%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA118+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : 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 06:33:05 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.53s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRA118+1 : TPTP v9.3.0. Released v9.3.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 4 21:19:53 EDT 2026
% 0.15/0.35 % CPUTime :
% 0.28/0.53 % SZS status Unsatisfiable
% 0.28/0.53 % SZS output start Proof
% 0.28/0.53 tff(f_type, type, (
% 0.28/0.53 f: $i > $i)).
% 0.28/0.53 tff(c_type, type, (
% 0.28/0.53 c: $i)).
% 0.28/0.53 tff(inj_0_type, type, (
% 0.28/0.53 inj_0: $i > $i)).
% 0.28/0.53 tff(r_type, type, (
% 0.28/0.53 r: ( $i * $i ) > $o)).
% 0.28/0.53 tff(1,plain,
% 0.28/0.53 ((f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.28/0.53 inference(commutativity,[status(thm)],[])).
% 0.28/0.53 tff(2,plain,
% 0.28/0.53 ((f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) <=> (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c)))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[1])).
% 0.28/0.53 tff(3,plain,
% 0.28/0.53 ((~(f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c))))))))))) <=> (~(f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[2])).
% 0.28/0.53 tff(4,plain,
% 0.28/0.53 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.28/0.53 inference(rewrite,[status(thm)],[])).
% 0.28/0.53 tff(5,plain,
% 0.28/0.53 (![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.28/0.53 inference(rewrite,[status(thm)],[])).
% 0.28/0.53 tff(6,plain,
% 0.28/0.53 (![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.28/0.53 inference(rewrite,[status(thm)],[])).
% 0.28/0.53 tff(7,axiom,(![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pfinj')).
% 0.28/0.53 tff(8,plain,
% 0.28/0.53 (![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.28/0.53 tff(9,plain,(
% 0.28/0.53 ![X: $i, Y: $i] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.28/0.53 inference(skolemize,[status(sab)],[8])).
% 0.28/0.53 tff(10,plain,
% 0.28/0.53 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.28/0.53 tff(11,plain,
% 0.28/0.53 (![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.28/0.53 tff(12,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(f(f(f(c)))))))) = f(f(f(f(f(f(c)))))))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(13,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(c)))))))) = f(f(f(f(f(f(c))))))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.28/0.53 tff(14,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(c)))) = f(f(c)))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(15,plain,
% 0.28/0.53 (inj_0(f(f(f(c)))) = f(f(c))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.28/0.53 tff(16,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(f(f(f(f(f(c)))))))))) = f(f(f(f(f(f(f(f(c)))))))))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(17,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(f(f(c)))))))))) = f(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.28/0.53 tff(18,assumption,(f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))), introduced(assumption)).
% 0.28/0.53 tff(19,plain,
% 0.28/0.53 (inj_0(f(f(f(f(c))))) = inj_0(f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[18])).
% 0.28/0.53 tff(20,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(c))))) = f(f(f(c))))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(21,plain,
% 0.28/0.53 (inj_0(f(f(f(f(c))))) = f(f(f(c)))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[20, 11])).
% 0.28/0.53 tff(22,plain,
% 0.28/0.53 (f(f(f(c))) = inj_0(f(f(f(f(c)))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[21])).
% 0.28/0.53 tff(23,plain,
% 0.28/0.53 (f(f(f(c))) = f(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.53 inference(transitivity,[status(thm)],[22, 19, 17])).
% 0.28/0.53 tff(24,plain,
% 0.28/0.53 (inj_0(f(f(f(c)))) = inj_0(f(f(f(f(f(f(f(f(c)))))))))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[23])).
% 0.28/0.53 tff(25,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(f(c))))))))) = inj_0(f(f(f(c))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[24])).
% 0.28/0.53 tff(26,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(f(f(c))))))))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(27,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(f(f(c)))))))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[26, 11])).
% 0.28/0.53 tff(28,plain,
% 0.28/0.53 (f(f(f(f(f(f(f(c))))))) = inj_0(f(f(f(f(f(f(f(f(c)))))))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[27])).
% 0.28/0.53 tff(29,plain,
% 0.28/0.53 (f(f(f(f(f(f(f(c))))))) = f(f(c))),
% 0.28/0.53 inference(transitivity,[status(thm)],[28, 25, 15])).
% 0.28/0.53 tff(30,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(c)))))))) = inj_0(f(f(c)))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[29])).
% 0.28/0.53 tff(31,plain,
% 0.28/0.53 (inj_0(f(f(c))) = inj_0(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[30])).
% 0.28/0.53 tff(32,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(c))) = f(c))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(33,plain,
% 0.28/0.53 (inj_0(f(f(c))) = f(c)),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[32, 11])).
% 0.28/0.53 tff(34,plain,
% 0.28/0.53 (f(c) = inj_0(f(f(c)))),
% 0.28/0.53 inference(symmetry,[status(thm)],[33])).
% 0.28/0.53 tff(35,plain,
% 0.28/0.53 (f(c) = f(f(f(f(f(f(c))))))),
% 0.28/0.53 inference(transitivity,[status(thm)],[34, 31, 13])).
% 0.28/0.53 tff(36,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(c)) = c)),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(37,plain,
% 0.28/0.53 (inj_0(f(c)) = c),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[36, 11])).
% 0.28/0.53 tff(38,assumption,(f(c) = f(f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.53 tff(39,plain,
% 0.28/0.53 (inj_0(f(c)) = inj_0(f(f(f(f(f(f(c)))))))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[38])).
% 0.28/0.53 tff(40,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(c))))))) = inj_0(f(c))),
% 0.28/0.53 inference(symmetry,[status(thm)],[39])).
% 0.28/0.53 tff(41,plain,
% 0.28/0.53 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(f(f(c))))))) = f(f(f(f(f(c))))))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(42,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(c))))))) = f(f(f(f(f(c)))))),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[41, 11])).
% 0.28/0.53 tff(43,plain,
% 0.28/0.53 (f(f(f(f(f(c))))) = inj_0(f(f(f(f(f(f(c)))))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[42])).
% 0.28/0.53 tff(44,plain,
% 0.28/0.53 (f(f(f(f(f(c))))) = c),
% 0.28/0.53 inference(transitivity,[status(thm)],[43, 40, 37])).
% 0.28/0.53 tff(45,plain,
% 0.28/0.53 (^[X: $i] : refl((~(f(X) = c)) <=> (~(f(X) = c)))),
% 0.28/0.53 inference(bind,[status(th)],[])).
% 0.28/0.53 tff(46,plain,
% 0.28/0.53 (![X: $i] : (~(f(X) = c)) <=> ![X: $i] : (~(f(X) = c))),
% 0.28/0.53 inference(quant_intro,[status(thm)],[45])).
% 0.28/0.53 tff(47,plain,
% 0.28/0.53 (![X: $i] : (~(f(X) = c)) <=> ![X: $i] : (~(f(X) = c))),
% 0.28/0.53 inference(rewrite,[status(thm)],[])).
% 0.28/0.53 tff(48,axiom,(![X: $i] : (~(f(X) = c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pfnc')).
% 0.28/0.53 tff(49,plain,
% 0.28/0.53 (![X: $i] : (~(f(X) = c))),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.28/0.53 tff(50,plain,(
% 0.28/0.53 ![X: $i] : (~(f(X) = c))),
% 0.28/0.53 inference(skolemize,[status(sab)],[49])).
% 0.28/0.53 tff(51,plain,
% 0.28/0.53 (![X: $i] : (~(f(X) = c))),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.28/0.53 tff(52,plain,
% 0.28/0.53 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(f(c))))) = c))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(53,plain,
% 0.28/0.53 (~(f(f(f(f(f(c))))) = c)),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.28/0.53 tff(54,plain,
% 0.28/0.53 ($false),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[53, 44])).
% 0.28/0.53 tff(55,plain,(~(f(c) = f(f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.53 tff(56,plain,
% 0.28/0.53 ($false),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[55, 35])).
% 0.28/0.53 tff(57,plain,(~(f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.53 tff(58,plain,
% 0.28/0.53 (~(f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c)))))),
% 0.28/0.53 inference(modus_ponens,[status(thm)],[57, 3])).
% 0.28/0.53 tff(59,assumption,(f(f(f(f(f(f(f(f(f(c))))))))) = f(c)), introduced(assumption)).
% 0.28/0.53 tff(60,plain,
% 0.28/0.53 (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[59])).
% 0.28/0.53 tff(61,assumption,(f(c) = f(f(f(f(f(f(f(f(f(c)))))))))), introduced(assumption)).
% 0.28/0.53 tff(62,plain,
% 0.28/0.53 (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)),
% 0.28/0.53 inference(symmetry,[status(thm)],[61])).
% 0.28/0.53 tff(63,plain,
% 0.28/0.53 (inj_0(f(f(f(f(f(f(f(f(f(c)))))))))) = inj_0(f(c))),
% 0.28/0.53 inference(monotonicity,[status(thm)],[62])).
% 0.28/0.53 tff(64,plain,
% 0.28/0.53 (f(f(f(f(f(f(f(f(c)))))))) = inj_0(f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.28/0.53 inference(symmetry,[status(thm)],[17])).
% 0.28/0.53 tff(65,plain,
% 0.28/0.53 (f(f(f(f(f(f(f(f(c)))))))) = c),
% 0.28/0.53 inference(transitivity,[status(thm)],[64, 63, 37])).
% 0.28/0.53 tff(66,plain,
% 0.28/0.53 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(f(f(f(f(c)))))))) = c))),
% 0.28/0.53 inference(quant_inst,[status(thm)],[])).
% 0.28/0.53 tff(67,plain,
% 0.28/0.53 (~(f(f(f(f(f(f(f(f(c)))))))) = c)),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[66, 51])).
% 0.28/0.53 tff(68,plain,
% 0.28/0.53 ($false),
% 0.28/0.53 inference(unit_resolution,[status(thm)],[67, 65])).
% 0.28/0.54 tff(69,plain,(~(f(c) = f(f(f(f(f(f(f(f(f(c))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(70,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[69, 60])).
% 0.28/0.54 tff(71,plain,(~(f(f(f(f(f(f(f(f(f(c))))))))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(72,assumption,(f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))), introduced(assumption)).
% 0.28/0.54 tff(73,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(f(f(f(f(c)))))))))) = inj_0(f(f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[72])).
% 0.28/0.54 tff(74,plain,
% 0.28/0.54 (f(f(f(f(f(f(f(f(c)))))))) = f(c)),
% 0.28/0.54 inference(transitivity,[status(thm)],[64, 73, 33])).
% 0.28/0.54 tff(75,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(f(f(f(c))))))))) = inj_0(f(c))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[74])).
% 0.28/0.54 tff(76,plain,
% 0.28/0.54 (f(f(f(f(f(f(f(c))))))) = c),
% 0.28/0.54 inference(transitivity,[status(thm)],[28, 75, 37])).
% 0.28/0.54 tff(77,plain,
% 0.28/0.54 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(f(f(f(c))))))) = c))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(78,plain,
% 0.28/0.54 (~(f(f(f(f(f(f(f(c))))))) = c)),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[77, 51])).
% 0.28/0.54 tff(79,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[78, 76])).
% 0.28/0.54 tff(80,plain,(~(f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(81,assumption,(~r(f(f(f(f(f(f(f(f(f(c))))))))), c)), introduced(assumption)).
% 0.28/0.54 tff(82,assumption,(~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))), introduced(assumption)).
% 0.28/0.54 tff(83,plain,
% 0.28/0.54 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(f(f(f(f(f(c))))))))) = c))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(84,plain,
% 0.28/0.54 (~(f(f(f(f(f(f(f(f(f(c))))))))) = c)),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[83, 51])).
% 0.28/0.54 tff(85,plain,
% 0.28/0.54 ((c = f(c)) <=> (f(c) = c)),
% 0.28/0.54 inference(commutativity,[status(thm)],[])).
% 0.28/0.54 tff(86,plain,
% 0.28/0.54 ((f(c) = c) <=> (c = f(c))),
% 0.28/0.54 inference(symmetry,[status(thm)],[85])).
% 0.28/0.54 tff(87,plain,
% 0.28/0.54 ((~(f(c) = c)) <=> (~(c = f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[86])).
% 0.28/0.54 tff(88,plain,
% 0.28/0.54 ((~![X: $i] : (~(f(X) = c))) | (~(f(c) = c))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(89,plain,
% 0.28/0.54 (~(f(c) = c)),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[88, 51])).
% 0.28/0.54 tff(90,plain,
% 0.28/0.54 (~(c = f(c))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[89, 87])).
% 0.28/0.54 tff(91,assumption,(~r(f(c), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(92,assumption,(~r(f(f(f(f(c)))), c)), introduced(assumption)).
