%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN955+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:41:04 AM UTC 2025
% Result : Theorem 0.11s 0.35s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN955+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:01:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.35 % SZS status Theorem
% 0.11/0.35 % SZS output start Proof
% 0.11/0.35 tff(b_type, type, (
% 0.11/0.35 b: $i > $o)).
% 0.11/0.35 tff(tptp_fun_X_0_type, type, (
% 0.11/0.35 tptp_fun_X_0: $i)).
% 0.11/0.35 tff(a_type, type, (
% 0.11/0.35 a: $i > $o)).
% 0.11/0.35 tff(1,plain,
% 0.11/0.35 (^[X: $i] : refl((b(X) | (~a(X))) <=> (b(X) | (~a(X))))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(2,plain,
% 0.11/0.35 (![X: $i] : (b(X) | (~a(X))) <=> ![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.35 tff(3,plain,
% 0.11/0.35 (![X: $i] : (b(X) | (~a(X))) <=> ![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(4,plain,
% 0.11/0.35 ((~(![X: $i] : (a(X) => b(X)) => (?[X: $i] : a(X) => ?[X: $i] : b(X)))) <=> (~(?[X: $i] : b(X) | (~?[X: $i] : a(X)) | (~![X: $i] : (b(X) | (~a(X))))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(5,axiom,(~(![X: $i] : (a(X) => b(X)) => (?[X: $i] : a(X) => ?[X: $i] : b(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.35 tff(6,plain,
% 0.11/0.35 (~(?[X: $i] : b(X) | (~?[X: $i] : a(X)) | (~![X: $i] : (b(X) | (~a(X)))))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.35 tff(7,plain,
% 0.11/0.35 (![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(or_elim,[status(thm)],[6])).
% 0.11/0.35 tff(8,plain,
% 0.11/0.35 (![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.35 tff(9,plain,(
% 0.11/0.35 ![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(skolemize,[status(sab)],[8])).
% 0.11/0.35 tff(10,plain,
% 0.11/0.35 (![X: $i] : (b(X) | (~a(X)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.35 tff(11,plain,
% 0.11/0.35 (?[X: $i] : a(X) <=> ?[X: $i] : a(X)),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(12,plain,
% 0.11/0.35 (?[X: $i] : a(X)),
% 0.11/0.35 inference(or_elim,[status(thm)],[6])).
% 0.11/0.35 tff(13,plain,
% 0.11/0.35 (?[X: $i] : a(X)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.35 tff(14,plain,(
% 0.11/0.35 a(X!0)),
% 0.11/0.35 inference(skolemize,[status(sab)],[13])).
% 0.11/0.35 tff(15,plain,
% 0.11/0.35 (((~![X: $i] : (b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)))) <=> ((~![X: $i] : (b(X) | (~a(X)))) | b(X!0) | (~a(X!0)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(16,plain,
% 0.11/0.35 ((~![X: $i] : (b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(17,plain,
% 0.11/0.35 ((~![X: $i] : (b(X) | (~a(X)))) | b(X!0) | (~a(X!0))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.35 tff(18,plain,
% 0.11/0.35 (b(X!0)),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[17, 14, 10])).
% 0.11/0.35 tff(19,plain,
% 0.11/0.35 (^[X: $i] : refl((~b(X)) <=> (~b(X)))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(20,plain,
% 0.11/0.35 (![X: $i] : (~b(X)) <=> ![X: $i] : (~b(X))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.35 tff(21,plain,
% 0.11/0.35 ((~?[X: $i] : b(X)) <=> (~?[X: $i] : b(X))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(22,plain,
% 0.11/0.35 (~?[X: $i] : b(X)),
% 0.11/0.35 inference(or_elim,[status(thm)],[6])).
% 0.11/0.35 tff(23,plain,
% 0.11/0.35 (~?[X: $i] : b(X)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.35 tff(24,plain,
% 0.11/0.35 (~?[X: $i] : b(X)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.11/0.35 tff(25,plain,
% 0.11/0.35 (~?[X: $i] : b(X)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.11/0.35 tff(26,plain,
% 0.11/0.35 (^[X: $i] : refl($oeq((~b(X)), (~b(X))))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(27,plain,(
% 0.11/0.35 ![X: $i] : (~b(X))),
% 0.11/0.35 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.11/0.35 tff(28,plain,
% 0.11/0.35 (![X: $i] : (~b(X))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.11/0.35 tff(29,plain,
% 0.11/0.35 ((~![X: $i] : (~b(X))) | (~b(X!0))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(30,plain,
% 0.11/0.35 ($false),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[29, 28, 18])).
% 0.11/0.35 % SZS output end Proof
% 0.11/0.35 % E exiting
%------------------------------------------------------------------------------