff(448,plain,((f(f(f(f(f(f(c)))))) = c) | (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))) | (~r(f(f(f(c))), c)) | r(f(c), c) | (f(c) = c) | r(f(f(f(f(f(f(c)))))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(449,plain,
% 0.30/0.53 (~r(f(f(f(f(f(f(c)))))), f(f(f(c))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[448, 429, 428, 416, 415, 414])).
% 0.30/0.53 tff(450,plain,
% 0.30/0.53 (((~![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(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(451,plain,
% 0.30/0.53 ((r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c))) <=> ((f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(452,plain,
% 0.30/0.53 (((~![Z: $i, 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(c)))))), f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c))))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[451])).
% 0.30/0.53 tff(453,plain,
% 0.30/0.53 (((~![Z: $i, 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(c)))))), f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(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(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))))),
% 0.30/0.53 inference(transitivity,[status(thm)],[452, 450])).
% 0.30/0.53 tff(454,plain,
% 0.30/0.53 ((~![Z: $i, 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(c)))))), f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(455,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = f(f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(f(c)))))), f(f(f(c))))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.30/0.53 tff(456,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[455, 99, 319, 20, 429, 418, 417, 449])).
% 0.30/0.53 tff(457,plain,(r(f(f(f(f(f(f(c)))))), f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | (f(c) = c) | (f(f(f(f(f(f(c)))))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(458,plain,
% 0.30/0.53 (f(f(f(f(f(f(c)))))) = c),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[457, 413, 49, 267, 260, 246])).
% 0.30/0.53 tff(459,assumption,(f(f(f(f(f(f(c)))))) = c), introduced(assumption)).
% 0.30/0.53 tff(460,assumption,(f(f(f(f(f(c))))) = c), introduced(assumption)).
% 0.30/0.53 tff(461,plain,
% 0.30/0.53 (c = f(f(f(f(f(c)))))),
% 0.30/0.53 inference(symmetry,[status(thm)],[460])).
% 0.30/0.53 tff(462,plain,
% 0.30/0.53 (f(c) = f(f(f(f(f(f(c))))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[461])).
% 0.30/0.53 tff(463,plain,
% 0.30/0.53 (f(c) = c),
% 0.30/0.53 inference(transitivity,[status(thm)],[462, 459])).
% 0.30/0.53 tff(464,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[415, 463])).
% 0.30/0.53 tff(465,plain,((~(f(f(f(f(f(c))))) = c)) | (f(c) = c) | (~(f(f(f(f(f(f(c)))))) = c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(466,plain,
% 0.30/0.53 (~(f(f(f(f(f(c))))) = c)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[465, 458, 260])).
% 0.30/0.53 tff(467,plain,
% 0.30/0.53 ((f(f(f(f(c)))) = f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(c)))), f(c)) | (c = f(f(f(f(c))))) | r(c, f(c)) | (c = f(c))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[373, 14])).
% 0.30/0.53 tff(468,plain,
% 0.30/0.53 (r(f(f(f(f(c)))), f(c))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[467, 242, 29, 65, 81, 241, 43])).
% 0.30/0.53 tff(469,plain,
% 0.30/0.53 (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[82])).
% 0.30/0.53 tff(470,plain,
% 0.30/0.53 (f(f(f(f(f(c))))) = c),
% 0.30/0.53 inference(transitivity,[status(thm)],[469, 459])).
% 0.30/0.53 tff(471,assumption,(~(f(f(f(f(f(c))))) = c)), introduced(assumption)).
% 0.30/0.53 tff(472,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[471, 470])).
% 0.30/0.53 tff(473,plain,((~(f(f(f(f(c)))) = f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (~(f(f(f(f(f(f(c)))))) = c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(474,plain,
% 0.30/0.53 (~(f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[473, 466, 458])).
% 0.30/0.53 tff(475,assumption,(r(f(f(f(f(f(c))))), f(c))), introduced(assumption)).
% 0.30/0.53 tff(476,plain,
% 0.30/0.53 (((~![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(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(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))) | (~r(f(c), f(f(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(477,plain,
% 0.30/0.53 (((~r(f(f(f(f(f(c))))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(c))) <=> ((~r(f(c), f(f(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(478,plain,
% 0.30/0.53 (((~![Z: $i, 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(c))))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | ((~r(f(c), f(f(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(c)))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[477])).
% 0.30/0.53 tff(479,plain,
% 0.30/0.53 (((~![Z: $i, 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(c))))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | (~r(f(c), f(f(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.30/0.53 inference(transitivity,[status(thm)],[478, 476])).
% 0.30/0.53 tff(480,plain,
% 0.30/0.53 ((~![Z: $i, 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(c))))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(c)))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(481,plain,
% 0.30/0.53 ((~![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(c)))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(c)))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.30/0.53 tff(482,plain,
% 0.30/0.53 (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[481, 135, 475, 58, 155, 333, 332])).
% 0.30/0.53 tff(483,assumption,(r(f(f(f(f(c)))), f(c))), introduced(assumption)).
% 0.30/0.53 tff(484,assumption,(~(f(f(f(f(c)))) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53 tff(485,plain,
% 0.30/0.53 (~r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[380, 135, 483, 29, 333, 332, 36])).
% 0.30/0.53 tff(486,plain,
% 0.30/0.53 (r(f(c), f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[211, 208, 475])).
% 0.30/0.53 tff(487,assumption,(r(f(c), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53 tff(488,plain,
% 0.30/0.53 ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[222, 135, 216, 487, 483, 29])).
% 0.30/0.53 tff(489,plain,
% 0.30/0.53 (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[488, 484])).
% 0.30/0.53 tff(490,assumption,(~r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
% 0.30/0.53 tff(491,assumption,(~r(f(f(c)), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53 tff(492,plain,
% 0.30/0.53 (((~![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(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(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(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(493,plain,
% 0.30/0.53 ((r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c)))) <=> (r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(494,plain,
% 0.30/0.53 (((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | (r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[493])).
% 0.30/0.53 tff(495,plain,
% 0.30/0.53 (((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.53 inference(transitivity,[status(thm)],[494, 492])).