% 0.28/0.54 tff(93,assumption,(f(c) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.28/0.54 tff(94,plain,
% 0.28/0.54 (f(f(f(f(f(c))))) = f(c)),
% 0.28/0.54 inference(symmetry,[status(thm)],[93])).
% 0.28/0.54 tff(95,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(c)))))) = inj_0(f(c))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[94])).
% 0.28/0.54 tff(96,plain,
% 0.28/0.54 ((~![Xk!0: $i] : (inj_0(f(Xk!0)) = Xk!0)) | (inj_0(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(97,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[96, 11])).
% 0.28/0.54 tff(98,plain,
% 0.28/0.54 (f(f(f(f(c)))) = inj_0(f(f(f(f(f(c))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[97])).
% 0.28/0.54 tff(99,plain,
% 0.28/0.54 (f(f(f(f(c)))) = c),
% 0.28/0.54 inference(transitivity,[status(thm)],[98, 95, 37])).
% 0.28/0.54 tff(100,plain,
% 0.28/0.54 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(c)))) = c))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(101,plain,
% 0.28/0.54 (~(f(f(f(f(c)))) = c)),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[100, 51])).
% 0.28/0.54 tff(102,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[101, 99])).
% 0.28/0.54 tff(103,plain,(~(f(c) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(104,assumption,(r(f(f(f(f(f(c))))), f(f(c)))), introduced(assumption)).
% 0.28/0.54 tff(105,assumption,(f(f(f(f(f(c))))) = f(f(c))), introduced(assumption)).
% 0.28/0.54 tff(106,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(c)))))) = inj_0(f(f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[105])).
% 0.28/0.54 tff(107,plain,
% 0.28/0.54 (inj_0(f(f(c))) = inj_0(f(f(f(f(f(c))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[106])).
% 0.28/0.54 tff(108,plain,
% 0.28/0.54 (f(c) = f(f(f(f(c))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[34, 107, 97])).
% 0.28/0.54 tff(109,plain,
% 0.28/0.54 (inj_0(f(c)) = inj_0(f(f(f(f(c)))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[108])).
% 0.28/0.54 tff(110,plain,
% 0.28/0.54 (inj_0(f(f(f(f(c))))) = inj_0(f(c))),
% 0.28/0.54 inference(symmetry,[status(thm)],[109])).
% 0.28/0.54 tff(111,plain,
% 0.28/0.54 (f(f(f(c))) = c),
% 0.28/0.54 inference(transitivity,[status(thm)],[22, 110, 37])).
% 0.28/0.54 tff(112,plain,
% 0.28/0.54 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(c))) = c))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(113,plain,
% 0.28/0.54 (~(f(f(f(c))) = c)),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[112, 51])).
% 0.28/0.54 tff(114,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[113, 111])).
% 0.28/0.54 tff(115,plain,(~(f(f(f(f(f(c))))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(116,plain,
% 0.28/0.54 ((c = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = c)),
% 0.28/0.54 inference(commutativity,[status(thm)],[])).
% 0.28/0.54 tff(117,plain,
% 0.28/0.54 ((f(f(f(f(f(c))))) = c) <=> (c = f(f(f(f(f(c))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[116])).
% 0.28/0.54 tff(118,plain,
% 0.28/0.54 ((~(f(f(f(f(f(c))))) = c)) <=> (~(c = f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[117])).
% 0.28/0.54 tff(119,plain,
% 0.28/0.54 (~(c = f(f(f(f(f(c))))))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[53, 118])).
% 0.28/0.54 tff(120,plain,
% 0.28/0.54 ((c = f(f(c))) <=> (f(f(c)) = c)),
% 0.28/0.54 inference(commutativity,[status(thm)],[])).
% 0.28/0.54 tff(121,plain,
% 0.28/0.54 ((f(f(c)) = c) <=> (c = f(f(c)))),
% 0.28/0.54 inference(symmetry,[status(thm)],[120])).
% 0.28/0.54 tff(122,plain,
% 0.28/0.54 ((~(f(f(c)) = c)) <=> (~(c = f(f(c))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[121])).
% 0.28/0.54 tff(123,plain,
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% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(124,plain,
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% 0.28/0.54 inference(unit_resolution,[status(thm)],[123, 51])).
% 0.28/0.54 tff(125,plain,
% 0.28/0.54 (~(c = f(f(c)))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.28/0.54 tff(126,assumption,(~r(f(f(f(f(c)))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(127,assumption,(~r(f(f(f(f(c)))), f(c))), introduced(assumption)).
% 0.28/0.54 tff(128,assumption,(f(f(f(f(c)))) = f(c)), introduced(assumption)).
% 0.28/0.54 tff(129,plain,
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% 0.28/0.54 inference(monotonicity,[status(thm)],[128])).
% 0.28/0.54 tff(130,plain,
% 0.28/0.54 (f(f(f(c))) = c),
% 0.28/0.54 inference(transitivity,[status(thm)],[22, 129, 37])).
% 0.28/0.54 tff(131,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[113, 130])).
% 0.28/0.54 tff(132,plain,(~(f(f(f(f(c)))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(133,plain,
% 0.28/0.54 ((f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))),
% 0.28/0.54 inference(commutativity,[status(thm)],[])).
% 0.28/0.54 tff(134,assumption,(f(f(f(f(c)))) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.28/0.54 tff(135,plain,
% 0.28/0.54 ((f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(c))))) = f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[134])).
% 0.28/0.54 tff(136,plain,
% 0.28/0.54 ((f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[135, 133])).
% 0.28/0.54 tff(137,plain,
% 0.28/0.54 ((f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) <=> (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[136])).
% 0.28/0.54 tff(138,plain,
% 0.28/0.54 (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[134])).
% 0.28/0.54 tff(139,plain,
% 0.28/0.54 (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[138])).
% 0.28/0.54 tff(140,assumption,(~(f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(141,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.28/0.54 tff(142,plain,((~(f(f(f(f(c)))) = f(f(f(f(f(c))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(143,plain,
% 0.28/0.54 (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[142, 134])).
% 0.28/0.54 tff(144,plain,
% 0.28/0.54 (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[143, 137])).
% 0.28/0.54 tff(145,assumption,(f(f(f(f(f(c))))) = f(f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.28/0.54 tff(146,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(c)))))) = inj_0(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[145])).
% 0.28/0.54 tff(147,plain,
% 0.28/0.54 (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[98, 146, 13])).
% 0.28/0.54 tff(148,plain,
% 0.28/0.54 (inj_0(f(f(f(f(c))))) = inj_0(f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[147])).
% 0.28/0.54 tff(149,plain,
% 0.28/0.54 (f(f(f(c))) = f(f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[22, 148, 42, 145])).
% 0.28/0.54 tff(150,plain,
% 0.28/0.54 (inj_0(f(f(f(c)))) = inj_0(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[149])).
% 0.28/0.54 tff(151,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(f(f(c)))))))) = inj_0(f(f(f(c))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[150])).
% 0.28/0.54 tff(152,plain,
% 0.28/0.54 (f(f(f(f(f(f(c)))))) = inj_0(f(f(f(f(f(f(f(c))))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[13])).
% 0.28/0.54 tff(153,plain,
% 0.28/0.54 (f(f(f(f(f(f(c)))))) = f(f(c))),
% 0.28/0.54 inference(transitivity,[status(thm)],[152, 151, 15])).
% 0.28/0.54 tff(154,assumption,(f(f(f(f(f(f(c)))))) = f(f(c))), introduced(assumption)).
% 0.28/0.54 tff(155,plain,
% 0.28/0.54 (inj_0(f(f(f(f(f(f(c))))))) = inj_0(f(f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[154])).
% 0.28/0.54 tff(156,plain,
% 0.28/0.54 (inj_0(f(f(c))) = inj_0(f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[155])).
% 0.28/0.54 tff(157,plain,
% 0.28/0.54 (f(c) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[34, 156, 42])).
% 0.28/0.54 tff(158,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[103, 157])).
% 0.28/0.54 tff(159,plain,(~(f(f(f(f(f(f(c)))))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(160,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[159, 153])).
% 0.28/0.54 tff(161,plain,(~(f(f(f(f(f(c))))) = f(f(f(f(f(f(f(c))))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(162,assumption,(f(f(f(f(c)))) = f(f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(163,plain,
% 0.28/0.54 (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[162])).
% 0.28/0.54 tff(164,plain,
% 0.28/0.54 (f(f(f(f(f(f(f(c))))))) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[163])).
% 0.28/0.54 tff(165,plain,
% 0.28/0.54 (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[164])).
% 0.28/0.54 tff(166,assumption,(~(f(f(f(f(f(c))))) = f(f(f(f(f(f(f(c))))))))), introduced(assumption)).
% 0.28/0.54 tff(167,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.28/0.54 tff(168,plain,((~(f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(c))))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(169,plain,
% 0.28/0.54 (~(f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[168, 161])).
% 0.28/0.54 tff(170,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[169, 144])).
% 0.28/0.54 tff(171,plain,(~(f(f(f(f(c)))) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(172,plain,
% 0.28/0.54 (^[X: $i, Y: $i, Z: $i] : refl((r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.28/0.54 inference(bind,[status(th)],[])).
% 0.28/0.54 tff(173,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(quant_intro,[status(thm)],[172])).
% 0.28/0.54 tff(174,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(175,plain,
% 0.28/0.54 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = Y) | (X = Z)) <=> ((X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> (((X = Z) | (X = Y)) | (Y = Z)))), rewrite((((X = Z) | (X = Y)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), ((((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, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> (r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)))), rewrite(((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.28/0.54 inference(bind,[status(th)],[])).
% 0.28/0.54 tff(176,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(quant_intro,[status(thm)],[175])).
% 0.28/0.54 tff(177,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rn3acl')).
% 0.28/0.54 tff(178,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.28/0.54 tff(179,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.28/0.54 tff(180,plain,(
% 0.28/0.54 ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(skolemize,[status(sab)],[179])).
% 0.28/0.54 tff(181,plain,
% 0.28/0.54 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.28/0.54 tff(182,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(c)))))) | r(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(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | r(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(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(183,plain,
% 0.28/0.54 ((r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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)))))) | 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(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(184,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(c)))))) | r(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(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[183])).
% 0.28/0.54 tff(185,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | r(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(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.28/0.54 inference(transitivity,[status(thm)],[184, 182])).
% 0.28/0.54 tff(186,plain,
% 0.28/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c)) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)))),
% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
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% 0.28/0.54 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.28/0.54 tff(188,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[187, 181, 103, 91, 126, 171, 132, 127])).
% 0.28/0.54 tff(189,plain,(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))))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(190,plain,
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% 0.28/0.54 inference(unit_resolution,[status(thm)],[189, 126, 91])).
% 0.28/0.54 tff(191,assumption,(f(f(c)) = f(f(f(f(c))))), introduced(assumption)).
% 0.28/0.54 tff(192,plain,
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% 0.28/0.54 inference(symmetry,[status(thm)],[191])).
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% 0.28/0.54 (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[192])).
% 0.28/0.54 tff(194,plain,
% 0.28/0.54 (f(f(f(c))) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(symmetry,[status(thm)],[193])).
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% 0.28/0.54 (inj_0(f(f(c))) = inj_0(f(f(f(f(c)))))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[191])).
% 0.28/0.54 tff(196,plain,
% 0.28/0.54 (f(c) = f(f(f(f(f(c)))))),
% 0.28/0.54 inference(transitivity,[status(thm)],[34, 195, 21, 194])).
% 0.28/0.54 tff(197,plain,
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% 0.28/0.54 inference(unit_resolution,[status(thm)],[103, 196])).
% 0.28/0.54 tff(198,plain,(~(f(f(c)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(199,plain,
% 0.28/0.54 ((f(f(c)) = f(c)) <=> (f(c) = f(f(c)))),
% 0.28/0.54 inference(commutativity,[status(thm)],[])).
% 0.28/0.54 tff(200,plain,
% 0.28/0.54 ((f(c) = f(f(c))) <=> (f(f(c)) = f(c))),
% 0.28/0.54 inference(symmetry,[status(thm)],[199])).
% 0.28/0.54 tff(201,plain,
% 0.28/0.54 ((~(f(c) = f(f(c)))) <=> (~(f(f(c)) = f(c)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[200])).
% 0.28/0.54 tff(202,assumption,(f(c) = f(f(c))), introduced(assumption)).
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% 0.28/0.54 inference(monotonicity,[status(thm)],[202])).
% 0.28/0.54 tff(204,plain,
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% 0.28/0.54 inference(symmetry,[status(thm)],[203])).
% 0.28/0.54 tff(205,plain,
% 0.28/0.54 (f(f(c)) = f(c)),
% 0.28/0.54 inference(symmetry,[status(thm)],[202])).
