%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN551+3 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:39:33 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN551+3 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:38:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $i > $i)).
% 0.20/0.38 tff(g_type, type, (
% 0.20/0.38 g: $i > $i)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i > $i)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.38 tptp_fun_Y_3: $i > $i)).
% 0.20/0.38 tff(1,assumption,(~((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) | (X!2 = g(f(X!2)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (X!2 = g(f(X!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,assumption,(X!2 = g(f(X!2))), introduced(assumption)).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (g(f(X!2)) = X!2),
% 0.20/0.38 inference(symmetry,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.38 inference(symmetry,[status(thm)],[6])).
% 0.20/0.38 tff(8,assumption,(~(f(X!2) = f(g(f(X!2))))), introduced(assumption)).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,((f(X!2) = f(g(f(X!2)))) | (~(X!2 = g(f(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.38 inference(symmetry,[status(thm)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (g(f(X!2)) = g(f(g(f(X!2))))),
% 0.20/0.38 inference(symmetry,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (f(X!2) = f(g(f(X!2)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[10, 4])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.38 inference(symmetry,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (g(f(g(f(X!2)))) = g(f(X!2))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (g(f(g(f(X!2)))) = X!2),
% 0.20/0.38 inference(transitivity,[status(thm)],[17, 5])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (f(g(f(g(f(X!2))))) = f(X!2)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (f(X!2) = f(g(f(g(f(X!2)))))),
% 0.20/0.38 inference(symmetry,[status(thm)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[16, 20])).
% 0.20/0.38 tff(22,assumption,(~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))), introduced(assumption)).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,((f(g(f(X!2))) = f(g(f(g(f(X!2)))))) | (~(X!2 = g(f(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(g(f(g(f(X!2)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 3])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (((~(X!2 = g(f(X!2)))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) | ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.20/0.38 tff(28,assumption,(~((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2)))), introduced(assumption)).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))) | (tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (f(g(tptp_fun_Y_1(f(X!2)))) = tptp_fun_Y_1(f(X!2))),
% 0.20/0.38 inference(symmetry,[status(thm)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (g(f(g(tptp_fun_Y_1(f(X!2))))) = g(tptp_fun_Y_1(f(X!2)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2)))))),
% 0.20/0.38 inference(symmetry,[status(thm)],[32])).
% 0.20/0.38 tff(34,assumption,(![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))), introduced(assumption)).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2))))))) | (g(tptp_fun_Y_1(f(X!2))) = X!2))) <=> ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2))))))) | (g(tptp_fun_Y_1(f(X!2))) = X!2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | ((~(g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2))))))) | (g(tptp_fun_Y_1(f(X!2))) = X!2))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) | (~(g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2))))))) | (g(tptp_fun_Y_1(f(X!2))) = X!2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~(g(tptp_fun_Y_1(f(X!2))) = g(f(g(tptp_fun_Y_1(f(X!2))))))) | (g(tptp_fun_Y_1(f(X!2))) = X!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (g(tptp_fun_Y_1(f(X!2))) = X!2),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (X!2 = g(tptp_fun_Y_1(f(X!2)))),
% 0.20/0.38 inference(symmetry,[status(thm)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (f(X!2) = f(g(tptp_fun_Y_1(f(X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (f(g(tptp_fun_Y_1(f(X!2)))) = f(X!2)),
% 0.20/0.38 inference(symmetry,[status(thm)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(X!2)) = f(X!2)),
% 0.20/0.38 inference(transitivity,[status(thm)],[30, 42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))) | (~(tptp_fun_Y_1(f(X!2)) = f(X!2)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (~(tptp_fun_Y_1(f(X!2)) = f(X!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[44, 28])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.20/0.38 tff(47,plain,(((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))) | (~![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[47, 27])).
% 0.20/0.38 tff(49,assumption,((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))), introduced(assumption)).
