%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN321+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN321+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:30:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_g_type, type, (
% 0.11/0.36 big_g: ( $i * $i ) > $o)).
% 0.11/0.36 tff(elem_4_type, type, (
% 0.11/0.36 elem_4: $i)).
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: $i > $i)).
% 0.11/0.36 tff(1,assumption,(~![Z: $i] : big_g(elem!4, Z)), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : rewrite((~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> ![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : refl((~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> ![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : rewrite((~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> ![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> ![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[7, 5])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) <=> (big_f(X, Y) | ![Z: $i] : big_g(X, Z))), rewrite((![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)) <=> (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))), (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))), rewrite(((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))), (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> ![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : trans(monotonicity(monotonicity(rewrite((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) <=> (big_f(X, Y) | ![Z: $i] : big_g(X, Z))), (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) <=> ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))))), rewrite((![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)) <=> (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))), ((((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))), rewrite((((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))), ((((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z))) <=> ![X: $i, Y: $i] : ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))) <=> (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : ((?[Z: $i] : big_f(X, Z) => ![Z: $i] : big_g(X, Z)) => (![Z: $i] : (big_g(Z, Z) => big_f(Z, Y)) => (big_f(X, Y) <=> ![Z: $i] : big_g(X, Z))))) <=> (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,axiom,(~?[X: $i, Y: $i] : ((?[Z: $i] : big_f(X, Z) => ![Z: $i] : big_g(X, Z)) => (![Z: $i] : (big_g(Z, Z) => big_f(Z, Y)) => (big_f(X, Y) <=> ![Z: $i] : big_g(X, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_3_2')).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : nnf_neg(nnf_neg(refl($oeq(big_f(X, Y), big_f(X, Y))), refl($oeq((~big_f(X, Y)), (~big_f(X, Y)))), nnf_pos(proof_bind(^[Z: $i] : refl($oeq(big_g(X, Z), big_g(X, Z)))), $oeq(![Z: $i] : big_g(X, Z), ![Z: $i] : big_g(X, Z))), sk($oeq((~![Z: $i] : big_g(X, Z)), (~big_g(X, tptp_fun_Z_0(X))))), $oeq((~(big_f(X, Y) <=> ![Z: $i] : big_g(X, Z))), ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))))), nnf_neg(nnf_pos(proof_bind(^[Z: $i] : refl($oeq(((~big_g(Z, Z)) | big_f(Z, Y)), ((~big_g(Z, Z)) | big_f(Z, Y))))), $oeq(![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)), ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)))), $oeq((~(~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)))), ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)))), nnf_neg(monotonicity(nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~big_f(X, Z)), (~big_f(X, Z))))), $oeq((~?[Z: $i] : big_f(X, Z)), ![Z: $i] : (~big_f(X, Z)))), nnf_pos(proof_bind(^[Z: $i] : refl($oeq(big_g(X, Z), big_g(X, Z)))), $oeq(![Z: $i] : big_g(X, Z), ![Z: $i] : big_g(X, Z))), $oeq(((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z)), (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))), $oeq((~(~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))), (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))), $oeq((~((big_f(X, Y) <=> ![Z: $i] : big_g(X, Z)) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~((~?[Z: $i] : big_f(X, Z)) | ![Z: $i] : big_g(X, Z))))), (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(21,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))),
% 0.11/0.37 inference(nnf-neg,[status(sab)],[19, 20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((big_f(X, Y) | ![Z: $i] : big_g(X, Z)) & ((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X)))) & ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y)) & (![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 8])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 3])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))) <=> ((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 ((~((~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))))) <=> (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))) <=> ((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))) <=> ((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~((~((~big_f(X, Y)) | (~big_g(X, tptp_fun_Z_0(X))))) | (~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, Y))) | (~(big_f(X, Y) | ![Z: $i] : big_g(X, Z))) | (~(![Z: $i] : (~big_f(X, Z)) | ![Z: $i] : big_g(X, Z)))))) | (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (~((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))) | (![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z))) | ![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![Z: $i] : (~big_f(elem!4, Z))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))) | (big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 ((~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (big_f(elem!4, elem!4)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 ((~![Z: $i] : (~big_f(elem!4, Z))) | (~big_f(elem!4, elem!4))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[43, 42, 37])).
% 0.11/0.37 tff(45,plain,(![Z: $i] : big_g(elem!4, Z)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(46,assumption,(~big_g(elem!4, elem!4)), introduced(assumption)).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 ((~![Z: $i] : big_g(elem!4, Z)) | big_g(elem!4, elem!4)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[47, 45, 46])).
% 0.11/0.38 tff(49,plain,(big_g(elem!4, elem!4)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))) | ![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[50, 32])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | ((~big_g(elem!4, elem!4)) | big_f(elem!4, elem!4))) <=> ((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~big_g(elem!4, elem!4)) | big_f(elem!4, elem!4))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 ((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | ((~big_g(elem!4, elem!4)) | big_f(elem!4, elem!4))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~big_g(elem!4, elem!4)) | big_f(elem!4, elem!4)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (big_f(elem!4, elem!4)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[54, 51, 49])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (((~![Z: $i] : ((~big_g(Z, Z)) | big_f(Z, elem!4))) | (~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~(big_f(elem!4, elem!4) | ![Z: $i] : big_g(elem!4, Z))) | (~(![Z: $i] : (~big_f(elem!4, Z)) | ![Z: $i] : big_g(elem!4, Z)))) | ((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 ((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[56, 32])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4))))) | (~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ((~big_f(elem!4, elem!4)) | (~big_g(elem!4, tptp_fun_Z_0(elem!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (~big_g(elem!4, tptp_fun_Z_0(elem!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((~![Z: $i] : big_g(elem!4, Z)) | big_g(elem!4, tptp_fun_Z_0(elem!4))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 60, 45])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------