% 0.28/0.54 tff(206,plain,
% 0.28/0.54 (f(f(c)) = c),
% 0.28/0.54 inference(transitivity,[status(thm)],[205, 34, 204, 37])).
% 0.28/0.54 tff(207,plain,
% 0.28/0.54 ($false),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[124, 206])).
% 0.28/0.54 tff(208,plain,(~(f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(209,plain,
% 0.28/0.54 (~(f(f(c)) = f(c))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.28/0.54 tff(210,assumption,(~r(c, f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(211,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (c = f(f(f(f(f(c)))))) | r(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))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (c = f(f(f(f(f(c)))))) | r(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))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(212,plain,
% 0.28/0.54 ((r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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)) <=> ((f(f(f(f(c)))) = c) | (c = f(f(f(f(f(c)))))) | r(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))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(213,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (c = f(f(f(f(f(c)))))) | r(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)))),
% 0.28/0.54 inference(monotonicity,[status(thm)],[212])).
% 0.28/0.54 tff(214,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), 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))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (c = f(f(f(f(f(c)))))) | r(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))),
% 0.28/0.54 inference(transitivity,[status(thm)],[213, 211])).
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% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
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% 0.28/0.54 inference(modus_ponens,[status(thm)],[215, 214])).
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% 0.28/0.54 inference(unit_resolution,[status(thm)],[216, 181, 101, 119, 210, 126, 171, 92])).
% 0.28/0.54 tff(218,plain,(r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.28/0.54 tff(219,plain,
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% 0.28/0.54 inference(bind,[status(th)],[])).
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% 0.28/0.54 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(223,axiom,(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rsym')).
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% 0.28/0.54 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.28/0.54 tff(225,plain,(
% 0.28/0.54 ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.28/0.54 inference(skolemize,[status(sab)],[224])).
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% 0.28/0.54 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.28/0.54 tff(227,plain,
% 0.28/0.54 (((~![X: $i, Y: $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)))))))) <=> ((~![X: $i, Y: $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)))))))),
% 0.28/0.54 inference(rewrite,[status(thm)],[])).
% 0.28/0.54 tff(228,plain,
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% 0.28/0.54 inference(quant_inst,[status(thm)],[])).
% 0.28/0.54 tff(229,plain,
% 0.28/0.54 ((~![X: $i, Y: $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))))))),
% 0.28/0.54 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.28/0.54 tff(230,plain,
% 0.28/0.54 (~r(f(f(f(f(f(c))))), f(c))),
% 0.28/0.54 inference(unit_resolution,[status(thm)],[229, 226, 91])).
% 0.28/0.54 tff(231,assumption,(~r(f(c), f(f(c)))), introduced(assumption)).
% 0.28/0.54 tff(232,assumption,(~r(f(f(f(f(f(c))))), f(f(c)))), introduced(assumption)).
% 0.28/0.54 tff(233,assumption,(~(f(c) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.28/0.54 tff(234,plain,
% 0.28/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.28/0.55 inference(rewrite,[status(thm)],[])).
% 0.28/0.55 tff(235,plain,
% 0.28/0.55 ((r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c))))))) <=> (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.28/0.55 inference(rewrite,[status(thm)],[])).
% 0.28/0.55 tff(236,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.28/0.55 inference(monotonicity,[status(thm)],[235])).
% 0.28/0.55 tff(237,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.28/0.55 inference(transitivity,[status(thm)],[236, 234])).
% 0.28/0.55 tff(238,plain,
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% 0.28/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.28/0.55 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.28/0.55 tff(240,plain,
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% 0.28/0.55 tff(241,plain,(r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
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% 0.28/0.55 inference(unit_resolution,[status(thm)],[241, 103])).
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% 0.28/0.55 (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.28/0.55 inference(unit_resolution,[status(thm)],[242, 231, 91])).
% 0.28/0.55 tff(244,assumption,(~r(f(f(c)), f(f(f(f(f(c))))))), introduced(assumption)).
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% 0.28/0.55 (((~![X: $i, Y: $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)))))))) <=> ((~![X: $i, Y: $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)))))))),
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% 0.28/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.28/0.55 tff(249,plain,(r(f(f(c)), f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c))))), inference(lemma,lemma(discharge,[]))).
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% 0.28/0.55 tff(251,assumption,(r(f(f(f(f(c)))), f(c))), introduced(assumption)).
% 0.28/0.55 tff(252,plain,
% 0.28/0.55 ((f(f(c)) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(c)))),
% 0.28/0.55 inference(commutativity,[status(thm)],[])).
% 0.28/0.55 tff(253,plain,
% 0.28/0.55 ((f(f(f(f(f(c))))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(f(c))))))),
% 0.28/0.55 inference(symmetry,[status(thm)],[252])).
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% 0.28/0.55 ((~(f(f(f(f(f(c))))) = f(f(c)))) <=> (~(f(f(c)) = f(f(f(f(f(c)))))))),
% 0.28/0.55 inference(monotonicity,[status(thm)],[253])).
% 0.28/0.55 tff(255,plain,
% 0.28/0.55 (~(f(f(c)) = f(f(f(f(f(c))))))),
% 0.28/0.55 inference(modus_ponens,[status(thm)],[115, 254])).
% 0.28/0.55 tff(256,assumption,(r(c, f(f(f(f(f(c))))))), introduced(assumption)).
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% 0.28/0.55 inference(bind,[status(th)],[])).
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% 0.28/0.55 inference(quant_intro,[status(thm)],[257])).
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% 0.28/0.55 inference(rewrite,[status(thm)],[])).
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% 0.28/0.55 inference(bind,[status(th)],[])).
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% 0.28/0.55 inference(quant_intro,[status(thm)],[260])).
% 0.28/0.55 tff(262,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rn3cl')).
% 0.28/0.55 tff(263,plain,
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% 0.28/0.55 inference(modus_ponens,[status(thm)],[262, 261])).
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% 0.28/0.55 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.28/0.55 tff(265,plain,(
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% 0.28/0.55 inference(skolemize,[status(sab)],[264])).
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% 0.28/0.55 inference(modus_ponens,[status(thm)],[265, 258])).
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% 0.28/0.55 inference(rewrite,[status(thm)],[])).
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% 0.28/0.55 inference(rewrite,[status(thm)],[])).
% 0.28/0.55 tff(269,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.28/0.55 inference(monotonicity,[status(thm)],[268])).
% 0.28/0.55 tff(270,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.28/0.55 inference(transitivity,[status(thm)],[269, 267])).
% 0.28/0.55 tff(271,plain,
% 0.28/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(f(c))))),
% 0.28/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.28/0.55 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.28/0.55 tff(273,plain,
% 0.28/0.55 (~r(c, f(f(c)))),
% 0.28/0.55 inference(unit_resolution,[status(thm)],[272, 266, 125, 119, 256, 250, 255])).
% 0.28/0.55 tff(274,assumption,(~r(c, f(f(c)))), introduced(assumption)).
% 0.28/0.55 tff(275,assumption,(~r(c, f(c))), introduced(assumption)).
% 0.28/0.55 tff(276,plain,
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% 0.28/0.55 inference(rewrite,[status(thm)],[])).
% 0.28/0.55 tff(277,plain,
% 0.28/0.55 ((r(f(c), f(f(c))) | r(c, f(f(c))) | r(c, f(c)) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c))) <=> (r(c, f(f(c))) | r(c, f(c)) | (c = f(c)) | (c = f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))),
% 0.28/0.55 inference(rewrite,[status(thm)],[])).
% 0.28/0.55 tff(278,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | r(c, f(f(c))) | r(c, f(c)) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(c, f(c)) | (c = f(c)) | (c = f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c)))))),
% 0.28/0.55 inference(monotonicity,[status(thm)],[277])).
% 0.28/0.55 tff(279,plain,
% 0.28/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | r(c, f(f(c))) | r(c, f(c)) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | r(c, f(c)) | (c = f(c)) | (c = f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c))))),
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% 0.37/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | r(c, f(f(c))) | r(c, f(c)) | (f(c) = f(f(c))) | (c = f(f(c))) | (c = f(c)))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | r(c, f(c)) | (c = f(c)) | (c = f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(c)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[280, 279])).
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% 0.37/0.55 ($false),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[281, 181, 275, 90, 274, 125, 208, 231])).
% 0.37/0.55 tff(283,plain,(r(f(c), f(f(c))) | r(c, f(c)) | r(c, f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.55 tff(284,plain,
% 0.37/0.55 (r(c, f(c))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[283, 273, 231])).
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% 0.37/0.55 ((f(f(f(f(f(f(c)))))) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.37/0.55 inference(commutativity,[status(thm)],[])).
% 0.37/0.55 tff(286,plain,
% 0.37/0.55 ((f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.37/0.55 inference(symmetry,[status(thm)],[285])).
% 0.37/0.55 tff(287,plain,
% 0.37/0.55 ((~(f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[286])).
% 0.37/0.55 tff(288,plain,
% 0.37/0.55 (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[169, 287])).
% 0.37/0.55 tff(289,plain,
% 0.37/0.55 ((f(f(f(f(f(f(c)))))) = f(c)) <=> (f(c) = f(f(f(f(f(f(c)))))))),
% 0.37/0.55 inference(commutativity,[status(thm)],[])).
% 0.37/0.55 tff(290,plain,
% 0.37/0.55 ((f(c) = f(f(f(f(f(f(c))))))) <=> (f(f(f(f(f(f(c)))))) = f(c))),
% 0.37/0.55 inference(symmetry,[status(thm)],[289])).
% 0.37/0.55 tff(291,plain,
% 0.37/0.55 ((~(f(c) = f(f(f(f(f(f(c)))))))) <=> (~(f(f(f(f(f(f(c)))))) = f(c)))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[290])).
% 0.37/0.55 tff(292,plain,
% 0.37/0.55 (~(f(f(f(f(f(f(c)))))) = f(c))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[55, 291])).
% 0.37/0.55 tff(293,assumption,(r(f(f(f(f(f(f(c)))))), f(c))), introduced(assumption)).
% 0.37/0.55 tff(294,plain,
% 0.37/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(295,plain,
% 0.37/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(296,plain,
% 0.37/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.37/0.55 tff(297,plain,
% 0.37/0.55 ((~r(f(f(f(f(f(f(c)))))), 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)))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[296, 266, 132, 251, 293])).
% 0.37/0.55 tff(298,plain,
% 0.37/0.55 (~r(f(f(f(f(f(f(c)))))), f(f(f(f(c)))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[297, 292, 288])).
% 0.37/0.55 tff(299,plain,
% 0.37/0.55 ((~![X: $i] : (~(f(X) = c))) | (~(f(f(f(f(f(f(c)))))) = c))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(300,plain,
% 0.37/0.56 (~(f(f(f(f(f(f(c)))))) = c)),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[299, 51])).
% 0.37/0.56 tff(301,assumption,(r(c, f(c))), introduced(assumption)).
% 0.37/0.56 tff(302,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(303,plain,
% 0.37/0.56 (((~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = c)) <=> ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(304,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[303])).
% 0.37/0.56 tff(305,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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)))),
% 0.37/0.56 inference(transitivity,[status(thm)],[304, 302])).
% 0.37/0.56 tff(306,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = c))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(307,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(f(c)))))) = c) | (~r(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))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.37/0.56 tff(308,plain,
% 0.37/0.56 ((f(f(f(f(f(f(c)))))) = f(c)) | (~r(f(f(f(f(f(f(c)))))), c))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[307, 266, 301, 90, 300, 293])).
% 0.37/0.56 tff(309,plain,
% 0.37/0.56 (~r(f(f(f(f(f(f(c)))))), c)),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[308, 292])).
% 0.37/0.56 tff(310,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(311,plain,
% 0.37/0.56 ((r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))) <=> ((f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(312,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[311])).
% 0.37/0.56 tff(313,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[312, 310])).
% 0.37/0.56 tff(314,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(315,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(f(f(c)))))), f(f(f(f(c))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.37/0.56 tff(316,plain,
% 0.37/0.56 ($false),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[315, 181, 101, 300, 92, 309, 298, 288])).
% 0.37/0.56 tff(317,plain,((~r(f(f(f(f(f(f(c)))))), f(c))) | r(f(f(f(f(c)))), c) | (~r(f(f(f(f(c)))), f(c))) | (~r(c, f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.56 tff(318,plain,
% 0.37/0.56 (~r(f(f(f(f(f(f(c)))))), f(c))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[317, 284, 251, 92])).
% 0.37/0.56 tff(319,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(320,plain,
% 0.37/0.56 (((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c)) <=> ((f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(321,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[320])).
% 0.37/0.56 tff(322,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[321, 319])).
