%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN323+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:45 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN323+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n002.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 12:32:17 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(big_f_type, type, (
% 0.11/0.38 big_f: ( $i * $i ) > $o)).
% 0.11/0.38 tff(big_g_type, type, (
% 0.11/0.38 big_g: ( $i * $i ) > $o)).
% 0.11/0.38 tff(elem_1_type, type, (
% 0.11/0.38 elem_1: $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (((~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))) | $false) <=> (~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 ((~$true) <=> $false),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (((~big_g(elem!1, elem!1)) | big_g(elem!1, elem!1)) <=> $true),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 ((~(~big_g(elem!1, elem!1))) <=> big_g(elem!1, elem!1)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (((~big_g(elem!1, elem!1)) | $false) <=> (~big_g(elem!1, elem!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)) <=> $true),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> (~$true)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> $false),
% 0.11/0.38 inference(transitivity,[status(thm)],[7, 2])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))) <=> ((~big_g(elem!1, elem!1)) | $false)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))) <=> (~big_g(elem!1, elem!1))),
% 0.11/0.38 inference(transitivity,[status(thm)],[9, 5])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))))) <=> (~(~big_g(elem!1, elem!1)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 ((~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))))) <=> big_g(elem!1, elem!1)),
% 0.11/0.38 inference(transitivity,[status(thm)],[11, 4])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 ((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) <=> (~big_g(elem!1, elem!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))))) <=> ((~big_g(elem!1, elem!1)) | big_g(elem!1, elem!1))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[13, 12])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))))) <=> $true),
% 0.11/0.38 inference(transitivity,[status(thm)],[14, 3])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 ((~((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))))))) <=> (~$true)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 ((~((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))))))) <=> $false),
% 0.11/0.38 inference(transitivity,[status(thm)],[16, 2])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (((~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))))))) <=> ((~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))) | $false)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (((~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))))))) <=> (~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[18, 1])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 ((~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) | big_g(elem!1, elem!1))) | (~((~big_g(elem!1, elem!1)) | (~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (^[Y: $i, X_0: $i, X: $i] : refl((~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))) <=> (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))) <=> ![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![Y: $i] : ![X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))) <=> ![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(pull_quant,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (^[Y: $i] : trans(monotonicity(trans(monotonicity(pull_quant((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) <=> ?[X: $i] : (~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)))), pull_quant((~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))) <=> ?[X: $i] : (~((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))), (((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))) <=> (?[X: $i] : (~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | ?[X: $i] : (~((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))), pull_quant((?[X: $i] : (~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | ?[X: $i] : (~((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))) <=> ?[X_0: $i, X: $i] : ((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))), (((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))) <=> ?[X_0: $i, X: $i] : ((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))), ((~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> (~?[X_0: $i, X: $i] : ((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))))), pull_quant((~?[X_0: $i, X: $i] : ((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0))))))) <=> ![X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))), ((~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![Y: $i] : ![X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[27, 23])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (^[Y: $i] : rewrite((~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> ![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (^[Y: $i] : rewrite((![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)) & ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))) <=> (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![Y: $i] : (![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)) & ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))) <=> ![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))) <=> (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 ((~?[Y: $i] : (![X: $i] : ((big_f(X, Y) => big_f(Y, X)) => big_g(X, Y)) => (~![X: $i] : ((big_f(X, Y) => big_f(Y, X)) => (~big_g(X, Y)))))) <=> (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(36,axiom,(~?[Y: $i] : (![X: $i] : ((big_f(X, Y) => big_f(Y, X)) => big_g(X, Y)) => (~![X: $i] : ((big_f(X, Y) => big_f(Y, X)) => (~big_g(X, Y)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_4_2')).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (~?[Y: $i] : ((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (^[Y: $i] : nnf_neg(nnf_neg(nnf_pos(proof_bind(^[X: $i] : refl($oeq(((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)), ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))))), $oeq(![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)), ![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)))), $oeq((~(~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)))), ![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)))), nnf_neg(nnf_pos(proof_bind(^[X: $i] : refl($oeq(((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))), ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))), $oeq(![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))), ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))), $oeq((~(~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))), ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))), $oeq((~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X))))))), (![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)) & ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(42,plain,(
% 0.11/0.38 ![Y: $i] : (![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y)) & ![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))),
% 0.11/0.38 inference(nnf-neg,[status(sab)],[40, 41])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![Y: $i] : (~((~![X: $i] : ((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~![X: $i] : ((~big_g(X, Y)) | (~((~big_f(X, Y)) | big_f(Y, X)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![Y: $i, X_0: $i, X: $i] : (~((~((~((~big_f(X, Y)) | big_f(Y, X))) | big_g(X, Y))) | (~((~big_g(X_0, Y)) | (~((~big_f(X_0, Y)) | big_f(Y, X_0)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 31])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[44, 21])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------