%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW319+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:11:41 AM UTC 2026
% Result : Theorem 215.60s 33.61s
% Output : CNFRefutation 215.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW319+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 15:39:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 215.60/33.61 % SZS status Theorem for theBenchmark.p
% 215.60/33.61 % SZS output start CNFRefutation for theBenchmark.p
% 215.60/33.61 fof(fact_singleton__iff, axiom, ! [X0] : ! [X1] : ! [X2] : ((hBOOL(hAPP(hAPP('c$umember'(X2),X1),hAPP(hAPP('c$uSet$uOinsert'(X2),X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X2,'tc$uHOL$uObool'))))) <=> X1 = X0))).
% 215.60/33.61 fof(fact_empty__subsetI, axiom, ! [X0] : ! [X1] : hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))),X0))).
% 215.60/33.61 fof(fact_subset__insertI, axiom, ! [X0] : ! [X1] : ! [X2] : hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X2,'tc$uHOL$uObool')),X1),hAPP(hAPP('c$uSet$uOinsert'(X2),X0),X1)))).
% 215.60/33.61 fof(fact_weaken, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : (('c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X3,X2,X1) => (hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X3),'tc$uHOL$uObool')),X0),X1)) => 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X3,X2,X0))))).
% 215.60/33.61 fof(fact_subset__insert__iff, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : ((hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),X2),hAPP(hAPP('c$uSet$uOinsert'(X3),X1),X0))) <=> ((hBOOL(hAPP(hAPP('c$umember'(X3),X1),X2)) => hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X3,'tc$uHOL$uObool')),X2),hAPP(hAPP('c$uSet$uOinsert'(X3),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X3,'tc$uHOL$uObool'))))),X0))) & (~hBOOL(hAPP(hAPP('c$umember'(X3),X1),X2)) => hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),X2),X0))))))).
% 215.60/33.61 fof(fact_Diff__cancel, axiom, ! [X0] : ! [X1] : hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),X0),X0) = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))).
% 215.60/33.61 fof(fact_Collect__def, axiom, ! [X0] : ! [X1] : hAPP('c$uSet$uOCollect'(X1),X0) = X0).
% 215.60/33.61 fof(fact_singleton__conv2, axiom, ! [X0] : ! [X1] : hAPP('c$uSet$uOCollect'(X1),hAPP('c$ufequal',X0)) = hAPP(hAPP('c$uSet$uOinsert'(X1),X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')))).
% 215.60/33.61 fof(conj_0, hypothesis, 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'v$uts'))).
% 215.60/33.61 fof(conj_1, conjecture, ('c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) & 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG','v$uts'))).
% 215.60/33.61 fof(negated_conjecture, negated_conjecture, ~(('c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) & 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG','v$uts'))), inference(negate_conjecture, [status(cth)], [conj_1])).
% 215.60/33.61 cnf(c38, plain, hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X2),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))))) | X1 != X2, inference(clausification, [status(esa)], [fact_singleton__iff])).
% 215.60/33.61 cnf(c49, plain, hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X1)), inference(clausification, [status(esa)], [fact_empty__subsetI])).
% 215.60/33.61 cnf(c90, plain, hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X2),X1))), inference(clausification, [status(esa)], [fact_subset__insertI])).
% 215.60/33.61 cnf(c94, plain, ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,X2) | ~hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')),X3),X2)) | 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,X3), inference(clausification, [status(esa)], [fact_weaken])).
% 215.60/33.61 cnf(c102, plain, hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X2),X3))) | ~X4(X0,X1,X3,X2), inference(clausification, [status(esa)], [fact_subset__insert__iff])).
% 215.60/33.61 cnf(c107, plain, X0(X1,X2,X3,X4) | ~hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X1,'tc$uHOL$uObool')),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),X2),hAPP(hAPP('c$uSet$uOinsert'(X1),X4),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))))),X3)) | ~hBOOL(hAPP(hAPP('c$umember'(X1),X4),X2)), inference(clausification, [status(esa)], [fact_subset__insert__iff])).