% 0.20/0.38 tff(50,assumption,(f(X!2) = f(g(f(X!2)))), introduced(assumption)).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (f(g(f(X!2))) = f(X!2)),
% 0.20/0.38 inference(symmetry,[status(thm)],[50])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(X!2)) = tptp_fun_Y_1(f(g(f(X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(g(f(X!2)))) = tptp_fun_Y_1(f(X!2))),
% 0.20/0.38 inference(symmetry,[status(thm)],[52])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 ((tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))) <=> (tptp_fun_Y_1(f(X!2)) = f(X!2))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[53, 51])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 ((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))) <=> (~(tptp_fun_Y_1(f(X!2)) = f(X!2)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.38 tff(56,assumption,(~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))), introduced(assumption)).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))) | (~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (~(tptp_fun_Y_1(f(X!2)) = f(X!2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (g(tptp_fun_Y_1(f(g(f(X!2))))) = g(tptp_fun_Y_1(f(X!2)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (f(g(tptp_fun_Y_1(f(g(f(X!2)))))) = f(g(tptp_fun_Y_1(f(X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2))))))) <=> (tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[53, 61])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[63, 56])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[64, 62])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 ((~((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2)))) | (~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[66, 65, 59, 49])).
% 0.20/0.38 tff(68,plain,(((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))) | (~((~(tptp_fun_Y_1(f(X!2)) = f(g(tptp_fun_Y_1(f(X!2)))))) | (tptp_fun_Y_1(f(X!2)) = f(X!2)))) | (~(f(X!2) = f(g(f(X!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 ((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[68, 48, 11])).
% 0.20/0.38 tff(70,assumption,(f(g(f(X!2))) = f(g(f(g(f(X!2)))))), introduced(assumption)).
% 0.20/0.38 tff(71,assumption,((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))), introduced(assumption)).
% 0.20/0.38 tff(72,assumption,(![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))), introduced(assumption)).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))) | ((~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))) | (~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))))) <=> ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))) | (~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))) | (~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))) | ((~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))) | (~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 ((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))) | (~(f(g(f(X!2))) = f(g(f(g(f(X!2))))))) | (~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[75, 72, 71, 70])).
% 0.20/0.38 tff(77,plain,((~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))) | (~((~(tptp_fun_Y_1(f(g(f(X!2)))) = f(g(tptp_fun_Y_1(f(g(f(X!2)))))))) | (tptp_fun_Y_1(f(g(f(X!2)))) = f(g(f(X!2)))))) | (~(f(g(f(X!2))) = f(g(f(g(f(X!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 (~![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[77, 69, 25])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 ((![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) <=> (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 ((![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))) <=> (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 (((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))) <=> ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0))) <=> ((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 ((((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) <=> (((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[82, 81])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 (((((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X)))))) <=> ((((X!0 = f(g(X!0))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X!0))) | ((X!2 = g(f(X!2))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X!2)))) & (![X: $i] : ((~(X = f(g(X)))) | (~((~(tptp_fun_Y_1(X) = f(g(tptp_fun_Y_1(X))))) | (tptp_fun_Y_1(X) = X)))) | ![X: $i] : ((~(X = g(f(X)))) | (~((~(tptp_fun_Y_3(X) = g(f(tptp_fun_Y_3(X))))) | (tptp_fun_Y_3(X) = X))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[83, 80])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(86,plain,