% 0.30/0.53 tff(496,plain,
% 0.30/0.53 ((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(497,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.30/0.53 tff(498,plain,
% 0.30/0.53 (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[497, 99, 491, 22, 36, 490])).
% 0.30/0.53 tff(499,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[498, 489, 484])).
% 0.30/0.53 tff(500,plain,((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(501,plain,
% 0.30/0.53 (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[500, 486, 485, 484, 483])).
% 0.30/0.53 tff(502,plain,
% 0.30/0.53 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(503,plain,
% 0.30/0.53 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(504,plain,
% 0.30/0.54 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.30/0.54 tff(505,plain,
% 0.30/0.54 ($false),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[504, 208, 501, 482])).
% 0.30/0.54 tff(506,plain,((~r(f(f(f(f(f(c))))), f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54 tff(507,plain,
% 0.30/0.54 (~r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[506, 474, 468, 315, 80])).
% 0.30/0.54 tff(508,plain,
% 0.30/0.54 (((~![Z: $i, 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(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), c) | (c = f(c)) | r(c, f(c)) | (f(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))) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), c) | (c = f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = c))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(509,plain,
% 0.30/0.54 ((r(f(f(f(f(f(c))))), c) | r(c, f(c)) | r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c)) <=> (r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), c) | (c = f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = c))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(510,plain,
% 0.30/0.54 (((~![Z: $i, 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(c))))), c) | r(c, f(c)) | r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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))) | (r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), c) | (c = f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = c)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[509])).
% 0.30/0.54 tff(511,plain,
% 0.30/0.54 (((~![Z: $i, 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(c))))), c) | r(c, f(c)) | r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(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))) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), c) | (c = f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = c))),
% 0.30/0.54 inference(transitivity,[status(thm)],[510, 508])).
% 0.30/0.54 tff(512,plain,
% 0.30/0.54 ((~![Z: $i, 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(c))))), c) | r(c, f(c)) | r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(513,plain,
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% 0.30/0.54 inference(modus_ponens,[status(thm)],[512, 511])).
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% 0.30/0.54 inference(unit_resolution,[status(thm)],[513, 99])).
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% 0.30/0.54 tff(516,plain,
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% 0.30/0.54 (((~![Z: $i, 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(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), 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(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (~r(c, f(f(f(c))))))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
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% 0.30/0.54 inference(monotonicity,[status(thm)],[518])).
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% 0.30/0.54 inference(transitivity,[status(thm)],[519, 517])).
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% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
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% 0.30/0.54 inference(modus_ponens,[status(thm)],[527, 526])).
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% 0.30/0.54 inference(unit_resolution,[status(thm)],[528, 208, 525])).
% 0.30/0.54 tff(530,plain,
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% 0.30/0.54 inference(unit_resolution,[status(thm)],[259, 233])).
% 0.30/0.54 tff(531,plain,
% 0.30/0.54 (((~![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(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = 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(c) = c) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(f(c), c)))),
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% 0.30/0.54 (((~![Z: $i, 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), c)) | (~r(f(f(f(f(c)))), c)) | (f(c) = c) | (f(f(f(f(c)))) = 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(c) = c) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(f(c), c))))),
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% 0.30/0.54 inference(modus_ponens,[status(thm)],[541, 555])).
% 0.30/0.54 tff(557,plain,
% 0.30/0.54 (((~![Z: $i, 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(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(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))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(558,plain,
% 0.30/0.54 ((r(f(f(f(f(c)))), c) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)) <=> (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(559,plain,
% 0.30/0.54 (((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[558])).
% 0.30/0.54 tff(560,plain,
% 0.30/0.54 (((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.30/0.55 inference(transitivity,[status(thm)],[559, 557])).
% 0.30/0.55 tff(561,plain,
% 0.30/0.55 ((~![Z: $i, 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(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(562,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.30/0.55 tff(563,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[562, 99, 556, 552, 87, 538, 227, 223])).
% 0.30/0.55 tff(564,plain,(r(f(f(c)), f(c)) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(565,plain,
% 0.30/0.55 (r(f(f(c)), f(c))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[564, 81, 43])).
% 0.30/0.55 tff(566,plain,
% 0.30/0.55 (r(f(c), f(f(c)))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[314, 565])).
% 0.30/0.55 tff(567,plain,
% 0.30/0.55 (((~![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(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(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(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(c, f(f(c)))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(568,plain,
% 0.30/0.55 (((~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(f(c), f(f(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(c, f(f(c)))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(569,plain,
% 0.30/0.55 (((~![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(f(c), f(f(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(c, f(f(c))))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[568])).
% 0.30/0.55 tff(570,plain,
% 0.30/0.55 (((~![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(f(c), f(f(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(c, f(f(c)))))),
% 0.30/0.55 inference(transitivity,[status(thm)],[569, 567])).
% 0.30/0.55 tff(571,plain,
% 0.30/0.55 ((~![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)))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(572,plain,
% 0.30/0.55 ((~![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(c)))) | (c = f(c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (~r(c, f(c))) | (~r(c, f(f(c))))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.30/0.55 tff(573,plain,
% 0.30/0.55 (~r(c, f(f(c)))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[572, 135, 233, 525, 276, 566, 80])).
% 0.30/0.55 tff(574,assumption,(~r(c, f(f(c)))), introduced(assumption)).
% 0.30/0.55 tff(575,assumption,(~(c = f(f(c)))), introduced(assumption)).
% 0.30/0.55 tff(576,plain,
% 0.30/0.55 (~r(f(f(f(f(f(c))))), c)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[547, 135, 415, 261, 475, 58, 541])).
% 0.30/0.55 tff(577,plain,
% 0.30/0.55 (((~![Z: $i, 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(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(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(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(c))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(578,plain,
% 0.30/0.55 ((r(f(f(f(f(f(c))))), c) | r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c)) <=> (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(c))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(579,plain,
% 0.30/0.55 (((~![Z: $i, 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(c))))), c) | r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(c)))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[578])).
% 0.30/0.55 tff(580,plain,
% 0.30/0.55 (((~![Z: $i, 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(c))))), c) | r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(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))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(c))))),
% 0.30/0.55 inference(transitivity,[status(thm)],[579, 577])).