% 0.37/0.56 tff(323,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(324,plain,
% 0.37/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))),
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% 0.37/0.56 tff(325,plain,
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% 0.37/0.56 tff(326,assumption,(~r(f(f(f(f(f(f(c)))))), f(f(c)))), introduced(assumption)).
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% 0.37/0.56 inference(monotonicity,[status(thm)],[328])).
% 0.37/0.56 tff(330,plain,
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% 0.37/0.56 inference(modus_ponens,[status(thm)],[159, 329])).
% 0.37/0.56 tff(331,plain,
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% 0.37/0.56 tff(333,plain,
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% 0.37/0.56 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.37/0.56 tff(334,plain,
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% 0.37/0.56 inference(unit_resolution,[status(thm)],[333, 226, 326])).
% 0.37/0.56 tff(335,assumption,(~r(f(c), f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.37/0.56 tff(336,assumption,(~(f(c) = f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.37/0.56 tff(337,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c))))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(338,plain,
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% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(339,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(c))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c)))))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[338])).
% 0.37/0.56 tff(340,plain,
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% 0.37/0.56 inference(transitivity,[status(thm)],[339, 337])).
% 0.37/0.56 tff(341,plain,
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% 0.37/0.56 tff(342,plain,
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% 0.37/0.56 inference(unit_resolution,[status(thm)],[342, 181, 208, 231, 336, 335, 334, 330])).
% 0.37/0.56 tff(344,plain,(r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(c), f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.56 tff(345,plain,
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% 0.37/0.56 tff(346,plain,
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% 0.37/0.56 inference(unit_resolution,[status(thm)],[345, 326, 231])).
% 0.37/0.56 tff(347,plain,
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% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.56 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.37/0.56 tff(350,plain,
% 0.37/0.56 (r(f(f(f(f(f(f(c)))))), f(c))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[349, 226, 346])).
% 0.37/0.56 tff(351,plain,
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% 0.37/0.56 tff(352,plain,
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% 0.37/0.56 tff(353,assumption,(~r(f(f(c)), c)), introduced(assumption)).
% 0.37/0.56 tff(354,plain,
% 0.37/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(355,plain,
% 0.37/0.56 ((r(f(f(c)), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(c)))) <=> ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(356,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[355])).
% 0.37/0.57 tff(357,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(f(c)))))), c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(c)))))) = c) | (f(f(f(f(f(f(c)))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[356, 354])).
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% 0.37/0.57 tff(361,plain,(r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(c)), c) | (~r(c, f(c))) | r(f(c), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(362,plain,
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% 0.37/0.57 tff(363,assumption,(f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.37/0.57 tff(364,plain,
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% 0.37/0.57 inference(symmetry,[status(thm)],[363])).
% 0.37/0.57 tff(365,plain,
% 0.37/0.57 (inj_0(f(f(f(f(f(c)))))) = inj_0(f(f(f(f(f(f(c)))))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[364])).
% 0.37/0.57 tff(366,plain,
% 0.37/0.57 (f(f(f(f(c)))) = f(f(f(f(f(c)))))),
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% 0.37/0.57 tff(367,plain,
% 0.37/0.57 ($false),
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% 0.37/0.57 tff(368,plain,(~(f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(369,assumption,(r(f(f(c)), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.37/0.57 tff(370,assumption,(r(f(f(f(f(f(f(c)))))), f(f(c)))), introduced(assumption)).
% 0.37/0.57 tff(371,assumption,(r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.37/0.57 tff(372,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(373,plain,
% 0.37/0.57 (((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(c)))) <=> ((f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(374,plain,
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% 0.37/0.57 inference(monotonicity,[status(thm)],[373])).
% 0.37/0.57 tff(375,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[374, 372])).
% 0.37/0.57 tff(376,plain,
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% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.57 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.37/0.57 tff(378,plain,
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% 0.37/0.57 tff(380,plain,
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% 0.37/0.57 inference(unit_resolution,[status(thm)],[379, 140, 370, 369])).
% 0.37/0.57 tff(381,assumption,(~r(f(f(f(f(f(f(c)))))), f(c))), introduced(assumption)).
% 0.37/0.57 tff(382,assumption,(f(f(f(f(f(c))))) = f(c)), introduced(assumption)).
% 0.37/0.57 tff(383,plain,
% 0.37/0.57 (f(c) = f(f(f(f(f(c)))))),
% 0.37/0.57 inference(symmetry,[status(thm)],[382])).
% 0.37/0.57 tff(384,plain,
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% 0.37/0.57 inference(unit_resolution,[status(thm)],[103, 383])).
% 0.37/0.57 tff(385,plain,(~(f(f(f(f(f(c))))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(386,assumption,(~r(f(f(f(f(f(c))))), f(c))), introduced(assumption)).
% 0.37/0.57 tff(387,plain,
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% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(388,plain,
% 0.37/0.57 ((r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(389,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[388])).
% 0.37/0.57 tff(390,plain,
% 0.37/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(c)) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(c)) | (f(f(f(f(f(f(c)))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(c)))),
% 0.37/0.57 inference(transitivity,[status(thm)],[389, 387])).
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% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.57 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.37/0.57 tff(393,plain,
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% 0.37/0.57 tff(395,plain,((f(f(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(f(f(c)))))), f(c)) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(396,plain,
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% 0.37/0.57 tff(397,plain,
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% 0.37/0.57 inference(unit_resolution,[status(thm)],[396, 362, 318, 250, 230])).
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% 0.37/0.57 tff(399,plain,
% 0.37/0.57 (r(f(c), f(f(c)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[398, 190, 92, 219, 91])).
% 0.37/0.57 tff(400,assumption,(~r(f(f(c)), f(c))), introduced(assumption)).
% 0.37/0.57 tff(401,assumption,(r(f(c), f(f(c)))), introduced(assumption)).
% 0.37/0.57 tff(402,plain,
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% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(403,plain,
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% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(404,plain,
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% 0.37/0.58 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.37/0.58 tff(405,plain,
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% 0.37/0.58 inference(unit_resolution,[status(thm)],[404, 226, 401, 400])).
% 0.37/0.58 tff(406,plain,(r(f(f(c)), f(c)) | (~r(f(c), f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(407,plain,
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% 0.37/0.58 inference(unit_resolution,[status(thm)],[406, 399])).
% 0.37/0.58 tff(408,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (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(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (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(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(409,plain,
% 0.37/0.58 (((~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(f(c)))))) <=> ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(410,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (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(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c))))))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[409])).
% 0.37/0.58 tff(411,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (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(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[410, 408])).
% 0.37/0.58 tff(412,plain,
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% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (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(c)) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.37/0.58 tff(414,plain,
% 0.37/0.58 (~r(f(f(c)), f(f(f(f(c)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[413, 266, 407, 209, 198, 132, 190])).
% 0.37/0.58 tff(415,plain,
% 0.37/0.58 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(416,plain,
% 0.37/0.58 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(417,plain,
% 0.37/0.58 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c)),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.37/0.58 tff(418,plain,
% 0.37/0.58 (r(f(f(f(f(f(c))))), c)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[417, 226, 219])).
% 0.37/0.58 tff(419,assumption,(~(f(f(c)) = f(f(f(f(c)))))), introduced(assumption)).
% 0.37/0.58 tff(420,assumption,(r(f(f(c)), f(c))), introduced(assumption)).
% 0.37/0.58 tff(421,plain,
% 0.37/0.58 ((f(f(c)) = f(f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[413, 266, 420, 209, 132, 251])).
% 0.37/0.58 tff(422,plain,
% 0.37/0.58 (~r(f(f(c)), f(f(f(f(c)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[421, 419])).
% 0.37/0.58 tff(423,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(424,plain,
% 0.37/0.58 ((r(f(f(f(f(c)))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(c)))))) <=> ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(425,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c)))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[424])).
% 0.37/0.58 tff(426,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c))),
% 0.37/0.58 inference(transitivity,[status(thm)],[425, 423])).
% 0.37/0.58 tff(427,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(c)), c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(c))))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(428,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(c)))) = c) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c)),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.37/0.58 tff(429,plain,
% 0.37/0.58 (r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[428, 181, 124, 353, 101, 92])).
% 0.37/0.58 tff(430,plain,
% 0.37/0.58 ($false),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[429, 422, 419])).
% 0.37/0.58 tff(431,plain,((f(f(c)) = f(f(f(f(c))))) | r(f(f(c)), c) | r(f(f(f(f(c)))), c) | (~r(f(f(c)), f(c))) | (~r(f(f(f(f(c)))), f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(432,plain,
% 0.37/0.58 (r(f(f(c)), c) | r(f(f(f(f(c)))), c) | (~r(f(f(c)), f(c))) | (~r(f(f(f(f(c)))), f(c)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[431, 198])).
% 0.37/0.58 tff(433,plain,
% 0.37/0.58 (r(f(f(c)), c)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[432, 407, 92, 190])).
% 0.37/0.58 tff(434,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(435,plain,
% 0.37/0.58 (((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(f(c))))))) <=> ((f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(436,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[435])).
% 0.37/0.58 tff(437,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c)))),
% 0.37/0.58 inference(transitivity,[status(thm)],[436, 434])).
% 0.37/0.58 tff(438,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(439,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | (~r(f(f(c)), c)) | (f(f(f(f(f(c))))) = 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(f(c))))), c))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.37/0.58 tff(440,plain,
% 0.37/0.58 (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[439, 266, 124, 433, 53, 255, 418])).
% 0.37/0.58 tff(441,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (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))))) | r(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))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | 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))))) | r(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))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(442,plain,
% 0.37/0.58 ((r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), 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)))))) <=> (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))))) | r(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))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(443,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), 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))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (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))))) | r(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)))))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[442])).
% 0.37/0.58 tff(444,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), 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))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | 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))))) | r(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))))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[443, 441])).
% 0.37/0.58 tff(445,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), 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))))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(446,plain,
% 0.37/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.37/0.58 tff(447,plain,
% 0.37/0.58 (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[446, 181])).
% 0.37/0.58 tff(448,plain,
% 0.37/0.58 (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(c)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[447, 255])).
% 0.37/0.58 tff(449,plain,
% 0.37/0.58 (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[448, 198, 171])).
% 0.37/0.58 tff(450,plain,
% 0.37/0.58 ($false),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[449, 440, 414, 126])).
% 0.37/0.58 tff(451,plain,(r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | r(f(c), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(452,plain,
% 0.37/0.58 (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[451, 91, 92])).
% 0.37/0.58 tff(453,plain,
% 0.37/0.58 (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[249, 104])).
% 0.37/0.58 tff(454,assumption,(~(f(f(f(f(c)))) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.37/0.58 tff(455,assumption,(r(f(f(f(f(c)))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.37/0.58 tff(456,plain,
% 0.37/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(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))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(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))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(457,plain,
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% 0.37/0.58 inference(rewrite,[status(thm)],[])).
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% 0.37/0.59 inference(monotonicity,[status(thm)],[457])).
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% 0.37/0.59 tff(462,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[461, 266, 455, 454, 369, 255])).
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[462, 419])).
% 0.37/0.59 tff(464,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[429, 463, 419])).
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% 0.37/0.59 tff(466,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[466, 453, 92, 452])).
% 0.37/0.59 tff(468,assumption,(r(f(f(c)), c)), introduced(assumption)).
% 0.37/0.59 tff(469,plain,
% 0.37/0.59 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(470,plain,
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% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.59 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.37/0.59 tff(472,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[471, 226, 274, 468])).
% 0.37/0.59 tff(473,plain,((~r(f(f(c)), c)) | r(c, f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(474,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[473, 467])).
% 0.37/0.59 tff(475,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(476,plain,
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% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(477,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[476])).
% 0.37/0.59 tff(478,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[477, 475])).
% 0.37/0.59 tff(479,plain,
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% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(480,plain,
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% 0.37/0.59 tff(481,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[480, 266, 474, 125, 119, 115, 104])).
% 0.37/0.59 tff(482,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[461, 266, 455, 171, 453, 255, 198])).
% 0.37/0.59 tff(483,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c))))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(484,plain,
% 0.37/0.59 (((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(f(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(f(c)))) = f(f(f(f(f(f(c)))))))) <=> ((f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c))))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(485,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(f(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(f(c)))) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c)))))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[484])).
% 0.37/0.59 tff(486,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(f(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(f(c)))) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c))))))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[485, 483])).
% 0.37/0.59 tff(487,plain,
% 0.37/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))) | (f(f(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(f(c)))) = f(f(f(f(f(f(c))))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(488,plain,
% 0.37/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(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(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(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(f(c)))))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.37/0.59 tff(489,plain,
% 0.37/0.59 (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[488, 266, 371, 368, 455, 171, 169])).
