%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN965+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 05:41:05 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN965+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 13:02:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: ( $i * $i ) > $o)).
% 0.12/0.38 tff(elem_1_type, type, (
% 0.12/0.38 elem_1: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: $i > $i)).
% 0.12/0.38 tff(1,assumption,((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,(~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))) | ![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 ((~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))) | (~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[7, 6, 4])).
% 0.12/0.38 tff(9,plain,((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[Z: $i, Y: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~![W: $i] : (~p(W, Y))) <=> (~![W: $i] : (~p(W, Y)))), (((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))) <=> ((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))), ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) <=> (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))), rewrite((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) <=> (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))), (((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))))), rewrite(((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))), (((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (^[Z: $i, Y: $i] : refl(((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[Z: $i, Y: $i] : rewrite(((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[15, 13])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[Z: $i, Y: $i] : trans(monotonicity(rewrite((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) <=> (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))), rewrite((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) <=> (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))), (((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))))), rewrite(((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))), (((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![Z: $i] : ![Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))) <=> (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) <=> (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,axiom,(~?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[Z: $i] : trans(sk($oeq((~![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))), (~?[Y: $i] : (((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))))), nnf_neg(proof_bind(^[Y: $i] : nnf_neg(nnf_neg(refl($oeq(p(Y, tptp_fun_X_0(Z)), p(Y, tptp_fun_X_0(Z)))), nnf_neg(proof_bind(^[W: $i] : refl($oeq((~p(W, Y)), (~p(W, Y))))), $oeq((~?[W: $i] : p(W, Y)), ![W: $i] : (~p(W, Y)))), $oeq((~((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y))), (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))), refl($oeq((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))), (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))), $oeq((~(((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))), ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))))), $oeq((~?[Y: $i] : (((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))), ![Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))))), $oeq((~![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))), ![Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(28,plain,(
% 0.12/0.39 ![Z: $i] : ![Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))),
% 0.12/0.39 inference(nnf-neg,[status(sab)],[26, 27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 11])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))) <=> ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 32, 9, 1])).
% 0.12/0.39 tff(40,plain,(~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | p(tptp_fun_X_0(elem!1), elem!1)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (p(tptp_fun_X_0(elem!1), elem!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(elem!1))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (p(elem!1, tptp_fun_X_0(elem!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1))) | (~p(elem!1, tptp_fun_X_0(elem!1)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))) <=> ((~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~(p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[52, 32])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 46])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))) | ![W: $i] : (~p(W, elem!1))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![W: $i] : (~p(W, elem!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 ((~![W: $i] : (~p(W, elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 56, 42])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------