%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN733+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN733+1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:41:56 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(q_type, type, (
% 0.12/0.37 q: $i > $o)).
% 0.12/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.37 tptp_fun_Y_0: $i > $i)).
% 0.12/0.37 tff(elem_1_type, type, (
% 0.12/0.37 elem_1: $i)).
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i] : refl((~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))) <=> (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[X: $i] : rewrite((p(X) & (q(X) | q(tptp_fun_Y_0(X)))) <=> (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X)))) <=> ![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (^[X: $i] : rewrite((p(X) & (q(tptp_fun_Y_0(X)) | q(X))) <=> (p(X) & (q(X) | q(tptp_fun_Y_0(X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X: $i] : (p(X) & (q(tptp_fun_Y_0(X)) | q(X))) <=> ![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) <=> ![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~(![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) => ?[Z: $i] : (p(Z) & q(Z)))) <=> (~((~![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))) | ?[Z: $i] : (p(Z) & q(Z))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(9,axiom,(~(![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X))) => ?[Z: $i] : (p(Z) & q(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','y2141')).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~((~![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))) | ?[Z: $i] : (p(Z) & q(Z)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i] : ?[Y: $i] : (p(X) & (q(Y) | q(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.37 tff(13,plain,(
% 0.12/0.37 ![X: $i] : (p(X) & (q(tptp_fun_Y_0(X)) | q(X)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : (p(X) & (q(X) | q(tptp_fun_Y_0(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))) | (~((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,assumption,((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))), introduced(assumption)).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![X: $i] : (~((~p(X)) | (~(q(X) | q(tptp_fun_Y_0(X))))))) | (~((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[20, 16, 19])).
% 0.12/0.37 tff(22,plain,(~((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))) | (q(elem!1) | q(tptp_fun_Y_0(elem!1)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (q(elem!1) | q(tptp_fun_Y_0(elem!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~p(elem!1)) | (~(q(elem!1) | q(tptp_fun_Y_0(elem!1))))) | p(elem!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (p(elem!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (^[Z: $i] : refl(((~p(Z)) | (~q(Z))) <=> ((~p(Z)) | (~q(Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![Z: $i] : ((~p(Z)) | (~q(Z))) <=> ![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[Z: $i] : trans(monotonicity(rewrite((p(Z) & q(Z)) <=> (~((~p(Z)) | (~q(Z))))), ((~(p(Z) & q(Z))) <=> (~(~((~p(Z)) | (~q(Z))))))), rewrite((~(~((~p(Z)) | (~q(Z))))) <=> ((~p(Z)) | (~q(Z)))), ((~(p(Z) & q(Z))) <=> ((~p(Z)) | (~q(Z)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![Z: $i] : (~(p(Z) & q(Z))) <=> ![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~?[Z: $i] : (p(Z) & q(Z))) <=> (~?[Z: $i] : (p(Z) & q(Z)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.12/0.38 inference(or_elim,[status(thm)],[10])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (~?[Z: $i] : (p(Z) & q(Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (^[Z: $i] : refl($oeq((~(p(Z) & q(Z))), (~(p(Z) & q(Z)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(37,plain,(
% 0.12/0.38 ![Z: $i] : (~(p(Z) & q(Z)))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[35, 36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![Z: $i] : ((~p(Z)) | (~q(Z)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(elem!1)) | (~q(elem!1)))) <=> ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(elem!1)) | (~q(elem!1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(elem!1)) | (~q(elem!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(elem!1)) | (~q(elem!1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~p(elem!1)) | (~q(elem!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (~q(elem!1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 26])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~(q(elem!1) | q(tptp_fun_Y_0(elem!1)))) | q(elem!1) | q(tptp_fun_Y_0(elem!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (q(tptp_fun_Y_0(elem!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 44, 24])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))) <=> ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | ((~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![Z: $i] : ((~p(Z)) | (~q(Z)))) | (~p(tptp_fun_Y_0(elem!1))) | (~q(tptp_fun_Y_0(elem!1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (~p(tptp_fun_Y_0(elem!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 39, 46])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (((~p(tptp_fun_Y_0(elem!1))) | (~(q(tptp_fun_Y_0(elem!1)) | q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) | p(tptp_fun_Y_0(elem!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[51, 50, 18])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------