% 0.30/0.55 tff(581,plain,
% 0.30/0.55 ((~![Z: $i, 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(c))))), c) | r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(582,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(c)))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.30/0.55 tff(583,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[582, 99, 482, 155, 576, 541, 575, 574])).
% 0.30/0.55 tff(584,plain,((~r(f(f(f(f(f(c))))), f(c))) | (c = f(f(c))) | r(c, f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(585,plain,
% 0.30/0.55 (~r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[584, 573, 276, 566, 80, 530, 529])).
% 0.30/0.55 tff(586,plain,
% 0.30/0.55 (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(c))) = f(c)) | r(f(f(f(c))), f(c)) | r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[181, 58])).
% 0.30/0.55 tff(587,plain,
% 0.30/0.55 (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[586, 585, 43, 81])).
% 0.30/0.55 tff(588,assumption,(~r(f(f(f(c))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.55 tff(589,assumption,(r(f(f(f(f(f(c))))), f(f(f(c))))), introduced(assumption)).
% 0.30/0.55 tff(590,plain,
% 0.30/0.55 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(591,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(592,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.30/0.55 tff(593,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[592, 208, 589, 588])).
% 0.30/0.55 tff(594,plain,((~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(595,plain,
% 0.30/0.55 (r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[594, 587])).
% 0.30/0.55 tff(596,plain,
% 0.30/0.55 (((~![Z: $i, 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)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(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))) | r(f(f(f(f(c)))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(597,plain,
% 0.30/0.55 ((r(f(f(f(f(c)))), f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c))) <=> (r(f(f(f(f(c)))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(598,plain,
% 0.30/0.55 (((~![Z: $i, 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(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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))) | (r(f(f(f(f(c)))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[597])).
% 0.30/0.55 tff(599,plain,
% 0.30/0.55 (((~![Z: $i, 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(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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))) | r(f(f(f(f(c)))), f(c)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.30/0.55 inference(transitivity,[status(thm)],[598, 596])).
% 0.30/0.55 tff(600,plain,
% 0.30/0.55 ((~![Z: $i, 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(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(601,plain,
% 0.30/0.55 ((~![Z: $i, 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)) | (f(c) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.30/0.55 tff(602,plain,
% 0.30/0.55 (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[601, 99, 246, 49, 89, 29, 14])).
% 0.30/0.55 tff(603,assumption,(r(f(f(f(c))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.55 tff(604,plain,
% 0.30/0.55 (((~![Z: $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(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(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))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(605,plain,
% 0.30/0.55 (((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c))))) <=> ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(606,plain,
% 0.40/0.56 (((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[605])).
% 0.40/0.56 tff(607,plain,
% 0.40/0.56 (((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[606, 604])).
% 0.40/0.56 tff(608,plain,
% 0.40/0.56 ((~![Z: $i, 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(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(609,plain,
% 0.40/0.56 ((~![Z: $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(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.40/0.56 tff(610,plain,
% 0.40/0.56 (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[609, 135, 603, 42, 14, 87, 602])).
% 0.40/0.56 tff(611,plain,
% 0.40/0.56 ((f(f(c)) = c) <=> (c = f(f(c)))),
% 0.40/0.56 inference(commutativity,[status(thm)],[])).
% 0.40/0.56 tff(612,plain,
% 0.40/0.56 ((c = f(f(c))) <=> (f(f(c)) = c)),
% 0.40/0.56 inference(symmetry,[status(thm)],[611])).
% 0.40/0.56 tff(613,plain,
% 0.40/0.56 ((~(c = f(f(c)))) <=> (~(f(f(c)) = c))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[612])).
% 0.40/0.56 tff(614,plain,
% 0.40/0.56 (~(f(f(c)) = c)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[276, 613])).
% 0.40/0.56 tff(615,plain,
% 0.40/0.56 (((~![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))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(616,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(617,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.40/0.56 tff(618,plain,
% 0.40/0.56 (~r(f(f(c)), c)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[617, 208, 573])).
% 0.40/0.56 tff(619,assumption,(r(c, f(f(f(c))))), introduced(assumption)).
% 0.40/0.56 tff(620,plain,
% 0.40/0.56 (((~![Z: $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(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(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(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(f(c))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(621,plain,
% 0.40/0.56 (((~r(c, f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c))))) <=> ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(f(c))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(622,plain,
% 0.40/0.56 (((~![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(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(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))) | ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(f(c)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[621])).
% 0.40/0.56 tff(623,plain,
% 0.40/0.56 (((~![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(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(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))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(f(c))))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[622, 620])).
% 0.40/0.56 tff(624,plain,
% 0.40/0.56 ((~![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(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(625,plain,
% 0.40/0.56 ((~![Z: $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(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(f(c)))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.40/0.56 tff(626,plain,
% 0.40/0.56 (~r(c, f(f(f(f(f(c))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[625, 135, 603, 42, 556, 619, 240])).
% 0.40/0.56 tff(627,plain,
% 0.40/0.56 (((~![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(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), 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))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(628,plain,
% 0.40/0.56 ((r(f(f(c)), c) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c)) <=> (r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(629,plain,
% 0.40/0.56 (((~![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(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(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))) | (r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[628])).
% 0.40/0.56 tff(630,plain,
% 0.40/0.56 (((~![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(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(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))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.56 inference(transitivity,[status(thm)],[629, 627])).
% 0.40/0.56 tff(631,plain,
% 0.40/0.56 ((~![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(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
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% 0.40/0.56 inference(modus_ponens,[status(thm)],[631, 630])).
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% 0.40/0.56 tff(634,plain,
% 0.40/0.56 (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[633, 614])).
% 0.40/0.56 tff(635,plain,
% 0.40/0.56 (((~![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(c)))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(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))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(c))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(636,plain,
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% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(637,plain,
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% 0.40/0.56 inference(monotonicity,[status(thm)],[636])).
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% 0.40/0.56 inference(transitivity,[status(thm)],[637, 635])).
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% 0.40/0.56 inference(unit_resolution,[status(thm)],[640, 135, 634, 216, 22, 566, 80])).
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% 0.40/0.56 inference(rewrite,[status(thm)],[])).