% 0.37/0.59 tff(490,plain,
% 0.37/0.59 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(491,plain,
% 0.37/0.59 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(492,plain,
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% 0.37/0.59 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.37/0.59 tff(493,plain,
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% 0.37/0.59 tff(494,plain,
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% 0.37/0.59 inference(symmetry,[status(thm)],[133])).
% 0.37/0.59 tff(495,plain,
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% 0.37/0.59 tff(496,plain,
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% 0.37/0.59 inference(modus_ponens,[status(thm)],[140, 495])).
% 0.37/0.59 tff(497,assumption,(r(f(f(c)), f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.37/0.59 tff(498,assumption,(r(f(f(f(f(f(c))))), f(f(f(f(f(f(c)))))))), introduced(assumption)).
% 0.37/0.59 tff(499,plain,
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% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(500,plain,
% 0.37/0.59 (((~r(f(f(c)), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c)))) <=> ((~r(f(f(f(f(f(c))))), f(f(f(f(f(f(c)))))))) | (~r(f(f(c)), f(f(f(f(f(f(c)))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(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(f(f(f(f(c))))))))),
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% 0.37/0.59 tff(501,plain,
% 0.37/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(f(f(c)))))))) | (~r(f(f(c)), f(f(f(f(f(f(c)))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(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(f(f(f(f(c)))))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[500])).
% 0.37/0.59 tff(502,plain,
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% 0.37/0.59 inference(transitivity,[status(thm)],[501, 499])).
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% 0.37/0.59 tff(505,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[504, 266, 115, 104, 498, 497])).
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% 0.37/0.59 tff(508,plain,
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% 0.37/0.59 tff(509,plain,
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% 0.37/0.59 inference(unit_resolution,[status(thm)],[508, 493, 104])).
% 0.37/0.60 tff(510,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(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))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(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))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(511,plain,
% 0.37/0.60 ((r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(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(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(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))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(512,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(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)))))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[511])).
% 0.37/0.60 tff(513,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(f(f(c))))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(f(c))))))) | (f(f(c)) = f(f(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))))))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[512, 510])).
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% 0.37/0.60 tff(518,plain,((~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.60 tff(519,plain,
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% 0.37/0.60 inference(unit_resolution,[status(thm)],[518, 104, 452])).
% 0.37/0.60 tff(520,assumption,(~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.37/0.60 tff(521,plain,
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% 0.37/0.60 tff(524,plain,
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% 0.37/0.60 tff(525,plain,
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% 0.37/0.60 inference(commutativity,[status(thm)],[])).
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% 0.37/0.60 inference(symmetry,[status(thm)],[525])).
% 0.37/0.60 tff(527,plain,
% 0.37/0.60 ((~(f(f(f(f(f(f(c)))))) = c)) <=> (~(c = f(f(f(f(f(f(c))))))))),
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% 0.37/0.60 tff(528,plain,
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% 0.37/0.60 inference(modus_ponens,[status(thm)],[300, 527])).
% 0.37/0.60 tff(529,plain,
% 0.37/0.60 (~(f(f(f(f(f(f(c)))))) = f(c))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[336, 291])).
% 0.37/0.60 tff(530,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(531,plain,
% 0.37/0.60 ((r(f(f(f(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(f(f(f(c))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c)))))))) <=> ((f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(532,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(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(f(f(f(c))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[531])).
% 0.37/0.60 tff(533,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(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(f(f(f(c))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[532, 530])).
% 0.37/0.60 tff(534,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(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(f(f(f(c))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(535,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.37/0.60 tff(536,plain,
% 0.37/0.60 ((f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[535, 181])).
% 0.37/0.60 tff(537,plain,
% 0.37/0.60 ((f(c) = f(f(f(f(f(f(c))))))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[536, 103])).
% 0.37/0.60 tff(538,plain,
% 0.37/0.60 (r(f(c), f(f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[537, 520, 336, 91, 140])).
% 0.37/0.60 tff(539,plain,
% 0.37/0.60 (r(f(f(f(f(f(f(c)))))), f(c))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[349, 226, 538])).
% 0.37/0.60 tff(540,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(541,plain,
% 0.37/0.60 (((~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(c)))))))) <=> ((c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(542,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c)))))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[541])).
% 0.37/0.60 tff(543,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[542, 540])).
% 0.37/0.60 tff(544,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(545,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (~r(f(f(f(f(f(f(c)))))), f(c))) | (f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.37/0.60 tff(546,plain,
% 0.37/0.60 ((f(f(f(f(f(f(c)))))) = f(c)) | (~r(c, f(f(f(f(f(f(c)))))))) | (c = f(f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[545, 266, 301, 90, 539])).
% 0.37/0.60 tff(547,plain,
% 0.37/0.60 (~r(c, f(f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[546, 529, 528])).
% 0.37/0.60 tff(548,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(549,plain,
% 0.37/0.60 ((r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (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(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(550,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c)))))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[549])).
% 0.37/0.60 tff(551,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[550, 548])).
% 0.37/0.60 tff(552,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(553,plain,
% 0.37/0.60 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(c))))))) | r(c, f(f(f(f(f(f(c))))))) | (c = f(f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(c)))))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.37/0.60 tff(554,plain,
% 0.37/0.60 ($false),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[553, 181, 119, 210, 547, 528, 524, 496])).
% 0.37/0.60 tff(555,plain,(r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.60 tff(556,plain,
% 0.37/0.60 (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(c))) | r(f(c), f(f(f(f(f(c))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[555, 55])).
% 0.37/0.60 tff(557,plain,
% 0.37/0.60 (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (~r(c, f(c))) | r(f(c), f(f(f(f(f(c))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[556, 368])).
% 0.37/0.60 tff(558,plain,
% 0.37/0.60 (~r(c, f(c))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[557, 481, 91, 519])).
% 0.37/0.60 tff(559,plain,
% 0.37/0.60 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(560,plain,
% 0.37/0.61 ((r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c))) <=> (r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(561,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c))))))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[560])).
% 0.37/0.61 tff(562,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[561, 559])).
% 0.37/0.61 tff(563,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(564,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c))))))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.37/0.61 tff(565,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[564, 181, 558, 90, 119, 481, 103, 91])).
% 0.37/0.61 tff(566,plain,((~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(567,plain,
% 0.37/0.61 (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[566, 91, 92])).
% 0.37/0.61 tff(568,plain,
% 0.37/0.61 (r(f(c), f(f(c)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[242, 567, 91])).
% 0.37/0.61 tff(569,plain,
% 0.37/0.61 (r(f(f(c)), f(c))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[406, 568])).
% 0.37/0.61 tff(570,assumption,(~r(f(c), c)), introduced(assumption)).
% 0.37/0.61 tff(571,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(572,plain,
% 0.37/0.61 ((r(f(c), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c))) <=> ((f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(573,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[572])).
% 0.37/0.61 tff(574,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)))),
% 0.37/0.61 inference(transitivity,[status(thm)],[573, 571])).
% 0.37/0.61 tff(575,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c)) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(576,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(f(f(f(c)))) = c) | r(f(c), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.37/0.61 tff(577,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[576, 181, 89, 101, 570, 92, 132, 127])).
% 0.37/0.61 tff(578,plain,(r(f(c), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(579,plain,
% 0.37/0.61 (r(f(c), c)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[578, 127, 92])).
% 0.37/0.61 tff(580,assumption,(r(f(c), c)), introduced(assumption)).
% 0.37/0.61 tff(581,assumption,(r(c, f(f(c)))), introduced(assumption)).
% 0.37/0.61 tff(582,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(583,plain,
% 0.37/0.61 (((~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c)) <=> ((f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(584,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[583])).
% 0.37/0.61 tff(585,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c)))),
% 0.37/0.61 inference(transitivity,[status(thm)],[584, 582])).
% 0.37/0.61 tff(586,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(587,plain,
% 0.37/0.61 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (~r(c, f(f(c)))) | (c = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), c))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.37/0.61 tff(588,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[587, 266, 89, 581, 125, 208, 401, 580])).
% 0.37/0.61 tff(589,plain,((~r(c, f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), c))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(590,plain,
% 0.37/0.61 (~r(c, f(f(c)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[589, 579, 401])).
% 0.37/0.61 tff(591,plain,
% 0.37/0.61 ((f(f(f(f(c)))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(c)))))),
% 0.37/0.61 inference(commutativity,[status(thm)],[])).
% 0.37/0.61 tff(592,assumption,(f(f(f(f(c)))) = f(f(c))), introduced(assumption)).
% 0.37/0.61 tff(593,plain,
% 0.37/0.61 (f(f(c)) = f(f(f(f(c))))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.37/0.61 tff(594,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[419, 593])).
% 0.37/0.61 tff(595,plain,((~(f(f(f(f(c)))) = f(f(c)))) | (f(f(c)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(596,plain,
% 0.37/0.61 (~(f(f(f(f(c)))) = f(f(c)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[595, 198])).
% 0.37/0.61 tff(597,assumption,(~(f(f(f(f(c)))) = f(f(c)))), introduced(assumption)).
% 0.37/0.61 tff(598,assumption,(~r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
% 0.37/0.61 tff(599,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(600,plain,
% 0.37/0.61 ((r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c)) <=> (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(601,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[600])).
% 0.37/0.61 tff(602,plain,
% 0.37/0.61 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[601, 599])).
% 0.37/0.61 tff(603,plain,
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% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
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% 0.37/0.61 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.37/0.61 tff(605,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[604, 181, 274, 125, 101, 92, 598, 597])).
% 0.37/0.61 tff(606,plain,(r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(607,plain,
% 0.37/0.61 (r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(f(f(f(f(c)))), c)),
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% 0.37/0.61 tff(608,plain,
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% 0.37/0.61 inference(unit_resolution,[status(thm)],[607, 590, 92])).
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% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(610,plain,
% 0.37/0.62 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c)))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(611,plain,
% 0.37/0.62 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(c))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.37/0.62 tff(612,plain,
% 0.37/0.62 (~r(f(c), f(f(f(f(c)))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[611, 226, 127])).
% 0.37/0.62 tff(613,assumption,(r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
% 0.37/0.62 tff(614,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(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))) | (~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))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(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))) | (~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))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(615,plain,
% 0.37/0.62 (((~r(f(f(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(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)))))))) <=> ((~r(f(f(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))) | (~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))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(616,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(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(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))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(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))) | (~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)))))))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[615])).
% 0.37/0.62 tff(617,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(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(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))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(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))) | (~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))))))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[616, 614])).
% 0.37/0.62 tff(618,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(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(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))))))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(619,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(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))) | (~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)))))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.37/0.62 tff(620,plain,
% 0.37/0.62 (~r(f(f(f(f(c)))), f(f(f(f(f(f(c)))))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[619, 266, 159, 370, 169, 613, 596])).
% 0.37/0.62 tff(621,assumption,(~r(f(c), f(f(f(f(c)))))), introduced(assumption)).
% 0.37/0.62 tff(622,plain,
% 0.37/0.62 ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(c))),
% 0.37/0.62 inference(commutativity,[status(thm)],[])).
% 0.37/0.62 tff(623,plain,
% 0.37/0.62 ((f(f(f(f(c)))) = f(c)) <=> (f(c) = f(f(f(f(c)))))),
% 0.37/0.62 inference(symmetry,[status(thm)],[622])).
% 0.37/0.62 tff(624,plain,
% 0.37/0.62 ((~(f(f(f(f(c)))) = f(c))) <=> (~(f(c) = f(f(f(f(c))))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[623])).
% 0.37/0.62 tff(625,plain,
% 0.37/0.62 (~(f(c) = f(f(f(f(c)))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[132, 624])).
% 0.37/0.62 tff(626,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(627,plain,
% 0.37/0.62 (((~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c)))))))) <=> ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(628,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c))))))))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[627])).
% 0.37/0.62 tff(629,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c)))))))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[628, 626])).
% 0.37/0.62 tff(630,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(631,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (~r(f(c), f(f(f(f(f(f(c))))))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.37/0.62 tff(632,plain,
% 0.37/0.62 (~r(f(c), f(f(f(f(f(f(c)))))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[631, 266, 208, 401, 55, 159, 370])).
% 0.37/0.62 tff(633,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(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))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(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))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(634,plain,
% 0.37/0.62 ((r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(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))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(635,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(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)))))))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[634])).
% 0.37/0.62 tff(636,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(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))))))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[635, 633])).
% 0.37/0.62 tff(637,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(638,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(f(f(c))))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(c)))))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.37/0.62 tff(639,plain,
% 0.37/0.62 ($false),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[638, 181, 55, 632, 169, 625, 621, 620])).
