%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN049-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:03 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN049-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 12:27:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_q_type, type, (
% 0.12/0.37 big_q: $i > $o)).
% 0.12/0.37 tff(g_type, type, (
% 0.12/0.37 g: $i > $i)).
% 0.12/0.37 tff(elem_0_type, type, (
% 0.12/0.37 elem_0: $i)).
% 0.12/0.37 tff(big_p_type, type, (
% 0.12/0.37 big_p: $i > $o)).
% 0.12/0.37 tff(f_type, type, (
% 0.12/0.37 f: $i > $i)).
% 0.12/0.37 tff(1,assumption,(~big_p(f(elem!0))), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[X: $i] : refl(big_p(X) <=> big_p(X))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : big_p(X) <=> ![X: $i] : big_p(X)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X: $i] : big_p(X) <=> ![X: $i] : big_p(X)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(![X: $i] : big_p(X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,(
% 0.12/0.37 ![X: $i] : big_p(X)),
% 0.12/0.37 inference(skolemize,[status(sab)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ((~![X: $i] : big_p(X)) | big_p(f(elem!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.37 tff(11,plain,(big_p(f(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[X: $i] : refl((big_q(g(X)) | (~big_p(f(X)))) <=> (big_q(g(X)) | (~big_p(f(X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i] : (big_q(g(X)) | (~big_p(f(X)))) <=> ![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : (big_q(g(X)) | (~big_p(f(X)))) <=> ![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[X: $i] : rewrite(((~big_p(f(X))) | big_q(g(X))) <=> (big_q(g(X)) | (~big_p(f(X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X: $i] : ((~big_p(f(X))) | big_q(g(X))) <=> ![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,axiom,(![X: $i] : ((~big_p(f(X))) | big_q(g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 ![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i] : (big_q(g(X)) | (~big_p(f(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![X: $i] : (big_q(g(X)) | (~big_p(f(X))))) | (big_q(g(elem!0)) | (~big_p(f(elem!0))))) <=> ((~![X: $i] : (big_q(g(X)) | (~big_p(f(X))))) | big_q(g(elem!0)) | (~big_p(f(elem!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X: $i] : (big_q(g(X)) | (~big_p(f(X))))) | (big_q(g(elem!0)) | (~big_p(f(elem!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![X: $i] : (big_q(g(X)) | (~big_p(f(X))))) | big_q(g(elem!0)) | (~big_p(f(elem!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (big_q(g(elem!0)) | (~big_p(f(elem!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (big_q(g(elem!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (^[X: $i] : refl((~big_q(X)) <=> (~big_q(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i] : (~big_q(X)) <=> ![X: $i] : (~big_q(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X: $i] : (~big_q(X)) <=> ![X: $i] : (~big_q(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,axiom,(![X: $i] : (~big_q(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i] : (~big_q(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,(
% 0.12/0.37 ![X: $i] : (~big_q(X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[31])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![X: $i] : (~big_q(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 ((~![X: $i] : (~big_q(X))) | (~big_q(g(elem!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------