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% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(644,plain,
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% 0.40/0.56 inference(monotonicity,[status(thm)],[643])).
% 0.40/0.56 tff(645,plain,
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% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
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% 0.40/0.57 inference(unit_resolution,[status(thm)],[668, 656, 81, 89, 43])).
% 0.40/0.57 tff(670,plain,
% 0.40/0.57 (((~![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(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (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))) | (c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(671,plain,
% 0.40/0.57 ((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)) <=> ((c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(672,plain,
% 0.40/0.57 (((~![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))) | ((c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c)))))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[671])).
% 0.40/0.57 tff(673,plain,
% 0.40/0.57 (((~![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))) | (c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[672, 670])).
% 0.40/0.57 tff(674,plain,
% 0.40/0.57 ((~![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))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(675,plain,
% 0.40/0.57 ((~![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(c))))) | r(c, f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.40/0.57 tff(676,plain,
% 0.40/0.57 (r(f(f(c)), f(f(f(f(c)))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[675, 99, 65, 669, 652, 618, 614])).
% 0.40/0.57 tff(677,plain,
% 0.40/0.57 (((~![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(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (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(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(678,plain,
% 0.40/0.57 (((~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))) <=> ((f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(679,plain,
% 0.40/0.57 (((~![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)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (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(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[678])).
% 0.40/0.57 tff(680,plain,
% 0.40/0.57 (((~![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)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (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(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[679, 677])).
% 0.40/0.57 tff(681,plain,
% 0.40/0.57 ((~![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)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(682,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.40/0.57 tff(683,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[682, 135, 634, 22, 87, 676, 652, 648])).
% 0.40/0.57 tff(684,plain,((~r(c, f(f(f(c))))) | r(f(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(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(685,plain,
% 0.40/0.57 (~r(c, f(f(f(c))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[684, 89, 81, 43, 603])).
% 0.40/0.57 tff(686,plain,
% 0.40/0.57 (((~![Z: $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))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(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))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(687,plain,
% 0.40/0.57 ((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))))) <=> (r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(688,plain,
% 0.40/0.57 (((~![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))) | (r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[687])).
% 0.40/0.57 tff(689,plain,
% 0.40/0.57 (((~![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))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[688, 686])).
% 0.40/0.57 tff(690,plain,
% 0.40/0.57 ((~![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)))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(691,plain,
% 0.40/0.58 ((~![Z: $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))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.40/0.58 tff(692,plain,
% 0.40/0.58 (r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[691, 99])).
% 0.40/0.58 tff(693,plain,
% 0.40/0.58 (r(f(f(f(c))), f(f(c))) | (c = f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(c))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[692, 163, 240])).
% 0.40/0.58 tff(694,plain,
% 0.40/0.58 (r(f(f(f(c))), f(f(c)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[693, 685, 573, 276])).
% 0.40/0.58 tff(695,plain,
% 0.40/0.58 (((~![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(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (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(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(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (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(f(c))))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(696,plain,
% 0.40/0.58 (((~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(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (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(f(c))))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(697,plain,
% 0.40/0.58 (((~![Z: $i, 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(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (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(f(c)))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[696])).
% 0.40/0.58 tff(698,plain,
% 0.40/0.58 (((~![Z: $i, 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(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (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(f(c))))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[697, 695])).
% 0.40/0.58 tff(699,plain,
% 0.40/0.58 ((~![Z: $i, 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)))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(700,plain,
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% 0.40/0.58 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.40/0.58 tff(701,plain,
% 0.40/0.58 (~r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[700, 135, 694, 163, 36, 14, 602])).
% 0.40/0.58 tff(702,plain,
% 0.40/0.58 (((~![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(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(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(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(703,plain,
% 0.40/0.58 (((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c)))) <=> ((f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(704,plain,
% 0.40/0.58 (((~![Z: $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(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(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(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[703])).
% 0.40/0.58 tff(705,plain,
% 0.40/0.58 (((~![Z: $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(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[704, 702])).
% 0.40/0.58 tff(706,plain,
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% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(707,plain,
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% 0.40/0.58 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.40/0.58 tff(708,plain,
% 0.40/0.58 ((f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(c))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[707, 135])).
% 0.40/0.58 tff(709,plain,
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% 0.40/0.58 inference(unit_resolution,[status(thm)],[708, 163, 42])).
% 0.40/0.58 tff(710,plain,
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% 0.40/0.58 inference(unit_resolution,[status(thm)],[709, 22])).
% 0.40/0.58 tff(711,plain,
% 0.40/0.58 (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[710, 694, 603])).
% 0.40/0.58 tff(712,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[497, 99, 711, 22, 36, 701, 87, 610])).
% 0.40/0.58 tff(713,plain,(r(f(f(f(f(c)))), f(c)) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(714,plain,
% 0.40/0.58 (r(f(f(f(f(c)))), f(c))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[713, 595, 81, 43])).
% 0.40/0.58 tff(715,assumption,(r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
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% 0.40/0.58 (((~![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))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(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))) | (~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(717,plain,
% 0.40/0.58 (((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(c))) | (~r(f(f(f(f(c)))), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c)))) <=> ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(718,plain,
% 0.40/0.58 (((~![Z: $i, 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(c))) | (~r(f(f(f(f(c)))), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = 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))) | ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c)))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[717])).
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% 0.40/0.58 inference(transitivity,[status(thm)],[718, 716])).
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% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
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% 0.40/0.58 inference(modus_ponens,[status(thm)],[720, 719])).
% 0.40/0.58 tff(722,plain,
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% 0.40/0.58 tff(723,plain,((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (~r(f(f(f(f(c)))), f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(724,plain,
% 0.40/0.58 (~r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[723, 565, 73, 714])).
% 0.40/0.58 tff(725,assumption,(~r(c, f(f(f(f(c)))))), introduced(assumption)).
% 0.40/0.58 tff(726,plain,
% 0.40/0.58 (((~![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(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(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))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(727,plain,
% 0.40/0.58 ((r(c, f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c)))))) <=> ((c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
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% 0.40/0.58 (((~![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(c))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (c = 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))) | ((c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[727])).