% 0.37/0.62 tff(640,plain,((~r(f(f(f(f(f(f(c)))))), f(f(c)))) | r(f(c), f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.62 tff(641,plain,
% 0.37/0.62 (~r(f(f(f(f(f(f(c)))))), f(f(c)))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[640, 612, 608, 401])).
% 0.37/0.62 tff(642,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(643,plain,
% 0.37/0.62 ((r(c, f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = c)) <=> (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(644,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c)))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[643])).
% 0.37/0.62 tff(645,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[644, 642])).
% 0.37/0.62 tff(646,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = c))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(647,plain,
% 0.37/0.62 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (f(f(f(f(f(f(c)))))) = c) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), c) | (f(f(f(f(f(f(c)))))) = f(f(c)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.37/0.62 tff(648,plain,
% 0.37/0.62 (r(f(f(f(f(f(f(c)))))), c)),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[647, 181, 590, 125, 300, 159, 641])).
% 0.37/0.62 tff(649,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(650,plain,
% 0.37/0.62 ((r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(651,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[650])).
% 0.37/0.62 tff(652,plain,
% 0.37/0.62 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[651, 649])).
% 0.45/0.63 tff(653,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(654,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(c)))))), f(f(c))) | (f(f(f(f(f(f(c)))))) = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.45/0.63 tff(655,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[654, 181, 520, 140, 115, 232, 159, 326])).
% 0.45/0.63 tff(656,plain,(r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(657,plain,
% 0.45/0.63 (r(f(f(f(f(f(f(c)))))), f(f(c))) | r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[656, 368])).
% 0.45/0.63 tff(658,plain,
% 0.45/0.63 (r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[657, 641, 232])).
% 0.45/0.63 tff(659,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(660,plain,
% 0.45/0.63 ((r(f(f(f(f(f(c))))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c))))))) <=> (r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(661,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[660])).
% 0.45/0.63 tff(662,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[661, 659])).
% 0.45/0.63 tff(663,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(664,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))),
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% 0.45/0.63 tff(665,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[664, 181, 274, 125, 119, 210, 115, 232])).
% 0.45/0.63 tff(666,plain,(r(c, f(f(c))) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(667,plain,
% 0.45/0.63 (r(c, f(f(f(f(f(c))))))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[666, 590, 232])).
% 0.45/0.63 tff(668,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(669,plain,
% 0.45/0.63 (((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = c)) <=> ((f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(670,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[669])).
% 0.45/0.63 tff(671,plain,
% 0.45/0.63 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[670, 668])).
% 0.45/0.63 tff(672,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = c))),
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% 0.45/0.63 tff(673,plain,
% 0.45/0.63 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(c)))))) = c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(f(c)))))), c)) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.45/0.63 tff(674,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[673, 266, 119, 667, 300, 658, 368, 648])).
% 0.45/0.63 tff(675,plain,(r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(c))))), f(f(c))) | (~r(f(c), f(f(c)))) | r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(676,plain,
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% 0.45/0.65 inference(transitivity,[status(thm)],[768, 766])).
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% 0.45/0.65 inference(modus_ponens,[status(thm)],[770, 769])).
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% 0.45/0.65 tff(774,plain,
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% 0.45/0.65 tff(775,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(776,plain,
% 0.45/0.65 (((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c))))))) <=> ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(777,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c))))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[776])).
% 0.45/0.65 tff(778,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.45/0.65 inference(transitivity,[status(thm)],[777, 775])).
% 0.45/0.65 tff(779,plain,
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% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.45/0.65 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c))))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[779, 778])).
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% 0.45/0.65 inference(unit_resolution,[status(thm)],[780, 266, 208, 401, 103, 115, 104])).
% 0.45/0.65 tff(782,plain,
% 0.45/0.65 (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[518, 104, 455])).
% 0.45/0.65 tff(783,plain,
% 0.45/0.65 (~r(c, f(c))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[557, 781, 210, 782])).
% 0.45/0.65 tff(784,plain,
% 0.45/0.65 ($false),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[564, 181, 783, 90, 119, 210, 103, 781])).
% 0.45/0.65 tff(785,plain,((~r(f(f(f(f(f(c))))), f(f(c)))) | r(c, f(f(f(f(f(c)))))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.65 tff(786,plain,
% 0.45/0.65 (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[785, 774, 759, 747])).
% 0.45/0.65 tff(787,plain,
% 0.45/0.65 (r(c, f(f(c)))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[666, 786, 774])).
% 0.45/0.65 tff(788,plain,
% 0.45/0.65 (~r(c, f(c))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[684, 266, 90, 787, 125, 208, 759])).
% 0.45/0.65 tff(789,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(790,plain,
% 0.45/0.65 ((r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c)))))) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(791,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[790])).
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% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c)))),
% 0.45/0.65 inference(transitivity,[status(thm)],[791, 789])).
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% 0.45/0.65 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (c = f(c)) | (c = f(f(f(f(c))))))),
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% 0.45/0.65 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(c))),
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% 0.45/0.65 inference(unit_resolution,[status(thm)],[794, 181, 788, 90, 132, 127, 755])).
% 0.45/0.65 tff(796,assumption,(r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))), introduced(assumption)).
% 0.45/0.65 tff(797,assumption,(r(c, f(f(f(f(c)))))), introduced(assumption)).
% 0.45/0.65 tff(798,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(799,plain,
% 0.45/0.65 (((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c)) <=> ((f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(800,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[799])).
% 0.45/0.65 tff(801,plain,
% 0.45/0.65 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))))),
% 0.45/0.65 inference(transitivity,[status(thm)],[800, 798])).
% 0.45/0.65 tff(802,plain,
% 0.45/0.65 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.45/0.65 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (c = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[802, 801])).
% 0.45/0.65 tff(804,plain,
% 0.45/0.65 ((~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[803, 266, 84, 797, 755])).
% 0.45/0.65 tff(805,plain,
% 0.45/0.65 (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[804, 796, 58])).
% 0.45/0.65 tff(806,assumption,(f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))), introduced(assumption)).
% 0.45/0.65 tff(807,plain,
% 0.45/0.65 (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))),
% 0.45/0.65 inference(symmetry,[status(thm)],[806])).
% 0.45/0.65 tff(808,plain,
% 0.45/0.65 (inj_0(f(f(f(f(f(f(f(f(f(c)))))))))) = inj_0(f(f(f(f(f(c))))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[807])).
% 0.45/0.65 tff(809,plain,
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% 0.45/0.65 tff(820,assumption,(f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))), introduced(assumption)).
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% 0.45/0.65 tff(822,assumption,(~(f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c))))))))))), introduced(assumption)).
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% 0.45/0.66 tff(837,plain,
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% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))))),
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% 0.45/0.66 tff(848,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))))),
% 0.45/0.66 inference(transitivity,[status(thm)],[847, 845])).
% 0.45/0.66 tff(849,plain,
% 0.45/0.66 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(850,plain,
% 0.45/0.66 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(c)), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.45/0.66 tff(851,plain,
% 0.45/0.66 ((f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[850, 181, 719, 198, 80, 844])).
% 0.45/0.66 tff(852,plain,
% 0.45/0.66 (r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[851, 58])).
% 0.45/0.66 tff(853,plain,
% 0.45/0.66 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), c)) | r(c, f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), c)) | r(c, f(f(f(f(f(c)))))))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(854,plain,
% 0.45/0.66 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), c)) | r(c, f(f(f(f(f(c)))))))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(855,plain,
% 0.45/0.66 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), c)) | r(c, f(f(f(f(f(c))))))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.45/0.66 tff(856,plain,
% 0.45/0.66 (~r(f(f(f(f(f(c))))), c)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[855, 226, 774])).
% 0.45/0.66 tff(857,plain,
% 0.45/0.66 (~r(f(c), c)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[589, 787, 759])).
% 0.45/0.66 tff(858,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(859,plain,
% 0.45/0.66 ((r(f(c), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(c)) | (f(c) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(c))) <=> ((f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(860,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(c)) | (f(c) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[859])).
% 0.45/0.66 tff(861,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(c)) | (f(c) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[860, 858])).
% 0.45/0.66 tff(862,plain,
% 0.45/0.66 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(c)) | (f(c) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(c)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(863,plain,
% 0.45/0.66 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | r(f(f(f(f(f(c))))), 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))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.45/0.66 tff(864,plain,
% 0.45/0.66 (r(f(f(f(f(f(c))))), f(c))),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[863, 181, 89, 53, 857, 856, 385])).
% 0.45/0.66 tff(865,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(866,plain,
% 0.45/0.66 ((r(f(c), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))) <=> ((f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(867,plain,
% 0.45/0.66 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[866])).
% 0.45/0.67 tff(868,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[867, 865])).
% 0.45/0.67 tff(869,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(870,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.45/0.67 tff(871,plain,
% 0.45/0.67 ((f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[870, 181, 612, 71, 625, 844])).
% 0.45/0.67 tff(872,plain,
% 0.45/0.67 (r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[871, 58])).
% 0.45/0.67 tff(873,plain,
% 0.45/0.67 ((f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) <=> (f(c) = f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.45/0.67 inference(commutativity,[status(thm)],[])).
% 0.45/0.67 tff(874,plain,
% 0.45/0.67 ((f(c) = f(f(f(f(f(f(f(f(f(c)))))))))) <=> (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.45/0.67 inference(symmetry,[status(thm)],[873])).
% 0.45/0.67 tff(875,plain,
% 0.45/0.67 ((~(f(c) = f(f(f(f(f(f(f(f(f(c))))))))))) <=> (~(f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[874])).
% 0.45/0.67 tff(876,plain,
% 0.45/0.67 (~(f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[69, 875])).
% 0.45/0.67 tff(877,assumption,(r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))), introduced(assumption)).
% 0.45/0.67 tff(878,assumption,(r(f(f(f(f(f(c))))), f(c))), introduced(assumption)).
% 0.45/0.67 tff(879,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(880,plain,
% 0.45/0.67 (((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(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(f(f(f(f(f(f(c))))))))))) <=> ((f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(881,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(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(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[880])).
% 0.45/0.67 tff(882,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(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(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[881, 879])).
% 0.45/0.67 tff(883,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(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(f(f(f(f(f(f(c)))))))))))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(884,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.45/0.67 tff(885,plain,
% 0.45/0.67 ((~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[884, 266, 878, 385, 877])).
% 0.45/0.67 tff(886,plain,
% 0.45/0.67 (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[885, 822, 876])).
% 0.45/0.67 tff(887,assumption,(~r(f(f(f(f(f(c))))), c)), introduced(assumption)).
% 0.45/0.67 tff(888,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(889,plain,
% 0.45/0.67 ((r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c))))))))))) <=> (r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(890,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c)))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[889])).
% 0.45/0.67 tff(891,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.45/0.67 inference(transitivity,[status(thm)],[890, 888])).
% 0.45/0.67 tff(892,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(893,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.45/0.67 tff(894,plain,
% 0.45/0.67 (r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[893, 181, 53, 84, 887, 81])).
% 0.45/0.67 tff(895,plain,
% 0.45/0.67 ($false),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[894, 886, 822])).
% 0.45/0.67 tff(896,plain,((f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.67 tff(897,plain,
% 0.45/0.67 (r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[896, 872, 817, 864, 856])).
% 0.45/0.67 tff(898,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(899,plain,
% 0.45/0.67 (((~r(c, f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c)) <=> ((~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(900,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[899])).
% 0.45/0.67 tff(901,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.45/0.67 inference(transitivity,[status(thm)],[900, 898])).
% 0.45/0.67 tff(902,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(903,plain,
% 0.45/0.67 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (c = f(f(c))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.45/0.67 tff(904,plain,
% 0.45/0.67 ($false),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[903, 266, 787, 125, 84, 80, 897, 852])).
% 0.45/0.67 tff(905,plain,(r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.67 tff(906,plain,
% 0.45/0.67 (r(f(f(f(f(c)))), f(c))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[905, 598])).
% 0.45/0.67 tff(907,plain,
% 0.45/0.67 (r(f(c), f(f(f(f(f(c))))))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[711, 92])).
% 0.45/0.67 tff(908,assumption,(r(f(c), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.45/0.67 tff(909,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(910,plain,
% 0.45/0.67 (((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c)) <=> ((f(c) = c) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(911,plain,
% 0.45/0.67 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c)))))))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[910])).
% 0.45/0.67 tff(912,plain,
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% 0.45/0.68 inference(monotonicity,[status(thm)],[954])).
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% 0.45/0.68 inference(transitivity,[status(thm)],[955, 953])).
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% 0.45/0.68 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.45/0.68 tff(959,plain,
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% 0.45/0.68 inference(unit_resolution,[status(thm)],[958, 266, 581, 125, 101, 613])).
