%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN050+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:03 AM UTC 2025
% Result : Theorem 0.18s 0.35s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN050+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 12:27:12 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.18/0.35 % SZS status Theorem
% 0.18/0.35 % SZS output start Proof
% 0.18/0.35 tff(big_r_type, type, (
% 0.18/0.35 big_r: $i > $o)).
% 0.18/0.35 tff(big_q_type, type, (
% 0.18/0.35 big_q: $i > $o)).
% 0.18/0.35 tff(elem_1_type, type, (
% 0.18/0.35 elem_1: $i)).
% 0.18/0.35 tff(big_p_type, type, (
% 0.18/0.35 big_p: $i > $o)).
% 0.18/0.35 tff(big_s_type, type, (
% 0.18/0.35 big_s: $i > $o)).
% 0.18/0.35 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.35 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.18/0.35 tff(1,plain,
% 0.18/0.35 (^[X1: $i, Y1: $i] : refl((~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))) <=> (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))))),
% 0.18/0.35 inference(bind,[status(th)],[])).
% 0.18/0.35 tff(2,plain,
% 0.18/0.35 (![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))) <=> ![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.35 tff(3,plain,
% 0.18/0.35 (^[X1: $i, Y1: $i] : rewrite((~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))) <=> (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))))),
% 0.18/0.35 inference(bind,[status(th)],[])).
% 0.18/0.35 tff(4,plain,
% 0.18/0.35 (![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))) <=> ![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.35 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.35 tff(5,plain,
% 0.18/0.35 (![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))) <=> ![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.35 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.35 tff(6,plain,
% 0.18/0.35 (^[X1: $i, Y1: $i] : rewrite((big_p(X1) & big_q(Y1) & ![Z1: $i] : (~big_r(Z1))) <=> (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1))))))),
% 0.18/0.35 inference(bind,[status(th)],[])).
% 0.18/0.35 tff(7,plain,
% 0.18/0.35 (![X1: $i, Y1: $i] : (big_p(X1) & big_q(Y1) & ![Z1: $i] : (~big_r(Z1))) <=> ![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.35 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.35 tff(8,plain,
% 0.18/0.35 (^[X1: $i, Y1: $i] : rewrite(((big_p(X1) & big_q(Y1)) & ![Z1: $i] : (~big_r(Z1))) <=> (big_p(X1) & big_q(Y1) & ![Z1: $i] : (~big_r(Z1))))),
% 0.18/0.35 inference(bind,[status(th)],[])).
% 0.18/0.35 tff(9,plain,
% 0.18/0.35 (![X1: $i, Y1: $i] : ((big_p(X1) & big_q(Y1)) & ![Z1: $i] : (~big_r(Z1))) <=> ![X1: $i, Y1: $i] : (big_p(X1) & big_q(Y1) & ![Z1: $i] : (~big_r(Z1)))),
% 0.18/0.35 inference(quant_intro,[status(thm)],[8])).
% 0.18/0.35 tff(10,plain,
% 0.18/0.35 ((~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))) <=> (~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1)))),
% 0.18/0.35 inference(rewrite,[status(thm)],[])).
% 0.18/0.35 tff(11,plain,
% 0.18/0.35 ((~(![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((big_p(X) & big_q(Y)) => (big_r(Z) & big_s(W))) => ?[X1: $i, Y1: $i] : ((big_p(X1) & big_q(Y1)) => ?[Z1: $i] : big_r(Z1)))) <=> (~((~![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W)))) | ?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))))),
% 0.18/0.35 inference(rewrite,[status(thm)],[])).
% 0.18/0.35 tff(12,axiom,(~(![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((big_p(X) & big_q(Y)) => (big_r(Z) & big_s(W))) => ?[X1: $i, Y1: $i] : ((big_p(X1) & big_q(Y1)) => ?[Z1: $i] : big_r(Z1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel20')).
% 0.18/0.35 tff(13,plain,
% 0.18/0.35 (~((~![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W)))) | ?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1)))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.35 tff(14,plain,
% 0.18/0.35 (~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))),
% 0.18/0.35 inference(or_elim,[status(thm)],[13])).
