%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN347+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:51 AM UTC 2025
% Result : Theorem 0.16s 0.41s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYN347+1 : TPTP v9.0.0. Released v2.0.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Jun 20 12:31:53 EDT 2025
% 0.16/0.37 % CPUTime :
% 0.16/0.41 % SZS status Theorem
% 0.16/0.41 % SZS output start Proof
% 0.16/0.41 tff(big_f_type, type, (
% 0.16/0.41 big_f: ( $i * $i ) > $o)).
% 0.16/0.41 tff(tptp_fun_Y_2_type, type, (
% 0.16/0.41 tptp_fun_Y_2: ( $i * $i ) > $i)).
% 0.16/0.41 tff(tptp_fun_Z1_1_type, type, (
% 0.16/0.41 tptp_fun_Z1_1: $i)).
% 0.16/0.41 tff(tptp_fun_Z2_0_type, type, (
% 0.16/0.41 tptp_fun_Z2_0: $i)).
% 0.16/0.41 tff(elem_3_type, type, (
% 0.16/0.41 elem_3: $i)).
% 0.16/0.41 tff(1,plain,
% 0.16/0.41 ((~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)))) <=> (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(2,plain,
% 0.16/0.41 ((~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : (((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)) | (big_f(Z1, Y) <=> big_f(Z2, Y)))) <=> (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(3,axiom,(~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : (((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)) | (big_f(Z1, Y) <=> big_f(Z2, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_17_3')).
% 0.16/0.41 tff(4,plain,
% 0.16/0.41 (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.16/0.41 tff(5,plain,
% 0.16/0.41 (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.16/0.41 tff(6,plain,
% 0.16/0.41 (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.16/0.41 tff(7,plain,
% 0.16/0.41 (~![Z1: $i, Z2: $i] : ?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1, Y) <=> big_f(Z2, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1, Z2)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.16/0.41 tff(8,plain,(
% 0.16/0.41 $oeq((~?[X1: $i, X2: $i] : ![Y: $i] : ((big_f(Z1!1, Y) <=> big_f(Z2!0, Y)) | ((big_f(X1, Y) <=> big_f(X2, Y)) <=> big_f(Z1!1, Z2!0)))), ![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0)))))),
% 0.16/0.41 inference(transitivity,[status(sab)],[7])).
% 0.16/0.41 tff(9,plain,
% 0.16/0.41 ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) | ((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(10,plain,
% 0.16/0.41 (~((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) | ((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.16/0.41 tff(11,plain,
% 0.16/0.41 (((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) | ((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0))) | (~(big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(12,plain,
% 0.16/0.41 (~(big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.16/0.41 tff(13,plain,
% 0.16/0.41 (((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) | ((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0))) | (~((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(14,plain,
% 0.16/0.41 (~((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.16/0.41 tff(15,plain,
% 0.16/0.41 (((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3)))))) <=> ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(16,plain,
% 0.16/0.41 ((~((big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))) | ((big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3))) <=> big_f(Z1!1, Z2!0)))) <=> (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3)))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(17,plain,
% 0.16/0.41 (((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~((big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))) | ((big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3))) <=> big_f(Z1!1, Z2!0))))) <=> ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.16/0.41 tff(18,plain,
% 0.16/0.41 (((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~((big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))) | ((big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3))) <=> big_f(Z1!1, Z2!0))))) <=> ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.16/0.41 tff(19,plain,
% 0.16/0.41 ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~((big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))) | ((big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Y_2(elem!3, elem!3))) <=> big_f(Z1!1, Z2!0))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(20,plain,
% 0.16/0.41 ((~![X1: $i, X2: $i] : (~((big_f(Z1!1, tptp_fun_Y_2(X2, X1)) <=> big_f(Z2!0, tptp_fun_Y_2(X2, X1))) | ((big_f(X1, tptp_fun_Y_2(X2, X1)) <=> big_f(X2, tptp_fun_Y_2(X2, X1))) <=> big_f(Z1!1, Z2!0))))) | (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3)))))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.16/0.41 tff(21,plain,
% 0.16/0.41 (~(big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[20, 8])).
% 0.16/0.41 tff(22,plain,
% 0.16/0.41 ((big_f(Z1!1, Z2!0) | (big_f(Z1!1, tptp_fun_Y_2(elem!3, elem!3)) <=> big_f(Z2!0, tptp_fun_Y_2(elem!3, elem!3)))) | (~big_f(Z1!1, Z2!0))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(23,plain,
% 0.16/0.41 (~big_f(Z1!1, Z2!0)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.16/0.41 tff(24,plain,
% 0.16/0.41 (((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0)) | (big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) | big_f(Z1!1, Z2!0)),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(25,plain,
% 0.16/0.41 (((big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1))) <=> big_f(Z1!1, Z2!0)) | (big_f(Z1!1, tptp_fun_Y_2(Z2!0, Z1!1)) <=> big_f(Z2!0, tptp_fun_Y_2(Z2!0, Z1!1)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.16/0.41 tff(26,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[25, 14, 12])).
% 0.16/0.41 % SZS output end Proof
% 0.16/0.41 % E exiting
%------------------------------------------------------------------------------