% 0.45/0.68 tff(960,plain,
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% 0.45/0.68 tff(962,plain,((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(f(f(c)))))), f(f(c)))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.68 tff(963,plain,
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% 0.45/0.68 tff(964,plain,
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% 0.45/0.68 tff(965,plain,
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% 0.45/0.68 inference(unit_resolution,[status(thm)],[345, 964, 231])).
% 0.45/0.68 tff(966,plain,
% 0.45/0.68 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
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% 0.45/0.68 inference(modus_ponens,[status(thm)],[967, 966])).
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% 0.45/0.68 tff(970,plain,
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% 0.45/0.68 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))),
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% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(973,plain,
% 0.45/0.68 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(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(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[972])).
% 0.45/0.69 tff(974,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(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(f(f(f(c)))))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(f(c)))))))) | (~r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c))))))))),
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% 0.45/0.69 tff(978,plain,(r(f(c), f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), c)) | r(c, f(c))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.69 tff(979,plain,
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% 0.45/0.69 tff(980,plain,
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% 0.45/0.69 tff(981,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(982,plain,
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% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(983,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c)))))),
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% 0.45/0.69 tff(984,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(c)), f(c))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), f(c))) | (f(f(c)) = f(c)) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
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% 0.45/0.69 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.45/0.69 tff(987,plain,
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% 0.45/0.69 tff(988,plain,
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% 0.45/0.69 tff(989,plain,
% 0.45/0.69 (r(f(f(f(f(c)))), f(f(c)))),
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% 0.45/0.69 tff(990,plain,
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% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(991,plain,
% 0.45/0.69 (((~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), 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(c) = f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(992,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c))))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[991])).
% 0.45/0.69 tff(993,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.45/0.69 inference(transitivity,[status(thm)],[992, 990])).
% 0.45/0.69 tff(994,plain,
% 0.45/0.69 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(c)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(995,plain,
% 0.45/0.69 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.45/0.69 tff(996,plain,
% 0.45/0.69 ($false),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[995, 266, 208, 979, 989, 132, 596, 918])).
% 0.45/0.69 tff(997,plain,(r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.69 tff(998,plain,
% 0.45/0.69 (r(f(f(f(f(c)))), c)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[997, 126])).
% 0.45/0.69 tff(999,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(1000,plain,
% 0.45/0.69 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(1001,plain,
% 0.45/0.69 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(c))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.45/0.69 tff(1002,plain,
% 0.45/0.69 ($false),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[1001, 266, 89, 101, 580, 765, 132, 251])).
% 0.45/0.69 tff(1003,plain,((~r(f(c), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.69 tff(1004,plain,
% 0.45/0.69 (~r(f(c), c)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[1003, 998, 906])).
% 0.45/0.69 tff(1005,plain,
% 0.45/0.69 (~r(f(c), c)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[1003, 765, 906])).
% 0.45/0.69 tff(1006,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(1007,plain,
% 0.45/0.69 ((r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c))))))) <=> ((f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(1008,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c)))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[1007])).
% 0.45/0.69 tff(1009,plain,
% 0.45/0.69 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c))),
% 0.45/0.70 inference(transitivity,[status(thm)],[1008, 1006])).
% 0.45/0.70 tff(1010,plain,
% 0.45/0.70 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(1011,plain,
% 0.45/0.70 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c)),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.45/0.70 tff(1012,plain,
% 0.45/0.70 ($false),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[1011, 181, 89, 53, 103, 91, 570, 887])).
% 0.45/0.70 tff(1013,plain,(r(f(f(f(f(f(c))))), c) | r(f(c), f(f(f(f(f(c)))))) | r(f(c), c)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.70 tff(1014,plain,
% 0.45/0.70 (r(f(c), f(f(f(f(f(c))))))),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[1013, 887, 570])).
% 0.45/0.70 tff(1015,plain,
% 0.45/0.70 (r(f(f(f(f(f(c))))), f(c))),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[921, 226, 1014])).
% 0.45/0.70 tff(1016,plain,
% 0.45/0.70 (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[896, 81, 817, 1015, 887])).
% 0.45/0.70 tff(1017,plain,
% 0.45/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(1018,plain,
% 0.45/0.70 ((r(f(c), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))) <=> ((f(c) = c) | r(f(c), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(1019,plain,
% 0.45/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[1018])).
% 0.45/0.70 tff(1020,plain,
% 0.45/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[1019, 1017])).
% 0.45/0.70 tff(1021,plain,
% 0.45/0.70 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(c) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(1022,plain,
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% 0.52/0.70 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.52/0.70 tff(1023,plain,
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% 0.52/0.70 inference(unit_resolution,[status(thm)],[1022, 181, 89, 570, 84, 1016, 81, 71])).
% 0.52/0.70 tff(1024,plain,(r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(c), c) | r(f(f(f(f(f(c))))), c)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.70 tff(1025,plain,
% 0.52/0.70 (r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[1024, 887, 1005])).
% 0.52/0.70 tff(1026,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1027,plain,
% 0.52/0.70 (((~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c))))))))))) <=> ((f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1028,plain,
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% 0.52/0.70 inference(monotonicity,[status(thm)],[1027])).
% 0.52/0.70 tff(1029,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.70 inference(transitivity,[status(thm)],[1028, 1026])).
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% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
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% 0.52/0.70 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.52/0.70 tff(1032,plain,
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% 0.52/0.70 inference(unit_resolution,[status(thm)],[1031, 266, 101, 84, 765, 57, 1025])).
% 0.52/0.70 tff(1033,plain,
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% 0.52/0.70 tff(1034,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1035,plain,
% 0.52/0.70 (((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c)))) <=> ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1036,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.52/0.70 inference(monotonicity,[status(thm)],[1035])).
% 0.52/0.70 tff(1037,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.52/0.70 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.52/0.70 tff(1038,plain,
% 0.52/0.70 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c))))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(1039,plain,
% 0.52/0.70 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.52/0.70 tff(1040,plain,
% 0.52/0.70 (~r(f(c), f(f(c)))),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[1039, 266, 208, 103, 1033, 369, 255])).
% 0.52/0.70 tff(1041,plain,
% 0.52/0.70 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1042,plain,
% 0.52/0.70 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(1043,plain,
% 0.52/0.70 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.52/0.70 tff(1044,plain,
% 0.52/0.70 (~r(c, f(c))),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[1043, 226, 1005])).
% 0.52/0.70 tff(1045,plain,
% 0.52/0.70 (r(c, f(f(c)))),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[283, 1044, 1040])).
% 0.52/0.70 tff(1046,plain,
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% 0.52/0.70 inference(unit_resolution,[status(thm)],[936, 1045])).
% 0.52/0.70 tff(1047,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1048,plain,
% 0.52/0.70 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(1049,plain,
% 0.52/0.70 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.52/0.70 tff(1050,plain,
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% 0.52/0.70 inference(unit_resolution,[status(thm)],[1049, 266, 124, 1046, 84, 80, 1025])).
% 0.52/0.70 tff(1051,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((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(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (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(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1052,plain,
% 0.52/0.70 ((r(f(f(f(f(f(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(f(f(f(c)))))))))) | (f(f(f(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(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(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(1053,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(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(f(f(f(c)))))))))) | (f(f(f(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(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((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(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.70 inference(monotonicity,[status(thm)],[1052])).
% 0.52/0.70 tff(1054,plain,
% 0.52/0.70 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(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(f(f(f(c)))))))))) | (f(f(f(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(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (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(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.71 inference(transitivity,[status(thm)],[1053, 1051])).
% 0.52/0.71 tff(1055,plain,
% 0.52/0.71 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(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(f(f(f(c)))))))))) | (f(f(f(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(f(f(f(c)))))))))))),
% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
% 0.52/0.71 tff(1056,plain,
% 0.52/0.71 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.52/0.71 tff(1057,plain,
% 0.52/0.71 ($false),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[1056, 181, 598, 596, 57, 80, 1050, 1032])).
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% 0.52/0.71 tff(1059,plain,
% 0.52/0.71 (r(f(f(f(f(f(c))))), c)),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[1058, 998, 598, 720])).
% 0.52/0.71 tff(1060,plain,
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% 0.52/0.71 tff(1061,plain,((~r(f(f(f(f(f(c))))), c)) | r(c, f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.71 tff(1062,plain,
% 0.52/0.71 (r(c, f(f(f(f(f(c))))))),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[1061, 1059])).
% 0.52/0.71 tff(1063,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[324, 266, 124, 119, 1062, 720, 255])).
% 0.52/0.71 tff(1064,plain,
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% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(1065,plain,
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% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(1066,plain,
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% 0.52/0.71 inference(monotonicity,[status(thm)],[1065])).
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% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.52/0.71 inference(modus_ponens,[status(thm)],[1068, 1067])).
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% 0.52/0.71 tff(1071,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[780, 266, 208, 1070, 103, 115, 726])).
% 0.52/0.71 tff(1072,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[709, 520, 401, 91])).
% 0.52/0.71 tff(1073,plain,
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% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(1074,plain,
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% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(1075,plain,
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% 0.52/0.71 inference(monotonicity,[status(thm)],[1074])).
% 0.52/0.71 tff(1076,plain,
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% 0.52/0.71 inference(transitivity,[status(thm)],[1075, 1073])).
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% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[1078, 181, 159, 1072, 598, 596, 288])).
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% 0.52/0.71 tff(1083,plain,
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% 0.52/0.71 tff(1084,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[296, 266, 132, 906, 1083])).
% 0.52/0.71 tff(1085,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[1084, 1079, 292, 288])).
% 0.52/0.71 tff(1086,plain,(r(f(f(f(f(f(f(c)))))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))) | (~r(f(c), f(f(c)))) | r(f(c), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.71 tff(1087,plain,
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% 0.52/0.71 tff(1088,plain,
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% 0.52/0.71 tff(1089,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[379, 368])).
% 0.52/0.71 tff(1090,plain,
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% 0.52/0.71 tff(1091,plain,
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% 0.52/0.71 tff(1092,plain,(r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.71 tff(1093,plain,
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% 0.52/0.71 inference(unit_resolution,[status(thm)],[1092, 598])).
% 0.52/0.71 tff(1094,plain,
% 0.52/0.71 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))),
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% 0.52/0.71 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.52/0.71 tff(1097,plain,
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% 0.52/0.71 tff(1098,plain,
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% 0.52/0.71 tff(1099,plain,
% 0.52/0.71 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
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% 0.52/0.71 tff(1100,plain,
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% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(1101,plain,
% 0.52/0.71 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))))),
% 0.52/0.71 inference(monotonicity,[status(thm)],[1100])).
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% 0.52/0.71 inference(transitivity,[status(thm)],[1101, 1099])).
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% 0.52/0.72 inference(monotonicity,[status(thm)],[1159])).
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% 0.52/0.72 inference(transitivity,[status(thm)],[1160, 1158])).
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% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
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% 0.52/0.72 inference(modus_ponens,[status(thm)],[1162, 1161])).
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% 0.52/0.72 tff(1166,plain,
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% 0.52/0.72 inference(unit_resolution,[status(thm)],[1165, 1154, 1148])).
% 0.52/0.72 tff(1167,assumption,(~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))), introduced(assumption)).
% 0.52/0.72 tff(1168,plain,
% 0.52/0.72 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(1169,plain,
% 0.52/0.72 ((r(f(f(f(f(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(f(f(f(f(c)))))))))) | (f(f(f(f(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(f(f(f(f(c))))))))))) <=> ((f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(1170,plain,
% 0.52/0.72 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(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(f(f(f(f(c)))))))))) | (f(f(f(f(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(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.72 inference(monotonicity,[status(thm)],[1169])).
% 0.52/0.72 tff(1171,plain,
% 0.52/0.72 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(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(f(f(f(f(c)))))))))) | (f(f(f(f(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(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.72 inference(transitivity,[status(thm)],[1170, 1168])).
% 0.52/0.72 tff(1172,plain,
% 0.52/0.72 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(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(f(f(f(f(c)))))))))) | (f(f(f(f(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(f(f(f(f(c)))))))))))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(1173,plain,
% 0.52/0.72 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)) | (f(f(f(f(c)))) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.52/0.72 tff(1174,plain,
% 0.52/0.72 ($false),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[1173, 181, 132, 127, 57, 82, 71, 1167])).
% 0.52/0.72 tff(1175,plain,(r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.72 tff(1176,plain,
% 0.52/0.72 (r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[1175, 1141, 1166])).
% 0.52/0.72 tff(1177,plain,
% 0.52/0.72 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(1178,plain,
% 0.52/0.72 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(1179,plain,
% 0.52/0.72 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.52/0.72 tff(1180,plain,
% 0.52/0.72 (r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[1179, 226, 1176])).