% 0.18/0.35 tff(15,plain,
% 0.18/0.35 (~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.35 tff(16,plain,
% 0.18/0.35 (~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.18/0.35 tff(17,plain,
% 0.18/0.35 (~?[X1: $i, Y1: $i] : ((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))),
% 0.18/0.35 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.18/0.35 tff(18,plain,
% 0.18/0.35 (^[X1: $i, Y1: $i] : nnf_neg(refl($oeq((big_p(X1) & big_q(Y1)), (big_p(X1) & big_q(Y1)))), nnf_neg(proof_bind(^[Z1: $i] : refl($oeq((~big_r(Z1)), (~big_r(Z1))))), $oeq((~?[Z1: $i] : big_r(Z1)), ![Z1: $i] : (~big_r(Z1)))), $oeq((~((~(big_p(X1) & big_q(Y1))) | ?[Z1: $i] : big_r(Z1))), ((big_p(X1) & big_q(Y1)) & ![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(19,plain,(
% 0.18/0.36 ![X1: $i, Y1: $i] : ((big_p(X1) & big_q(Y1)) & ![Z1: $i] : (~big_r(Z1)))),
% 0.18/0.36 inference(nnf-neg,[status(sab)],[17, 18])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (![X1: $i, Y1: $i] : (big_p(X1) & big_q(Y1) & ![Z1: $i] : (~big_r(Z1)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 (![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 (![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 ((~![X1: $i, Y1: $i] : (~((~big_p(X1)) | (~big_q(Y1)) | (~![Z1: $i] : (~big_r(Z1)))))) | (~((~big_p(elem!1)) | (~big_q(elem!1)) | (~![Z1: $i] : (~big_r(Z1)))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (~((~big_p(elem!1)) | (~big_q(elem!1)) | (~![Z1: $i] : (~big_r(Z1))))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (((~big_p(elem!1)) | (~big_q(elem!1)) | (~![Z1: $i] : (~big_r(Z1)))) | ![Z1: $i] : (~big_r(Z1))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 (![Z1: $i] : (~big_r(Z1))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 (((~big_p(elem!1)) | (~big_q(elem!1)) | (~![Z1: $i] : (~big_r(Z1)))) | big_p(elem!1)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(28,plain,
% 0.18/0.36 (big_p(elem!1)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.18/0.36 tff(29,plain,
% 0.18/0.36 (((~big_p(elem!1)) | (~big_q(elem!1)) | (~![Z1: $i] : (~big_r(Z1)))) | big_q(elem!1)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(30,plain,
% 0.18/0.36 (big_q(elem!1)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.18/0.36 tff(31,plain,
% 0.18/0.36 (^[X: $i, Y: $i, W: $i] : refl(((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))) <=> ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(32,plain,
% 0.18/0.36 (![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))) <=> ![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.36 tff(33,plain,
% 0.18/0.36 (^[X: $i, Y: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_p(X) & big_q(Y)) <=> (~((~big_p(X)) | (~big_q(Y))))), ((~(big_p(X) & big_q(Y))) <=> (~(~((~big_p(X)) | (~big_q(Y))))))), rewrite((~(~((~big_p(X)) | (~big_q(Y))))) <=> ((~big_p(X)) | (~big_q(Y)))), ((~(big_p(X) & big_q(Y))) <=> ((~big_p(X)) | (~big_q(Y))))), rewrite((big_r(tptp_fun_Z_0(Y, X)) & big_s(W)) <=> (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))), (((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W))) <=> (((~big_p(X)) | (~big_q(Y))) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))))), rewrite((((~big_p(X)) | (~big_q(Y))) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W))))) <=> ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))), (((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W))) <=> ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(34,plain,
% 0.18/0.36 (![X: $i, Y: $i, W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W))) <=> ![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.36 tff(35,plain,
% 0.18/0.36 (![X: $i, Y: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W))) <=> ![X: $i, Y: $i, W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W)))),
% 0.18/0.36 inference(pull_quant,[status(thm)],[])).
% 0.18/0.36 tff(36,plain,
% 0.18/0.36 (![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W))) <=> ![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(37,plain,
% 0.18/0.36 (![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W)))),
% 0.18/0.36 inference(or_elim,[status(thm)],[13])).
% 0.18/0.36 tff(38,plain,
% 0.18/0.36 (![X: $i, Y: $i] : ?[Z: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(Z) & big_s(W)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.36 tff(39,plain,(
% 0.18/0.36 ![X: $i, Y: $i] : ![W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[38])).
% 0.18/0.36 tff(40,plain,
% 0.18/0.36 (![X: $i, Y: $i, W: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(tptp_fun_Z_0(Y, X)) & big_s(W)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.36 tff(41,plain,
% 0.18/0.36 (![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.18/0.36 tff(42,plain,
% 0.18/0.36 (![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[41, 32])).
% 0.18/0.36 tff(43,plain,
% 0.18/0.36 (((~![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))) | ((~big_p(elem!1)) | (~big_q(elem!1)) | (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1)))))) <=> ((~![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))) | (~big_p(elem!1)) | (~big_q(elem!1)) | (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(44,plain,
% 0.18/0.36 ((~![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))) | ((~big_p(elem!1)) | (~big_q(elem!1)) | (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1)))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(45,plain,
% 0.18/0.36 ((~![X: $i, Y: $i, W: $i] : ((~big_p(X)) | (~big_q(Y)) | (~((~big_r(tptp_fun_Z_0(Y, X))) | (~big_s(W)))))) | (~big_p(elem!1)) | (~big_q(elem!1)) | (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.36 tff(46,plain,
% 0.18/0.36 ((~big_p(elem!1)) | (~big_q(elem!1)) | (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1))))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[45, 42])).
% 0.18/0.36 tff(47,plain,
% 0.18/0.36 (~((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1)))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[46, 30, 28])).
% 0.18/0.36 tff(48,plain,
% 0.18/0.36 (((~big_r(tptp_fun_Z_0(elem!1, elem!1))) | (~big_s(elem!1))) | big_r(tptp_fun_Z_0(elem!1, elem!1))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(49,plain,
% 0.18/0.36 (big_r(tptp_fun_Z_0(elem!1, elem!1))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.36 tff(50,plain,
% 0.18/0.36 ((~![Z1: $i] : (~big_r(Z1))) | (~big_r(tptp_fun_Z_0(elem!1, elem!1)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(51,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[50, 49, 26])).
% 0.18/0.36 % SZS output end Proof
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------