% 215.60/33.61 cnf(c133, plain, hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),X1),X1) = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')), inference(clausification, [status(esa)], [fact_Diff__cancel])).
% 215.60/33.61 cnf(c1394, plain, hAPP('c$uSet$uOCollect'(X0),X1) = X1, inference(clausification, [status(esa)], [fact_Collect__def])).
% 215.60/33.61 cnf(c1403, plain, hAPP('c$uSet$uOCollect'(X0),hAPP('c$ufequal',X1)) = hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))), inference(clausification, [status(esa)], [fact_singleton__conv2])).
% 215.60/33.61 cnf(c1603, plain, 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'v$uts')), inference(clausification, [status(esa)], [conj_0])).
% 215.60/33.61 cnf(c1604, plain, ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) | ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG','v$uts'), inference(clausification, [status(esa)], [negated_conjecture])).
% 215.60/33.61 cnf(d0, plain, hAPP('c$ufequal',X1) = hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))), inference(demodulation, [status(thm)], [c1403,c1394])).
% 215.60/33.61 cnf(d1, plain, ~hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X2)) | ~hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))))) | 'Ts236'(X0,hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X2,X1), inference(superposition, [status(thm)], [c133,c107])).
% 215.60/33.61 cnf(d2, plain, ~hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X2)) | ~hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP('c$ufequal',X1))) | 'Ts236'(X0,hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X2,X1), inference(demodulation, [status(thm)], [d1,d0])).
% 215.60/33.61 cnf(d3, plain, ~hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X2)) | ~hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP('c$ufequal',X1))) | 'Ts236'(X0,hAPP('c$ufequal',X1),X2,X1), inference(demodulation, [status(thm)], [d2,d0])).
% 215.60/33.61 cnf(d4, plain, ~hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP('c$ufequal',X1))) | 'Ts236'(X0,hAPP('c$ufequal',X1),X2,X1), inference(resolution, [status(thm)], [c49,d3])).
% 215.60/33.61 cnf(d5, plain, hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))))), inference(equality_resolution, [status(thm)], [c38])).
% 215.60/33.61 cnf(d6, plain, hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP('c$ufequal',X1))), inference(demodulation, [status(thm)], [d5,d0])).
% 215.60/33.61 cnf(d7, plain, 'Ts236'(X0,hAPP('c$ufequal',X1),X2,X1), inference(resolution, [status(thm)], [d6,d4])).
% 215.60/33.61 cnf(d8, plain, ~'Ts236'('tc$uHoare$u$uMirabelle$uOtriple'(X0),X1,X2,X3) | ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X4,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),X3),X2)) | 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X4,X1), inference(resolution, [status(thm)], [c102,c94])).
% 215.60/33.61 cnf(d9, plain, 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',X0) | ~'Ts236'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),X0,'v$uts','v$ut'), inference(resolution, [status(thm)], [d8,c1603])).
% 215.60/33.61 cnf(d10, plain, 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP('c$ufequal','v$ut')), inference(resolution, [status(thm)], [d9,d7])).
% 215.60/33.61 cnf(d11, plain, ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP('c$ufequal','v$ut')) | ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG','v$uts'), inference(demodulation, [status(thm)], [c1604,d0])).
% 215.60/33.61 cnf(d12, plain, ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),X2),X3)) | 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,X3), inference(resolution, [status(thm)], [c94,c90])).
% 215.60/33.61 cnf(d13, plain, 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG','v$uts'), inference(resolution, [status(thm)], [d12,c1603])).
% 215.60/33.61 cnf(d14, plain, ~'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP('c$ufequal','v$ut')), inference(resolution, [status(thm)], [d13,d11])).
% 215.60/33.61 cnf(d15, plain, $false, inference(resolution, [status(thm)], [d14,d10])).
% 215.60/33.61 % SZS output end CNFRefutation for theBenchmark.p
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