%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN947+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:41:03 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN947+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 13:01:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(q_type, type, (
% 0.12/0.36 q: $i > $o)).
% 0.12/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.36 tptp_fun_Y_0: $i > $i)).
% 0.12/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.36 tptp_fun_Y_1: $i > $i)).
% 0.12/0.36 tff(elem_2_type, type, (
% 0.12/0.36 elem_2: $i)).
% 0.12/0.36 tff(p_type, type, (
% 0.12/0.36 p: $i > $o)).
% 0.12/0.36 tff(r_type, type, (
% 0.12/0.36 r: $i > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[Z: $i] : refl((~(p(tptp_fun_Y_1(Z)) | r(Z))) <=> (~(p(tptp_fun_Y_1(Z)) | r(Z))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z))) <=> ![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 ((~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))) <=> (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 ((~(![X: $i] : ?[Y: $i] : (p(X) & q(Y)) => ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))) <=> (~((~![X: $i] : ?[Y: $i] : (p(X) & q(Y))) | ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,axiom,(~(![X: $i] : ?[Y: $i] : (p(X) & q(Y)) => ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (~((~![X: $i] : ?[Y: $i] : (p(X) & q(Y))) | ?[Z: $i] : ![Y: $i] : (p(Y) | r(Z)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.12/0.36 inference(or_elim,[status(thm)],[6])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~?[Z: $i] : ![Y: $i] : (p(Y) | r(Z))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (^[Z: $i] : sk($oeq((~![Y: $i] : (p(Y) | r(Z))), (~(p(tptp_fun_Y_1(Z)) | r(Z)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(12,plain,(
% 0.12/0.36 ![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.12/0.36 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 ((~![Z: $i] : (~(p(tptp_fun_Y_1(Z)) | r(Z)))) | (~(p(tptp_fun_Y_1(elem!2)) | r(elem!2)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (~(p(tptp_fun_Y_1(elem!2)) | r(elem!2))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 ((p(tptp_fun_Y_1(elem!2)) | r(elem!2)) | (~p(tptp_fun_Y_1(elem!2)))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (~p(tptp_fun_Y_1(elem!2))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))) | p(tptp_fun_Y_1(elem!2))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (^[X: $i] : refl((~((~p(X)) | (~q(tptp_fun_Y_0(X))))) <=> (~((~p(X)) | (~q(tptp_fun_Y_0(X))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X))))) <=> ![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (^[X: $i] : rewrite((p(X) & q(tptp_fun_Y_0(X))) <=> (~((~p(X)) | (~q(tptp_fun_Y_0(X))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (![X: $i] : (p(X) & q(tptp_fun_Y_0(X))) <=> ![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (![X: $i] : ?[Y: $i] : (p(X) & q(Y)) <=> ![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.12/0.36 inference(or_elim,[status(thm)],[6])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (![X: $i] : ?[Y: $i] : (p(X) & q(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.36 tff(27,plain,(
% 0.12/0.36 ![X: $i] : (p(X) & q(tptp_fun_Y_0(X)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[26])).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.36 tff(29,plain,
% 0.12/0.36 (![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.36 tff(30,plain,
% 0.12/0.36 ((~![X: $i] : (~((~p(X)) | (~q(tptp_fun_Y_0(X)))))) | (~((~p(tptp_fun_Y_1(elem!2))) | (~q(tptp_fun_Y_0(tptp_fun_Y_1(elem!2))))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(31,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.12/0.36 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------