%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN952+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.17s 0.34s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN952+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n007.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri Jun 20 13:03:20 EDT 2025
% 0.11/0.30 % CPUTime :
% 0.17/0.34 % SZS status Theorem
% 0.17/0.34 % SZS output start Proof
% 0.17/0.34 tff(p_type, type, (
% 0.17/0.34 p: $i > $o)).
% 0.17/0.34 tff(elem_0_type, type, (
% 0.17/0.34 elem_0: $i)).
% 0.17/0.34 tff(1,plain,
% 0.17/0.34 (^[X: $i] : refl(p(X) <=> p(X))),
% 0.17/0.34 inference(bind,[status(th)],[])).
% 0.17/0.34 tff(2,plain,
% 0.17/0.34 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.17/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.34 tff(3,plain,
% 0.17/0.34 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.17/0.34 inference(rewrite,[status(thm)],[])).
% 0.17/0.34 tff(4,plain,
% 0.17/0.34 ((~(![X: $i] : p(X) => ?[Y: $i] : p(Y))) <=> (~((~![X: $i] : p(X)) | ?[Y: $i] : p(Y)))),
% 0.17/0.34 inference(rewrite,[status(thm)],[])).
% 0.17/0.34 tff(5,axiom,(~(![X: $i] : p(X) => ?[Y: $i] : p(Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.17/0.34 tff(6,plain,
% 0.17/0.34 (~((~![X: $i] : p(X)) | ?[Y: $i] : p(Y))),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.17/0.34 tff(7,plain,
% 0.17/0.34 (![X: $i] : p(X)),
% 0.17/0.34 inference(or_elim,[status(thm)],[6])).
% 0.17/0.34 tff(8,plain,
% 0.17/0.34 (![X: $i] : p(X)),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.17/0.34 tff(9,plain,(
% 0.17/0.34 ![X: $i] : p(X)),
% 0.17/0.34 inference(skolemize,[status(sab)],[8])).
% 0.17/0.34 tff(10,plain,
% 0.17/0.34 (![X: $i] : p(X)),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.17/0.34 tff(11,plain,
% 0.17/0.34 ((~![X: $i] : p(X)) | p(elem!0)),
% 0.17/0.34 inference(quant_inst,[status(thm)],[])).
% 0.17/0.34 tff(12,plain,
% 0.17/0.34 (p(elem!0)),
% 0.17/0.34 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.17/0.34 tff(13,plain,
% 0.17/0.34 (^[Y: $i] : refl((~p(Y)) <=> (~p(Y)))),
% 0.17/0.34 inference(bind,[status(th)],[])).
% 0.17/0.34 tff(14,plain,
% 0.17/0.34 (![Y: $i] : (~p(Y)) <=> ![Y: $i] : (~p(Y))),
% 0.17/0.34 inference(quant_intro,[status(thm)],[13])).
% 0.17/0.34 tff(15,plain,
% 0.17/0.34 ((~?[Y: $i] : p(Y)) <=> (~?[Y: $i] : p(Y))),
% 0.17/0.34 inference(rewrite,[status(thm)],[])).
% 0.17/0.34 tff(16,plain,
% 0.17/0.34 (~?[Y: $i] : p(Y)),
% 0.17/0.34 inference(or_elim,[status(thm)],[6])).
% 0.17/0.34 tff(17,plain,
% 0.17/0.34 (~?[Y: $i] : p(Y)),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.17/0.34 tff(18,plain,
% 0.17/0.34 (~?[Y: $i] : p(Y)),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.17/0.34 tff(19,plain,
% 0.17/0.34 (~?[Y: $i] : p(Y)),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.17/0.34 tff(20,plain,
% 0.17/0.34 (^[Y: $i] : refl($oeq((~p(Y)), (~p(Y))))),
% 0.17/0.34 inference(bind,[status(th)],[])).
% 0.17/0.34 tff(21,plain,(
% 0.17/0.34 ![Y: $i] : (~p(Y))),
% 0.17/0.34 inference(nnf-neg,[status(sab)],[19, 20])).
% 0.17/0.34 tff(22,plain,
% 0.17/0.34 (![Y: $i] : (~p(Y))),
% 0.17/0.34 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.17/0.34 tff(23,plain,
% 0.17/0.34 ((~![Y: $i] : (~p(Y))) | (~p(elem!0))),
% 0.17/0.34 inference(quant_inst,[status(thm)],[])).
% 0.17/0.34 tff(24,plain,
% 0.17/0.34 ($false),
% 0.17/0.34 inference(unit_resolution,[status(thm)],[23, 22, 12])).
% 0.17/0.34 % SZS output end Proof
% 0.17/0.34 % E exiting
%------------------------------------------------------------------------------