%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN379+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:56 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN379+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:32:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_q_type, type, (
% 0.12/0.37 big_q: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(big_p_type, type, (
% 0.12/0.37 big_p: $i > $o)).
% 0.12/0.37 tff(elem_1_type, type, (
% 0.12/0.37 elem_1: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))) | $false) <=> (~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~$true) <=> $false),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1)) <=> $true),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1))) <=> (~$true)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1))) <=> $false),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (((~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))) | (~((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1)))) <=> ((~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))) | $false)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (((~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))) | (~((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1)))) <=> (~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))) | (~((~big_q(elem!1, elem!1, elem!1)) | (~big_p(elem!1)) | big_q(elem!1, elem!1, elem!1)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[Y: $i, Z_0: $i, X: $i, Z: $i] : rewrite((~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[Y: $i, Z_0: $i, X: $i, Z: $i] : refl((~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![Y: $i] : ![Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(pull_quant,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[Y: $i] : trans(monotonicity(trans(monotonicity(pull_quant((~![X: $i, Z: $i] : big_q(X, Y, Z)) <=> ?[X: $i, Z: $i] : (~big_q(X, Y, Z))), pull_quant((~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))) <=> ?[Z: $i] : ((~big_p(Z)) | big_q(Y, Y, Z))), (((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))) <=> (?[X: $i, Z: $i] : (~big_q(X, Y, Z)) | ?[Z: $i] : ((~big_p(Z)) | big_q(Y, Y, Z))))), pull_quant((?[X: $i, Z: $i] : (~big_q(X, Y, Z)) | ?[Z: $i] : ((~big_p(Z)) | big_q(Y, Y, Z))) <=> ?[Z_0: $i, X: $i, Z: $i] : ((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))), (((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))) <=> ?[Z_0: $i, X: $i, Z: $i] : ((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))), ((~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> (~?[Z_0: $i, X: $i, Z: $i] : ((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))))), pull_quant((~?[Z_0: $i, X: $i, Z: $i] : ((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0)))) <=> ![Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))), ((~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Y: $i] : ![Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[17, 13])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (^[Y: $i] : rewrite((~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))) <=> ![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[Y: $i] : trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : rewrite((big_p(Z) & (~big_q(Y, Y, Z))) <=> (~((~big_p(Z)) | big_q(Y, Y, Z))))), (![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))) <=> ![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))), ((![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))) <=> (![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))))), rewrite((![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z)))) <=> (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))))), ((![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))) <=> (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![Y: $i] : (![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))) <=> ![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))) <=> (~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~(![X: $i] : big_p(X) => ?[Y: $i] : (![X: $i, Z: $i] : big_q(X, Y, Z) => (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))))) <=> (~((~![X: $i] : big_p(X)) | ?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(26,axiom,(~(![X: $i] : big_p(X) => ?[Y: $i] : (![X: $i, Z: $i] : big_q(X, Y, Z) => (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2131')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~((~![X: $i] : big_p(X)) | ?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (~?[Y: $i] : ((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (^[Y: $i] : nnf_neg(nnf_neg(nnf_pos(proof_bind(^[X: $i, Z: $i] : refl($oeq(big_q(X, Y, Z), big_q(X, Y, Z)))), $oeq(![X: $i, Z: $i] : big_q(X, Y, Z), ![X: $i, Z: $i] : big_q(X, Y, Z))), $oeq((~(~![X: $i, Z: $i] : big_q(X, Y, Z))), ![X: $i, Z: $i] : big_q(X, Y, Z))), nnf_neg(nnf_pos(proof_bind(^[Z: $i] : refl($oeq((big_p(Z) & (~big_q(Y, Y, Z))), (big_p(Z) & (~big_q(Y, Y, Z)))))), $oeq(![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))), ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))), $oeq((~(~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))), ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))), $oeq((~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z)))))), (![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(33,plain,(
% 0.12/0.38 ![Y: $i] : (![X: $i, Z: $i] : big_q(X, Y, Z) & ![Z: $i] : (big_p(Z) & (~big_q(Y, Y, Z))))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![Y: $i] : (~((~![X: $i, Z: $i] : big_q(X, Y, Z)) | (~![Z: $i] : (~((~big_p(Z)) | big_q(Y, Y, Z))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | ((~big_p(Z_0)) | big_q(Y, Y, Z_0))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![Y: $i, Z_0: $i, X: $i, Z: $i] : (~((~big_q(X, Y, Z)) | (~big_p(Z_0)) | big_q(Y, Y, Z_0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 11])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 9])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------