%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN956+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN956+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 13:01:48 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(b_type, type, (
% 0.18/0.37 b: $i > $o)).
% 0.18/0.37 tff(tptp_fun_X_0_type, type, (
% 0.18/0.37 tptp_fun_X_0: $i)).
% 0.18/0.37 tff(a_type, type, (
% 0.18/0.37 a: $i > $o)).
% 0.18/0.37 tff(1,assumption,(~a(X!0)), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (^[X: $i] : refl(a(X) <=> a(X))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![X: $i] : a(X) <=> ![X: $i] : a(X)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X: $i] : a(X) <=> ![X: $i] : a(X)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 ((~(?[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))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(6,axiom,(~(?[X: $i] : (a(X) => b(X)) => (![X: $i] : a(X) => ?[X: $i] : b(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (~(?[X: $i] : b(X) | (~![X: $i] : a(X)) | (~?[X: $i] : (b(X) | (~a(X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![X: $i] : a(X)),
% 0.18/0.37 inference(or_elim,[status(thm)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (![X: $i] : a(X)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.37 tff(10,plain,(
% 0.18/0.37 ![X: $i] : a(X)),
% 0.18/0.37 inference(skolemize,[status(sab)],[9])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (![X: $i] : a(X)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 ((~![X: $i] : a(X)) | a(X!0)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.18/0.37 tff(14,plain,(a(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (?[X: $i] : (b(X) | (~a(X))) <=> ?[X: $i] : (b(X) | (~a(X)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (?[X: $i] : (b(X) | (~a(X)))),
% 0.18/0.37 inference(or_elim,[status(thm)],[7])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (?[X: $i] : (b(X) | (~a(X)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,(
% 0.18/0.37 b(X!0) | (~a(X!0))),
% 0.18/0.37 inference(skolemize,[status(sab)],[17])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (b(X!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[18, 14])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (^[X: $i] : refl((~b(X)) <=> (~b(X)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![X: $i] : (~b(X)) <=> ![X: $i] : (~b(X))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 ((~?[X: $i] : b(X)) <=> (~?[X: $i] : b(X))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (~?[X: $i] : b(X)),
% 0.18/0.37 inference(or_elim,[status(thm)],[7])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (~?[X: $i] : b(X)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (~?[X: $i] : b(X)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (~?[X: $i] : b(X)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (^[X: $i] : refl($oeq((~b(X)), (~b(X))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(28,plain,(
% 0.18/0.37 ![X: $i] : (~b(X))),
% 0.18/0.37 inference(nnf-neg,[status(sab)],[26, 27])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![X: $i] : (~b(X))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~![X: $i] : (~b(X))) | (~b(X!0))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------