% 0.40/0.58 tff(729,plain,
% 0.40/0.58 (((~![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(c))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (c = 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))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[728, 726])).
% 0.40/0.58 tff(730,plain,
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% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(731,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(f(f(c))))) | r(c, f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.40/0.58 tff(732,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[731, 99, 268, 725, 575, 574, 36, 490])).
% 0.40/0.58 tff(733,plain,(r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(734,plain,
% 0.40/0.58 (r(c, f(f(f(f(c))))) | (c = f(f(c))) | r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
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% 0.40/0.58 tff(735,plain,
% 0.40/0.58 (r(c, f(f(f(f(c)))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[734, 724, 276, 573])).
% 0.40/0.58 tff(736,assumption,(~r(f(f(f(f(c)))), c)), introduced(assumption)).
% 0.40/0.58 tff(737,plain,
% 0.40/0.58 (((~![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))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(738,plain,
% 0.40/0.58 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(739,plain,
% 0.40/0.58 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.40/0.58 tff(740,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[739, 208, 658, 736])).
% 0.40/0.58 tff(741,plain,(r(f(f(f(f(c)))), c) | (~r(c, f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(742,plain,
% 0.40/0.58 (r(f(f(f(f(c)))), c)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[741, 735])).
% 0.40/0.58 tff(743,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), 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))) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(744,plain,
% 0.40/0.58 (((~r(f(f(f(f(c)))), c)) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), f(c))) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c)) <=> ((c = f(c)) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(745,plain,
% 0.40/0.59 (((~![Z: $i, 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(c))) | (~r(f(f(f(f(c)))), f(c))) | (c = f(c)) | (f(f(f(f(c)))) = 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))) | ((c = f(c)) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[744])).
% 0.40/0.59 tff(746,plain,
% 0.40/0.59 (((~![Z: $i, 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(c))) | (~r(f(f(f(f(c)))), f(c))) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c))),
% 0.40/0.59 inference(transitivity,[status(thm)],[745, 743])).
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% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(748,plain,
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% 0.40/0.59 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.40/0.59 tff(749,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[748, 135, 714, 233, 525, 29, 742, 67])).
% 0.40/0.59 tff(750,plain,(r(f(f(f(c))), f(c)) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(751,plain,
% 0.40/0.59 (r(f(f(f(c))), f(c))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[750, 43])).
% 0.40/0.59 tff(752,plain,
% 0.40/0.59 (((~![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)))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(753,plain,
% 0.40/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c)))))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(754,plain,
% 0.40/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(c))) | r(f(c), f(f(f(c))))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.40/0.59 tff(755,plain,
% 0.40/0.59 (r(f(c), f(f(f(c))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[754, 208, 751])).
% 0.40/0.59 tff(756,assumption,(~r(f(f(f(f(c)))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.40/0.59 tff(757,plain,
% 0.40/0.59 (((~![Z: $i, 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(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(758,plain,
% 0.40/0.59 ((r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(759,plain,
% 0.40/0.59 (((~![Z: $i, 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(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[758])).
% 0.40/0.59 tff(760,plain,
% 0.40/0.59 (((~![Z: $i, 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(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(transitivity,[status(thm)],[759, 757])).
% 0.40/0.59 tff(761,plain,
% 0.40/0.59 ((~![Z: $i, 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(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(762,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.40/0.59 tff(763,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[762, 99, 173, 58, 89, 29, 87, 756])).
% 0.40/0.59 tff(764,plain,(r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(765,plain,
% 0.40/0.59 (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[764, 173, 89])).
% 0.40/0.59 tff(766,plain,
% 0.40/0.59 (((~![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)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(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))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(767,plain,
% 0.40/0.59 (((~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))))) <=> ((f(f(f(c))) = f(c)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(768,plain,
% 0.40/0.59 (((~![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))) | ((f(f(f(c))) = f(c)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c)))))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[767])).
% 0.40/0.59 tff(769,plain,
% 0.40/0.59 (((~![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))) | (f(f(f(c))) = f(c)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.59 inference(transitivity,[status(thm)],[768, 766])).
% 0.40/0.59 tff(770,plain,
% 0.40/0.59 ((~![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)))))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(771,plain,
% 0.40/0.59 ((~![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)) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c)))))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.40/0.59 tff(772,plain,
% 0.40/0.59 (~r(c, f(c))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[771, 135, 43, 751, 233, 619, 240])).
% 0.40/0.59 tff(773,plain,
% 0.40/0.59 (r(f(f(f(f(c)))), f(c)) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(c)))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[358, 29, 65])).
% 0.40/0.59 tff(774,plain,
% 0.40/0.59 (r(c, f(f(f(f(c)))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[773, 772, 89, 233])).
% 0.40/0.59 tff(775,plain,
% 0.40/0.59 (r(f(f(f(f(c)))), c)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[741, 774])).
% 0.40/0.59 tff(776,plain,
% 0.40/0.59 (((~![Z: $i, 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(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(777,plain,
% 0.40/0.59 ((r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(778,plain,
% 0.40/0.59 (((~![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(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c))))))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[777])).
% 0.40/0.59 tff(779,plain,
% 0.40/0.59 (((~![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(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(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(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(transitivity,[status(thm)],[778, 776])).
% 0.40/0.59 tff(780,plain,
% 0.40/0.59 ((~![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(c)))))) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(781,plain,
% 0.40/0.59 ((~![Z: $i, 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(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.40/0.59 tff(782,plain,
% 0.40/0.59 (r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[781, 99])).
% 0.40/0.59 tff(783,plain,
% 0.40/0.59 (r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | r(c, f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[782, 58])).
% 0.40/0.59 tff(784,plain,
% 0.40/0.59 (r(f(f(f(f(f(c))))), f(c)) | (c = f(c)) | r(c, f(c)) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[783, 556])).
% 0.40/0.59 tff(785,plain,
% 0.40/0.59 (r(c, f(f(f(f(f(c))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[784, 772, 173, 233])).
% 0.40/0.59 tff(786,plain,
% 0.40/0.59 (((~![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(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(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(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(787,plain,
% 0.40/0.60 (((~r(f(f(f(f(c)))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)) <=> ((c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(788,plain,
% 0.40/0.60 (((~![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(c)))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | ((c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(f(f(f(f(c)))))))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[787])).
