%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN942+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:41:02 AM UTC 2025
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN942+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 13:03:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start Proof
% 0.20/0.36 tff(c_type, type, (
% 0.20/0.36 c: $i > $o)).
% 0.20/0.36 tff(tptp_fun_X_0_type, type, (
% 0.20/0.36 tptp_fun_X_0: $i)).
% 0.20/0.36 tff(a_type, type, (
% 0.20/0.36 a: $i > $o)).
% 0.20/0.36 tff(b_type, type, (
% 0.20/0.36 b: $i > $o)).
% 0.20/0.36 tff(1,plain,
% 0.20/0.36 ((~![X: $i] : (b(X) | (~a(X)))) <=> (~![X: $i] : (b(X) | (~a(X))))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(2,plain,
% 0.20/0.36 ((~((![X: $i] : (a(X) => (b(X) | c(X))) & (~![X: $i] : (a(X) => b(X)))) => ?[X: $i] : (a(X) & c(X)))) <=> (~((~(![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X)))))) | ?[X: $i] : (a(X) & c(X))))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(3,axiom,(~((![X: $i] : (a(X) => (b(X) | c(X))) & (~![X: $i] : (a(X) => b(X)))) => ?[X: $i] : (a(X) & c(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.36 tff(4,plain,
% 0.20/0.36 (~((~(![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X)))))) | ?[X: $i] : (a(X) & c(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.36 tff(5,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X))) & (~![X: $i] : (b(X) | (~a(X))))),
% 0.20/0.36 inference(or_elim,[status(thm)],[4])).
% 0.20/0.36 tff(6,plain,
% 0.20/0.36 (~![X: $i] : (b(X) | (~a(X)))),
% 0.20/0.36 inference(and_elim,[status(thm)],[5])).
% 0.20/0.36 tff(7,plain,
% 0.20/0.36 (~![X: $i] : (b(X) | (~a(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.36 tff(8,plain,
% 0.20/0.36 (~![X: $i] : (b(X) | (~a(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.36 tff(9,plain,
% 0.20/0.36 (~![X: $i] : (b(X) | (~a(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.36 tff(10,plain,(
% 0.20/0.36 ~(b(X!0) | (~a(X!0)))),
% 0.20/0.36 inference(skolemize,[status(sab)],[9])).
% 0.20/0.36 tff(11,plain,
% 0.20/0.36 (a(X!0)),
% 0.20/0.36 inference(or_elim,[status(thm)],[10])).
% 0.20/0.36 tff(12,plain,
% 0.20/0.36 (~b(X!0)),
% 0.20/0.36 inference(or_elim,[status(thm)],[10])).
% 0.20/0.36 tff(13,plain,
% 0.20/0.36 (^[X: $i] : refl((c(X) | b(X) | (~a(X))) <=> (c(X) | b(X) | (~a(X))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(14,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X))) <=> ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.36 tff(15,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X))) <=> ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(16,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(and_elim,[status(thm)],[5])).
% 0.20/0.36 tff(17,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.36 tff(18,plain,(
% 0.20/0.36 ![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(skolemize,[status(sab)],[17])).
% 0.20/0.36 tff(19,plain,
% 0.20/0.36 (![X: $i] : (c(X) | b(X) | (~a(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.36 tff(20,plain,
% 0.20/0.36 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)) | c(X!0))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(21,plain,
% 0.20/0.36 ((c(X!0) | b(X!0) | (~a(X!0))) <=> (b(X!0) | (~a(X!0)) | c(X!0))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(22,plain,
% 0.20/0.36 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (b(X!0) | (~a(X!0)) | c(X!0)))),
% 0.20/0.36 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.36 tff(23,plain,
% 0.20/0.36 (((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0))),
% 0.20/0.36 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.36 tff(24,plain,
% 0.20/0.36 ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | (c(X!0) | b(X!0) | (~a(X!0)))),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(25,plain,
% 0.20/0.36 ((~![X: $i] : (c(X) | b(X) | (~a(X)))) | b(X!0) | (~a(X!0)) | c(X!0)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.36 tff(26,plain,
% 0.20/0.36 (c(X!0)),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[25, 19, 12, 11])).
% 0.20/0.36 tff(27,plain,
% 0.20/0.36 (^[X: $i] : refl(((~a(X)) | (~c(X))) <=> ((~a(X)) | (~c(X))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(28,plain,
% 0.20/0.36 (![X: $i] : ((~a(X)) | (~c(X))) <=> ![X: $i] : ((~a(X)) | (~c(X)))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.36 tff(29,plain,
% 0.20/0.36 (^[X: $i] : trans(monotonicity(rewrite((a(X) & c(X)) <=> (~((~a(X)) | (~c(X))))), ((~(a(X) & c(X))) <=> (~(~((~a(X)) | (~c(X))))))), rewrite((~(~((~a(X)) | (~c(X))))) <=> ((~a(X)) | (~c(X)))), ((~(a(X) & c(X))) <=> ((~a(X)) | (~c(X)))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(30,plain,
% 0.20/0.36 (![X: $i] : (~(a(X) & c(X))) <=> ![X: $i] : ((~a(X)) | (~c(X)))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.36 tff(31,plain,
% 0.20/0.36 ((~?[X: $i] : (a(X) & c(X))) <=> (~?[X: $i] : (a(X) & c(X)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(32,plain,
% 0.20/0.36 (~?[X: $i] : (a(X) & c(X))),
% 0.20/0.36 inference(or_elim,[status(thm)],[4])).
% 0.20/0.36 tff(33,plain,
% 0.20/0.36 (~?[X: $i] : (a(X) & c(X))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.36 tff(34,plain,
% 0.20/0.36 (~?[X: $i] : (a(X) & c(X))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.20/0.36 tff(35,plain,
% 0.20/0.36 (~?[X: $i] : (a(X) & c(X))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.20/0.36 tff(36,plain,
% 0.20/0.36 (^[X: $i] : refl($oeq((~(a(X) & c(X))), (~(a(X) & c(X)))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(37,plain,(
% 0.20/0.36 ![X: $i] : (~(a(X) & c(X)))),
% 0.20/0.36 inference(nnf-neg,[status(sab)],[35, 36])).
% 0.20/0.36 tff(38,plain,
% 0.20/0.36 (![X: $i] : ((~a(X)) | (~c(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.36 tff(39,plain,
% 0.20/0.36 (![X: $i] : ((~a(X)) | (~c(X)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.36 tff(40,plain,
% 0.20/0.36 (((~![X: $i] : ((~a(X)) | (~c(X)))) | ((~a(X!0)) | (~c(X!0)))) <=> ((~![X: $i] : ((~a(X)) | (~c(X)))) | (~a(X!0)) | (~c(X!0)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(41,plain,
% 0.20/0.36 ((~![X: $i] : ((~a(X)) | (~c(X)))) | ((~a(X!0)) | (~c(X!0)))),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(42,plain,
% 0.20/0.36 ((~![X: $i] : ((~a(X)) | (~c(X)))) | (~a(X!0)) | (~c(X!0))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.36 tff(43,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[42, 11, 39, 26])).
% 0.20/0.36 % SZS output end Proof
% 0.20/0.36 % E exiting
%------------------------------------------------------------------------------