%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN732+1 : TPTP v9.0.0. Released v2.5.0.
% 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 05:39:56 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN732+1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:41:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(p_type, type, (
% 0.11/0.37 p: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_V_1_type, type, (
% 0.11/0.37 tptp_fun_V_1: $i > $i)).
% 0.11/0.37 tff(elem_2_type, type, (
% 0.11/0.37 elem_2: $i)).
% 0.11/0.37 tff(q_type, type, (
% 0.11/0.37 q: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[Z: $i, W: $i] : rewrite((~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> ![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[Z: $i, W: $i] : refl((~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![Z: $i] : ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(pull_quant,[status(thm)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[Z: $i] : trans(monotonicity(trans(monotonicity(pull_quant((~![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> ?[W: $i] : (p(Z, W) | q(W, Z))), (((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))) <=> ((~p(tptp_fun_V_1(Z), Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))))), pull_quant(((~p(tptp_fun_V_1(Z), Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))) <=> ?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))), (((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))) <=> ?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))), ((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> (~?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))))), pull_quant((~?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z)))) <=> ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))), ((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i] : ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[7, 5])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[8, 4])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (^[Z: $i] : rewrite((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[11, 9])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[Z: $i] : rewrite((p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![Z: $i] : (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> ![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ((~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))) <=> (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 ((~(![Y: $i] : (![X: $i] : p(X, Y) => ![U: $i] : q(U, Y)) => ?[Z: $i] : (?[V: $i] : p(V, Z) => ?[W: $i] : (p(Z, W) | q(W, Z))))) <=> (~((~![Y: $i] : ((~![X: $i] : p(X, Y)) | ![U: $i] : q(U, Y))) | ?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(17,axiom,(~(![Y: $i] : (![X: $i] : p(X, Y) => ![U: $i] : q(U, Y)) => ?[Z: $i] : (?[V: $i] : p(V, Z) => ?[W: $i] : (p(Z, W) | q(W, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x3411')).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~((~![Y: $i] : ((~![X: $i] : p(X, Y)) | ![U: $i] : q(U, Y))) | ?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.11/0.37 inference(or_elim,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (^[Z: $i] : nnf_neg(nnf_neg(sk($oeq(?[V: $i] : p(V, Z), p(tptp_fun_V_1(Z), Z))), $oeq((~(~?[V: $i] : p(V, Z))), p(tptp_fun_V_1(Z), Z))), nnf_neg(proof_bind(^[W: $i] : refl($oeq((~(p(Z, W) | q(W, Z))), (~(p(Z, W) | q(W, Z)))))), $oeq((~?[W: $i] : (p(Z, W) | q(W, Z))), ![W: $i] : (~(p(Z, W) | q(W, Z))))), $oeq((~((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))), (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(24,plain,(
% 0.11/0.37 ![Z: $i] : (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(nnf-neg,[status(sab)],[22, 23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (p(Z, W) | q(W, Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 12])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 2])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))) | (~(p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (~(p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2))) | p(tptp_fun_V_1(elem!2), elem!2)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (p(tptp_fun_V_1(elem!2), elem!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))) | (~p(tptp_fun_V_1(elem!2), elem!2))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 ((~![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))) | (~(p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[34, 27, 33])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------