% 0.40/0.60 tff(789,plain,
% 0.40/0.60 (((~![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(c)))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(transitivity,[status(thm)],[788, 786])).
% 0.40/0.60 tff(790,plain,
% 0.40/0.60 ((~![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(c)))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(791,plain,
% 0.40/0.60 ((~![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(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (~r(c, f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.40/0.60 tff(792,plain,
% 0.40/0.60 (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[791, 135, 556, 785, 87, 775, 67])).
% 0.40/0.60 tff(793,plain,
% 0.40/0.60 ((~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[365, 135, 65, 774, 656, 343])).
% 0.40/0.60 tff(794,plain,
% 0.40/0.60 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[793, 657])).
% 0.40/0.60 tff(795,plain,
% 0.40/0.60 (((~![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(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(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(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(796,plain,
% 0.40/0.60 (((~r(f(f(f(c))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c)) <=> ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(797,plain,
% 0.40/0.60 (((~![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(c))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(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))) | ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(f(c)))))))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[796])).
% 0.40/0.60 tff(798,plain,
% 0.40/0.60 (((~![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(c))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(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))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(transitivity,[status(thm)],[797, 795])).
% 0.40/0.60 tff(799,plain,
% 0.40/0.60 ((~![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(c))), c)) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(800,plain,
% 0.40/0.60 ((~![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(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(c, f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.40/0.60 tff(801,plain,
% 0.40/0.60 (~r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[800, 135, 42, 556, 785, 656, 343])).
% 0.40/0.60 tff(802,plain,
% 0.40/0.60 (((~![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(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(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))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(803,plain,
% 0.40/0.60 ((r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))) <=> (r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(804,plain,
% 0.40/0.60 (((~![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(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(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))) | (r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[803])).
% 0.40/0.60 tff(805,plain,
% 0.40/0.60 (((~![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(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(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))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.40/0.60 inference(transitivity,[status(thm)],[804, 802])).
% 0.40/0.60 tff(806,plain,
% 0.40/0.60 ((~![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(c))), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(807,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c)))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.40/0.60 tff(808,plain,
% 0.40/0.60 ($false),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[807, 99, 801, 42, 87, 794, 657, 792])).
% 0.40/0.60 tff(809,plain,((~r(c, f(f(f(c))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.60 tff(810,plain,
% 0.40/0.60 (~r(c, f(f(f(c))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[809, 173, 89, 43])).
% 0.40/0.60 tff(811,plain,
% 0.40/0.60 (r(f(f(f(c))), f(f(c)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[693, 574, 810, 276])).
% 0.40/0.60 tff(812,plain,
% 0.40/0.60 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[107, 29])).
% 0.40/0.60 tff(813,plain,
% 0.40/0.60 (r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[812, 88, 77, 89])).
% 0.40/0.60 tff(814,plain,
% 0.40/0.60 ((f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[189, 58, 155])).
% 0.40/0.60 tff(815,plain,
% 0.40/0.60 (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[814, 88, 173, 77])).
% 0.40/0.60 tff(816,plain,
% 0.40/0.60 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(817,plain,
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% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(818,plain,
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% 0.40/0.60 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.40/0.60 tff(819,plain,
% 0.40/0.60 (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[818, 208, 815])).
% 0.40/0.60 tff(820,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (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(f(f(f(c))))))) | (f(f(f(f(c)))) = f(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(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (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(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(821,plain,
% 0.40/0.60 (((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c)))) <=> ((f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (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(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(822,plain,
% 0.40/0.60 (((~![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(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (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(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[821])).
% 0.40/0.60 tff(823,plain,
% 0.40/0.60 (((~![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(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (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(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.60 inference(transitivity,[status(thm)],[822, 820])).
% 0.40/0.60 tff(824,plain,
% 0.40/0.60 ((~![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(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(825,plain,
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% 0.40/0.60 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.40/0.60 tff(826,plain,
% 0.40/0.60 (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[825, 135, 819, 22, 36, 813, 87])).
% 0.40/0.60 tff(827,plain,
% 0.40/0.60 (~(c = f(c))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[232, 77])).
% 0.40/0.60 tff(828,plain,
% 0.40/0.60 (r(c, f(c))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[283, 88, 77, 827, 574, 575])).
% 0.40/0.60 tff(829,assumption,(r(f(c), f(f(f(c))))), introduced(assumption)).
% 0.40/0.60 tff(830,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(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))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(831,plain,
% 0.40/0.60 (((~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))) <=> ((c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(832,plain,
% 0.40/0.60 (((~![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))) | ((c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c)))))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[831])).
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% 0.40/0.60 (((~![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))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c))))))),
% 0.40/0.61 inference(transitivity,[status(thm)],[832, 830])).
% 0.40/0.61 tff(834,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, 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)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(835,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(c, f(f(f(c)))))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.40/0.61 tff(836,plain,
% 0.40/0.61 (~r(c, f(f(f(c))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[835, 135, 829, 417, 827, 828, 240])).
% 0.40/0.61 tff(837,plain,
% 0.40/0.61 (r(f(f(f(c))), f(f(c)))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[693, 836, 574, 575])).
% 0.40/0.61 tff(838,plain,
% 0.40/0.61 ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(c))), f(f(c))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[198, 155])).
% 0.40/0.61 tff(839,plain,
% 0.40/0.61 (~r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[838, 837, 815])).
% 0.40/0.61 tff(840,plain,
% 0.40/0.61 (((~![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(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(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))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(841,plain,
% 0.40/0.61 ((r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(842,plain,
% 0.40/0.61 (((~![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(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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(f(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[841])).
% 0.40/0.61 tff(843,plain,
% 0.40/0.61 (((~![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(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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(f(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.61 inference(transitivity,[status(thm)],[842, 840])).
% 0.40/0.61 tff(844,plain,
% 0.40/0.61 ((~![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(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(845,plain,
% 0.40/0.61 ((~![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(f(c))))), f(f(f(c)))) | (f(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(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.40/0.61 tff(846,plain,
% 0.40/0.61 (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[845, 99, 839, 7, 14, 87, 826])).