% 0.20/0.38 ((?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))) <=> (?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.38 tff(88,plain,
% 0.20/0.38 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.38 tff(89,plain,
% 0.20/0.38 ((?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X)))) <=> (?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(90,plain,
% 0.20/0.38 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X))))) <=> (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[90, 85])).
% 0.20/0.40 tff(92,axiom,(~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((Y = f(g(Y))) => (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((Y = g(f(Y))) => (Y = X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_cute_thing')).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 85])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (~(?[X: $i] : ((X = f(g(X))) & ![Y: $i] : ((~(Y = f(g(Y)))) | (Y = X))) <=> ?[X: $i] : ((X = g(f(X))) & ![Y: $i] : ((~(Y = g(f(Y)))) | (Y = X))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.40 unexpected number of arguments: (let ((a!1 (exists ((X $i))
% 0.20/0.40 (let ((a!1 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (f (g Y))))))
% 0.20/0.40 (or a!1 (= Y X))))))
% 0.20/0.40 (and (= X (f (g X))) a!1))))
% 0.20/0.40 (a!2 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (f (g Y))))))
% 0.20/0.40 (or a!1 (= Y X!0)))))
% 0.20/0.40 (a!4 (~ (= X!0 (f (g X!0))) (= X!0 (f (g X!0)))))
% 0.20/0.40 (a!5 (lambda ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (f (g Y))))))
% 0.20/0.40 (refl (~ (or a!1 (= Y X!0)) (or a!1 (= Y X!0)))))))
% 0.20/0.40 (a!7 (lambda ((X $i))
% 0.20/0.40 (let ((a!1 (not (= X (f (g X)))))
% 0.20/0.40 (a!2 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (f (g Y))))))
% 0.20/0.40 (or a!1 (= Y X)))))
% 0.20/0.40 (a!3 (= (Y!1 X) (f (g (Y!1 X))))))
% 0.20/0.40 (let ((a!4 (not (or (not a!3) (= (Y!1 X) X))))
% 0.20/0.40 (a!5 (and (= X (f (g X))) a!2)))
% 0.20/0.40 (nnf-neg (refl (~ a!1 a!1))
% 0.20/0.40 (sk (~ (not a!2) a!4))
% 0.20/0.40 (~ (not a!5) (or a!1 a!4)))))))
% 0.20/0.40 (a!8 (forall ((X $i))
% 0.20/0.40 (let ((a!1 (not (= X (f (g X)))))
% 0.20/0.40 (a!2 (= (Y!1 X) (f (g (Y!1 X))))))
% 0.20/0.40 (let ((a!3 (not (or (not a!2) (= (Y!1 X) X)))))
% 0.20/0.40 (or a!1 a!3)))))
% 0.20/0.40 (a!9 (exists ((X $i))
% 0.20/0.40 (let ((a!1 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (g (f Y))))))
% 0.20/0.40 (or a!1 (= Y X))))))
% 0.20/0.40 (and (= X (g (f X))) a!1))))
% 0.20/0.40 (a!10 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (g (f Y))))))
% 0.20/0.40 (or a!1 (= Y X!2)))))
% 0.20/0.40 (a!12 (~ (= X!2 (g (f X!2))) (= X!2 (g (f X!2)))))
% 0.20/0.40 (a!13 (lambda ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (g (f Y))))))
% 0.20/0.40 (refl (~ (or a!1 (= Y X!2)) (or a!1 (= Y X!2)))))))
% 0.20/0.40 (a!15 (lambda ((X $i))
% 0.20/0.40 (let ((a!1 (not (= X (g (f X)))))
% 0.20/0.40 (a!2 (forall ((Y $i))
% 0.20/0.40 (let ((a!1 (not (= Y (g (f Y))))))
% 0.20/0.40 (or a!1 (= Y X)))))
% 0.20/0.40 (a!3 (= (Y!3 X) (g (f (Y!3 X))))))
% 0.20/0.40 (let ((a!4 (not (or (not a!3) (= (Y!3 X) X))))
% 0.20/0.40 (a!5 (and (= X (g (f X))) a!2)))
% 0.20/0.40 (nnf-neg (refl (~ a!1 a!1))
% 0.20/0.40 (sk (~ (not a!2) a!4))
% 0.20/0.40 (~ (not a!5) (or a!1 a!4)))))))
% 0.20/0.40 (a!16 (forall ((X $i))
% 0.20/0.40 (let ((a!1 (not (= X (g (f X)))))
% 0.20/0.40 (a!2 (= (Y!3 X) (g (f (Y!3 X))))))
% 0.20/0.40 (let ((a!3 (not (or (not a!2) (= (Y!3 X) X)))))
% 0.20/0.40 (or a!1 a!3))))))
% 0.20/0.40 (let ((a!3 (and (= X!0 (f (g X!0))) a!2)) (a!11 (and (= X!2 (g (f X!2))) a!10)))
% 0.20/0.40 (let ((a!6 (trans (sk (~ a!1 a!3))
% 0.20/0.40 (monotonicity (refl a!4)
% 0.20/0.40 (nnf-pos (proof-bind a!5) (~ a!2 a!2))
% 0.20/0.40 (~ a!3 a!3))
% 0.20/0.40 (~ a!1 a!3)))
% 0.20/0.40 (a!14 (trans (sk (~ a!9 a!11))
% 0.20/0.40 (monotonicity (refl a!12)
% 0.20/0.40 (nnf-pos (proof-bind a!13) (~ a!10 a!10))
% 0.20/0.40 (~ a!11 a!11))
% 0.20/0.40 (~ a!9 a!11))))
% 0.20/0.40 (nnf-neg a!6
% 0.20/0.40 (nnf-neg (proof-bind a!7) (~ (not a!1) a!8))
% 0.20/0.40 a!14
% 0.20/0.40 (nnf-neg (proof-bind a!15) (~ (not a!9) a!16))
% 0.20/0.40 (~ (not (= a!1 a!9)) (and (or a!3 a!11) (or a!8 a!16)))))))
% 0.20/0.40 Proof display could not be completed: unexpected number of arguments
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------