% 0.52/0.72 tff(1181,plain,
% 0.52/0.72 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(1182,plain,
% 0.52/0.72 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(1183,plain,
% 0.52/0.72 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c)))))),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.52/0.72 tff(1184,plain,
% 0.52/0.72 (r(f(f(c)), f(f(f(f(c)))))),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[1183, 226, 1112])).
% 0.52/0.72 tff(1185,plain,
% 0.52/0.72 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(1186,plain,
% 0.52/0.72 (((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c))))))))))) <=> ((f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1187,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))))))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[1186])).
% 0.52/0.73 tff(1188,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.73 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.52/0.73 tff(1189,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(1190,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.52/0.73 tff(1191,plain,
% 0.52/0.73 ((f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1190, 266, 1184, 198, 1180])).
% 0.52/0.73 tff(1192,plain,
% 0.52/0.73 (~r(f(f(c)), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1191, 1147, 58])).
% 0.52/0.73 tff(1193,assumption,(r(f(c), f(f(f(f(f(f(f(f(f(c))))))))))), introduced(assumption)).
% 0.52/0.73 tff(1194,plain,
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% 0.52/0.73 inference(rewrite,[status(thm)],[])).
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% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(1196,plain,
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% 0.52/0.73 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 0.52/0.73 tff(1197,plain,
% 0.52/0.73 ($false),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1196, 226, 1193, 82])).
% 0.52/0.73 tff(1198,plain,((~r(f(c), f(f(f(f(f(f(f(f(f(c))))))))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.73 tff(1199,plain,
% 0.52/0.73 (~r(f(c), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1198, 1166])).
% 0.52/0.73 tff(1200,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1201,plain,
% 0.52/0.73 ((r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(c)))) <=> (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1202,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c))))))))))))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[1201])).
% 0.52/0.73 tff(1203,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))))),
% 0.52/0.73 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.52/0.73 tff(1204,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(c))))),
% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(1205,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(c))) | (f(c) = f(f(c))) | (f(f(c)) = f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(f(c)), f(f(f(f(f(f(f(f(f(c)))))))))) | r(f(c), f(f(f(f(f(f(f(f(f(c)))))))))) | (f(c) = f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.52/0.73 tff(1206,plain,
% 0.52/0.73 (r(f(c), f(f(c)))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1205, 181, 208, 1199, 69, 1147, 1192])).
% 0.52/0.73 tff(1207,plain,
% 0.52/0.73 (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[675, 1206, 92, 1141])).
% 0.52/0.73 tff(1208,plain,
% 0.52/0.73 ($false),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[785, 1207, 1206, 1132, 1143])).
% 0.52/0.73 tff(1209,plain,(r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.73 tff(1210,plain,
% 0.52/0.73 (~r(c, f(f(c)))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1114, 1209])).
% 0.52/0.73 tff(1211,plain,
% 0.52/0.73 (r(c, f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[283, 231, 1210])).
% 0.52/0.73 tff(1212,plain,
% 0.52/0.73 (r(f(c), c)),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1127, 1211])).
% 0.52/0.73 tff(1213,plain,
% 0.52/0.73 (~r(f(f(f(f(c)))), f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1003, 1212, 1209])).
% 0.52/0.73 tff(1214,plain,
% 0.52/0.73 (~r(c, f(f(f(f(f(c))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[916, 1212, 1131])).
% 0.52/0.73 tff(1215,plain,
% 0.52/0.73 (~r(f(f(f(f(f(c))))), c)),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1061, 1214])).
% 0.52/0.73 tff(1216,plain,
% 0.52/0.73 (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1165, 1215, 1211])).
% 0.52/0.73 tff(1217,plain,
% 0.52/0.73 (r(f(f(f(f(c)))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1175, 1216, 1213])).
% 0.52/0.73 tff(1218,plain,
% 0.52/0.73 ((f(f(f(f(f(c))))) = f(c)) <=> (f(c) = f(f(f(f(f(c))))))),
% 0.52/0.73 inference(commutativity,[status(thm)],[])).
% 0.52/0.73 tff(1219,plain,
% 0.52/0.73 ((f(c) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(c))),
% 0.52/0.73 inference(symmetry,[status(thm)],[1218])).
% 0.52/0.73 tff(1220,plain,
% 0.52/0.73 ((~(f(c) = f(f(f(f(f(c))))))) <=> (~(f(f(f(f(f(c))))) = f(c)))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[1219])).
% 0.52/0.73 tff(1221,plain,
% 0.52/0.73 (~(f(f(f(f(f(c))))) = f(c))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[103, 1220])).
% 0.52/0.73 tff(1222,plain,
% 0.52/0.73 (r(f(c), f(f(f(f(f(c))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[242, 232, 231])).
% 0.52/0.73 tff(1223,plain,
% 0.52/0.73 (r(f(f(f(f(f(c))))), f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[921, 226, 1222])).
% 0.52/0.73 tff(1224,plain,
% 0.52/0.73 (r(c, f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[283, 274, 231])).
% 0.52/0.73 tff(1225,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1226,plain,
% 0.52/0.73 (((~r(c, f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c)) <=> ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1227,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c)))))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[1226])).
% 0.52/0.73 tff(1228,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.52/0.73 inference(transitivity,[status(thm)],[1227, 1225])).
% 0.52/0.73 tff(1229,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = c))),
% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(1230,plain,
% 0.52/0.73 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c)))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.52/0.73 tff(1231,plain,
% 0.52/0.73 ((~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = f(c))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1230, 266, 1224, 90, 53, 1223])).
% 0.52/0.73 tff(1232,plain,
% 0.52/0.73 (~r(f(f(f(f(f(c))))), c)),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1231, 1221])).
% 0.52/0.73 tff(1233,plain,
% 0.52/0.73 (~r(f(f(c)), c)),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[473, 274])).
% 0.52/0.73 tff(1234,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1235,plain,
% 0.52/0.73 ((r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c)))) <=> ((f(f(c)) = c) | r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1236,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[1235])).
% 0.52/0.73 tff(1237,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.73 inference(transitivity,[status(thm)],[1236, 1234])).
% 0.52/0.73 tff(1238,plain,
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% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(1239,plain,
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% 0.52/0.73 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.52/0.73 tff(1240,plain,
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% 0.52/0.73 tff(1241,plain,(r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.73 tff(1242,plain,
% 0.52/0.73 (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[1241, 231, 1210])).
% 0.52/0.73 tff(1243,plain,
% 0.52/0.73 (~r(f(f(c)), c)),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[473, 1210])).
% 0.52/0.73 tff(1244,plain,
% 0.52/0.73 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(1245,plain,
% 0.52/0.73 ((r(f(f(c)), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))) <=> ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1246,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c)))),
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% 0.52/0.74 tff(1247,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | (f(f(c)) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c))),
% 0.52/0.74 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.52/0.74 tff(1248,plain,
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% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(1249,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = c) | r(f(f(c)), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c))) | r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.52/0.74 tff(1250,plain,
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% 0.52/0.74 tff(1251,plain,
% 0.52/0.74 (r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[893, 181, 53, 84, 887, 817, 81])).
% 0.52/0.74 tff(1252,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
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% 0.52/0.74 tff(1253,plain,
% 0.52/0.74 (((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(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(f(f(f(f(f(f(c))))))))))) <=> ((f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1254,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(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(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))))),
% 0.52/0.74 inference(monotonicity,[status(thm)],[1253])).
% 0.52/0.74 tff(1255,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(f(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(f(f(f(f(f(f(c)))))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.74 inference(transitivity,[status(thm)],[1254, 1252])).
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% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(1257,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c))))))))))) | (f(f(f(f(f(c))))) = f(f(f(f(f(f(f(f(f(c)))))))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))),
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% 0.52/0.74 tff(1258,plain,
% 0.52/0.74 ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(f(f(f(f(f(f(c)))))))))))),
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% 0.52/0.74 tff(1260,plain,(r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(f(f(f(c))))), c)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(1261,plain,
% 0.52/0.74 (r(f(f(f(f(f(f(f(f(f(c))))))))), c)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1260, 1242, 1215])).
% 0.52/0.74 tff(1262,plain,
% 0.52/0.74 ($false),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1031, 266, 101, 84, 1209, 57, 1261, 1217])).
% 0.52/0.74 tff(1263,plain,(r(f(c), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(1264,plain,
% 0.52/0.74 (r(f(f(c)), f(c))),
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% 0.52/0.74 tff(1265,plain,
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% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1266,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~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)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(c))))),
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% 0.52/0.74 tff(1267,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~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)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(c)))),
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% 0.52/0.74 tff(1268,plain,
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% 0.52/0.74 inference(unit_resolution,[status(thm)],[1267, 266, 1264, 209, 115, 1155, 385])).
% 0.52/0.74 tff(1269,plain,
% 0.52/0.74 (r(c, f(f(f(f(f(c))))))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[666, 1268, 1210])).
% 0.52/0.74 tff(1270,plain,
% 0.52/0.74 (~r(f(c), c)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[916, 1269, 1131])).
% 0.52/0.74 tff(1271,plain,
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% 0.52/0.74 inference(unit_resolution,[status(thm)],[1127, 1270])).
% 0.52/0.74 tff(1272,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1273,plain,
% 0.52/0.74 ((r(c, f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c)) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1274,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))))),
% 0.52/0.74 inference(monotonicity,[status(thm)],[1273])).
% 0.52/0.74 tff(1275,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)))),
% 0.52/0.74 inference(transitivity,[status(thm)],[1274, 1272])).
% 0.52/0.74 tff(1276,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(1277,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 0.52/0.74 tff(1278,plain,
% 0.52/0.74 ($false),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1277, 181, 1271, 90, 84, 82, 81, 71])).
% 0.52/0.74 tff(1279,plain,(r(f(f(f(f(f(f(f(f(f(c))))))))), f(c)) | r(f(f(f(f(f(f(f(f(f(c))))))))), c)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(1280,plain,
% 0.52/0.74 (r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1279, 81])).
% 0.52/0.74 tff(1281,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1282,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c))))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(1283,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(c))) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))) | (f(f(c)) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(c)) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(c)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 0.52/0.74 tff(1284,plain,
% 0.52/0.74 (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(c)))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1283, 266, 1264, 209, 1280, 80, 71])).
% 0.52/0.74 tff(1285,plain,
% 0.52/0.74 ($false),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1249, 181, 124, 1243, 84, 80, 81, 1284])).
% 0.52/0.74 tff(1286,plain,(r(f(f(f(f(f(f(f(f(f(c))))))))), c)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(1287,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(1288,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(1289,plain,
% 0.52/0.74 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c)))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 0.52/0.74 tff(1290,plain,
% 0.52/0.74 (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[1289, 266, 101, 84, 1209, 1286, 58])).
% 0.52/0.74 tff(1291,plain,
% 0.52/0.74 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1292,plain,
% 0.52/0.75 ((r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c)) <=> (r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1293,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))))),
% 0.52/0.75 inference(monotonicity,[status(thm)],[1292])).
% 0.52/0.75 tff(1294,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.52/0.75 inference(transitivity,[status(thm)],[1293, 1291])).
% 0.52/0.75 tff(1295,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(f(c))))), c) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(1296,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 0.52/0.75 tff(1297,plain,
% 0.52/0.75 (r(f(f(f(f(f(c))))), c)),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[1296, 181, 1210, 125, 53, 115, 1268])).
% 0.52/0.75 tff(1298,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1299,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(1300,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), c)) | (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = c) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.52/0.75 tff(1301,plain,
% 0.52/0.75 (~r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c))))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[1300, 266, 53, 84, 1297, 825, 1286])).
% 0.52/0.75 tff(1302,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1303,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(1304,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 0.52/0.75 tff(1305,plain,
% 0.52/0.75 (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[1304, 266, 101, 53, 829, 1209, 1297])).
% 0.52/0.75 tff(1306,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1307,plain,
% 0.52/0.75 ((r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c))))))) <=> ((f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(1308,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))))),
% 0.52/0.75 inference(monotonicity,[status(thm)],[1307])).
% 0.52/0.75 tff(1309,plain,
% 0.52/0.75 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))))),
% 0.52/0.75 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.52/0.75 tff(1310,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(1311,plain,
% 0.52/0.75 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(f(c)))))) | (f(f(f(f(f(f(f(f(f(c))))))))) = f(f(f(f(c))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(f(c)))))) | r(f(f(f(f(f(f(f(f(f(c))))))))), f(f(f(f(c)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.52/0.75 tff(1312,plain,
% 0.52/0.75 ($false),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[1311, 181, 1305, 829, 825, 1301, 1290, 58])).
% 0.52/0.75 % SZS output end Proof
% 0.52/0.75 % E exiting
%------------------------------------------------------------------------------