% 0.40/0.61 tff(847,assumption,(~r(f(f(c)), f(f(f(c))))), introduced(assumption)).
% 0.40/0.61 tff(848,assumption,(r(f(f(f(c))), f(f(c)))), introduced(assumption)).
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% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(887,plain,
% 0.40/0.62 (((~![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(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (c = f(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))) | ((c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c)))))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[886])).
% 0.40/0.62 tff(888,plain,
% 0.40/0.62 (((~![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(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (c = f(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))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[887, 885])).
% 0.40/0.62 tff(889,plain,
% 0.40/0.62 ((~![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(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(f(f(c))))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(890,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c)))))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.40/0.62 tff(891,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[890, 135, 65, 884, 556, 883, 87, 765])).
% 0.40/0.62 tff(892,plain,(r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(893,plain,
% 0.40/0.62 (r(f(f(f(f(f(c))))), f(c))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[892, 89, 43])).
% 0.40/0.62 tff(894,plain,
% 0.40/0.62 (r(f(c), f(f(f(f(f(c))))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[211, 208, 893])).
% 0.40/0.62 tff(895,plain,
% 0.40/0.62 (((~![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(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), 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(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(896,plain,
% 0.40/0.62 (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(c))))) <=> ((f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(897,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(c) = f(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(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[896])).
% 0.40/0.62 tff(898,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(c) = f(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(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[897, 895])).
% 0.40/0.62 tff(899,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(900,plain,
% 0.40/0.62 ((~![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(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.40/0.62 tff(901,plain,
% 0.40/0.62 ((f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[900, 135])).
% 0.40/0.62 tff(902,plain,
% 0.40/0.62 ((f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[901, 42])).
% 0.40/0.62 tff(903,plain,
% 0.40/0.62 ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[902, 216])).
% 0.40/0.62 tff(904,plain,
% 0.40/0.62 (~r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[903, 894, 755, 49])).
% 0.40/0.62 tff(905,plain,
% 0.40/0.62 (((~![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(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(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))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(906,plain,
% 0.40/0.62 (((~r(f(f(f(f(f(c))))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c))) <=> ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(907,plain,
% 0.40/0.62 (((~![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(f(f(c))))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(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))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(c)))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[906])).
% 0.40/0.62 tff(908,plain,
% 0.40/0.62 (((~![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(f(f(c))))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(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))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[907, 905])).
% 0.40/0.62 tff(909,plain,
% 0.40/0.62 ((~![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(f(f(c))))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(910,plain,
% 0.40/0.62 ((~![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(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(c)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.40/0.62 tff(911,plain,
% 0.40/0.62 (~r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[910, 135, 893, 58, 7, 755, 49])).
% 0.40/0.62 tff(912,assumption,(r(c, f(c))), introduced(assumption)).
% 0.40/0.62 tff(913,plain,
% 0.40/0.62 (~r(c, f(f(f(c))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[835, 135, 829, 417, 242, 912, 240])).
% 0.40/0.62 tff(914,plain,
% 0.40/0.62 (((~![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(c)))))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (~r(c, f(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(f(c)))))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(915,plain,
% 0.40/0.62 (((~r(c, f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c))) <=> ((f(c) = f(f(f(f(f(c)))))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(916,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (c = f(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))) | ((f(c) = f(f(f(f(f(c)))))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c)))))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[915])).
% 0.40/0.62 tff(917,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (c = f(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))) | (f(c) = f(f(f(f(f(c)))))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[916, 914])).
% 0.40/0.62 tff(918,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.63 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.48/0.63 tff(920,plain,
% 0.48/0.63 (~r(c, f(f(f(f(f(c))))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[919, 135, 216, 487, 242, 912, 556])).
% 0.48/0.63 tff(921,assumption,(~r(f(f(f(f(f(c))))), f(f(f(c))))), introduced(assumption)).
% 0.48/0.63 tff(922,plain,
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% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(923,plain,
% 0.48/0.63 ((r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(924,plain,
% 0.48/0.63 (((~![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(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(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(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[923])).
% 0.48/0.63 tff(925,plain,
% 0.48/0.63 (((~![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(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(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(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[924, 922])).
% 0.48/0.63 tff(926,plain,
% 0.48/0.63 ((~![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(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c)))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(927,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.48/0.63 tff(928,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[927, 99, 921, 7, 556, 920, 913, 240])).
% 0.48/0.63 tff(929,plain,((~r(c, f(c))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (c = f(c)) | (~r(f(c), f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(930,plain,
% 0.48/0.63 (~r(c, f(c))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[929, 911, 755, 49, 233, 894])).
% 0.48/0.63 tff(931,plain,
% 0.48/0.63 (r(c, f(f(c)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[283, 88, 77, 827, 241, 575])).
% 0.48/0.63 tff(932,plain,
% 0.48/0.63 (r(c, f(f(f(f(c)))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[773, 241, 89, 827])).
% 0.48/0.63 tff(933,plain,
% 0.48/0.63 (((~![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(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(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(f(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(934,plain,
% 0.48/0.63 (((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c)))))) <=> ((c = f(f(f(f(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(935,plain,
% 0.48/0.63 (((~![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(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = 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))) | ((c = f(f(f(f(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[934])).
% 0.48/0.63 tff(936,plain,
% 0.48/0.63 (((~![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(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = 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))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[935, 933])).
% 0.48/0.63 tff(937,plain,
% 0.48/0.63 ((~![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(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(938,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.48/0.63 tff(939,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[938, 135, 65, 932, 575, 931, 36, 813])).
% 0.48/0.63 tff(940,plain,(r(f(f(c)), f(c)) | (c = f(f(c))) | (f(f(c)) = f(c)) | r(c, f(c)) | r(f(f(f(f(c)))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(941,plain,
% 0.48/0.63 (r(f(f(c)), f(c))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[940, 930, 73, 276, 89])).
% 0.48/0.63 tff(942,plain,
% 0.48/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(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(c)), f(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(943,plain,
% 0.48/0.63 (((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(c))) <=> ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(944,plain,
% 0.48/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(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(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c)))))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[943])).
