%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN948+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN948+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:03:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(a_type, type, (
% 0.20/0.38 a: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.38 tptp_fun_Y_0: $i > $i)).
% 0.20/0.38 tff(elem_1_type, type, (
% 0.20/0.38 elem_1: $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i] : rewrite((a(X, tptp_fun_Y_0(X)) & a(tptp_fun_Y_0(X), tptp_fun_Y_0(X))) <=> (~((~a(X, tptp_fun_Y_0(X))) | (~a(tptp_fun_Y_0(X), tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i] : (a(X, tptp_fun_Y_0(X)) & a(tptp_fun_Y_0(X), tptp_fun_Y_0(X))) <=> ![X: $i] : (~((~a(X, tptp_fun_Y_0(X))) | (~a(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) <=> ![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((~(![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))) <=> (~((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(~(![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))),
% 0.20/0.38 inference(or_elim,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,(
% 0.20/0.38 ![X: $i] : (a(X, tptp_fun_Y_0(X)) & a(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i] : (~((~a(X, tptp_fun_Y_0(X))) | (~a(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~![X: $i] : (~((~a(X, tptp_fun_Y_0(X))) | (~a(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))))) | (~((~a(elem!1, tptp_fun_Y_0(elem!1))) | (~a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~((~a(elem!1, tptp_fun_Y_0(elem!1))) | (~a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (((~a(elem!1, tptp_fun_Y_0(elem!1))) | (~a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))) | a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[Z: $i] : refl((~a(Z, Z)) <=> (~a(Z, Z)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![Z: $i] : (~a(Z, Z)) <=> ![Z: $i] : (~a(Z, Z))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~?[Z: $i] : a(Z, Z)) <=> (~?[Z: $i] : a(Z, Z))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~?[Z: $i] : a(Z, Z)),
% 0.20/0.38 inference(or_elim,[status(thm)],[6])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (~?[Z: $i] : a(Z, Z)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (~?[Z: $i] : a(Z, Z)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (~?[Z: $i] : a(Z, Z)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (^[Z: $i] : refl($oeq((~a(Z, Z)), (~a(Z, Z))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(23,plain,(
% 0.20/0.38 ![Z: $i] : (~a(Z, Z))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[21, 22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![Z: $i] : (~a(Z, Z))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![Z: $i] : (~a(Z, Z))) | (~a(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 24, 14])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------