% 0.48/0.63 tff(945,plain,
% 0.48/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(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(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[944, 942])).
% 0.48/0.63 tff(946,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(c)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(947,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c)))))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.48/0.63 tff(948,plain,
% 0.48/0.63 (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[947, 135, 941, 73, 216, 22, 894])).
% 0.48/0.63 tff(949,plain,
% 0.48/0.63 (r(f(c), f(f(c)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[314, 941])).
% 0.48/0.63 tff(950,plain,
% 0.48/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (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))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(951,plain,
% 0.48/0.63 (((~r(f(f(f(c))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(c))) <=> ((~r(f(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(952,plain,
% 0.48/0.63 (((~![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(c))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = 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(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[951])).
% 0.48/0.63 tff(953,plain,
% 0.48/0.63 (((~![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(c))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = 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(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(c))), f(f(c)))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[952, 950])).
% 0.48/0.63 tff(954,plain,
% 0.48/0.63 ((~![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(c))), f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(c)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(955,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = f(f(c))) | (~r(f(f(f(c))), f(c))) | (f(c) = f(f(c))) | (~r(f(f(f(c))), f(f(c))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.48/0.64 tff(956,plain,
% 0.48/0.64 (~r(f(f(f(c))), f(f(c)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[955, 135, 43, 751, 163, 949, 80])).
% 0.48/0.64 tff(957,plain,
% 0.48/0.64 (((~![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(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(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(f(f(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(958,plain,
% 0.48/0.64 ((r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c)))) <=> (r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(959,plain,
% 0.48/0.64 (((~![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(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(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(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(f(f(f(c))))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[958])).
% 0.48/0.64 tff(960,plain,
% 0.48/0.64 (((~![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(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(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(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[959, 957])).
% 0.48/0.64 tff(961,plain,
% 0.48/0.64 ((~![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(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(962,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(c))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.48/0.64 tff(963,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[962, 99, 956, 163, 948, 22, 904, 42])).
% 0.48/0.64 tff(964,plain,(r(f(f(f(f(c)))), f(c)) | (f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(965,plain,
% 0.48/0.64 (r(f(f(f(f(c)))), f(c))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[964, 38])).
% 0.48/0.64 tff(966,plain,
% 0.48/0.64 (~(f(c) = f(f(f(c))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[48, 38])).
% 0.48/0.64 tff(967,plain,
% 0.48/0.64 (r(f(f(f(c))), f(c))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[750, 38])).
% 0.48/0.64 tff(968,plain,
% 0.48/0.64 (r(f(c), f(f(f(c))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[754, 208, 967])).
% 0.48/0.64 tff(969,plain,
% 0.48/0.64 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(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))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(970,plain,
% 0.48/0.64 (((~r(f(f(f(f(c)))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c))) <=> ((~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(971,plain,
% 0.48/0.64 (((~![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(c)))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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))) | ((~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c)))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[970])).
% 0.48/0.64 tff(972,plain,
% 0.48/0.64 (((~![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(c)))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(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))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[971, 969])).
% 0.48/0.64 tff(973,plain,
% 0.48/0.64 ((~![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(c)))), f(c))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(974,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.48/0.64 tff(975,plain,
% 0.48/0.64 (~r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[974, 135, 968, 966, 965, 29, 14])).
% 0.48/0.64 tff(976,plain,
% 0.48/0.64 (((~![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)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(977,plain,
% 0.48/0.64 ((~![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)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(978,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.48/0.64 tff(979,plain,
% 0.48/0.64 (~r(f(f(f(c))), f(f(f(f(c)))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[978, 208, 975])).
% 0.48/0.64 tff(980,assumption,(f(f(f(c))) = f(f(f(f(c))))), introduced(assumption)).
% 0.48/0.64 tff(981,plain,
% 0.48/0.64 (f(f(f(f(c)))) = f(f(f(c)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[980])).
% 0.48/0.64 tff(982,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[14, 981])).
% 0.48/0.64 tff(983,plain,(~(f(f(f(c))) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(984,plain,
% 0.48/0.64 (~(f(f(c)) = f(c))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[72, 38])).
% 0.48/0.64 tff(985,plain,
% 0.48/0.64 (~(c = f(c))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[232, 984])).
% 0.48/0.64 tff(986,plain,
% 0.48/0.64 (~r(c, f(f(f(c))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[835, 135, 968, 966, 985, 912, 240])).
% 0.48/0.64 tff(987,plain,
% 0.48/0.64 (((~![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(c))))) | r(c, f(f(f(f(c))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(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))) | (c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(988,plain,
% 0.48/0.64 ((r(c, f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(c))))) <=> ((c = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(989,plain,
% 0.48/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(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(f(c))))) | r(c, f(f(f(f(c))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[988])).
% 0.48/0.64 tff(990,plain,
% 0.48/0.64 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(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(f(c))))) | r(c, f(f(f(f(c))))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(c))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[989, 987])).
% 0.48/0.64 tff(991,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(c)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(992,plain,
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% 0.48/0.64 inference(unit_resolution,[status(thm)],[992, 99, 65, 986, 240, 983, 979])).
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% 0.48/0.64 tff(998,plain,(~r(c, f(c))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(999,plain,
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% 0.48/0.64 inference(unit_resolution,[status(thm)],[275, 38])).
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% 0.48/0.65 inference(rewrite,[status(thm)],[])).
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[222, 135, 216, 1030, 965, 29, 87])).
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% 0.48/0.65 tff(1033,plain,
% 0.48/0.65 (((~![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(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(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))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(1034,plain,
% 0.48/0.65 ((r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c))))) <=> (r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(1035,plain,
% 0.48/0.65 (((~![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(c)))), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | (r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[1034])).
% 0.48/0.65 tff(1036,plain,
% 0.48/0.65 (((~![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(c)))), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(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))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.48/0.65 tff(1037,plain,
% 0.48/0.65 ((~![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(c)))), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(1038,plain,
% 0.48/0.65 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.48/0.65 tff(1039,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[1038, 99, 1032, 42, 14, 87, 1031, 975])).
% 0.48/0.65 % SZS output end Proof
% 0.48/0.65 % E exiting
%------------------------------------------------------------------------------