%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:33:02 AM UTC 2026
% Result : Theorem 21.30s 3.61s
% Output : CNFRefutation 21.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:05:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.30/3.61 % SZS status Theorem for theBenchmark.p
% 21.30/3.61 % SZS output start CNFRefutation for theBenchmark.p
% 21.30/3.61 fof(p1, axiom, ! [X0] : (('ilf$utype'(X0,'binary$urelation$utype') => ! [X1] : (('ilf$utype'(X1,'binary$urelation$utype') => (subset(X0,X1) <=> ! [X2] : (('ilf$utype'(X2,'set$utype') => ! [X3] : (('ilf$utype'(X3,'set$utype') => (member('ordered$upair'(X2,X3),X0) => member('ordered$upair'(X2,X3),X1)))))))))))).
% 21.30/3.61 fof(p2, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => (member('ordered$upair'(X1,X2),'identity$urelation$uof'(X0)) <=> (member(X1,X0) & X1 = X2))))))))).
% 21.30/3.61 fof(p5, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => (member(X2,'cross$uproduct'(X0,X1)) <=> ? [X3] : (('ilf$utype'(X3,'set$utype') & ? [X4] : (('ilf$utype'(X4,'set$utype') & (member(X3,X0) & (member(X4,X1) & X2 = 'ordered$upair'(X3,X4))))))))))))))).
% 21.30/3.61 fof(p8, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => 'ilf$utype'('identity$urelation$uof'(X0),'binary$urelation$utype')))).
% 21.30/3.61 fof(p9, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => (subset(X0,X1) <=> ! [X2] : (('ilf$utype'(X2,'set$utype') => (member(X2,X0) => member(X2,X1)))))))))).
% 21.30/3.61 fof(p11, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ('ilf$utype'(X0,'binary$urelation$utype') <=> ('relation$ulike'(X0) & 'ilf$utype'(X0,'set$utype')))))).
% 21.30/3.61 fof(p19, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ('relation$ulike'(X0) <=> ! [X1] : (('ilf$utype'(X1,'set$utype') => (member(X1,X0) => ? [X2] : (('ilf$utype'(X2,'set$utype') & ? [X3] : (('ilf$utype'(X3,'set$utype') & X1 = 'ordered$upair'(X2,X3)))))))))))).
% 21.30/3.61 fof(p27, axiom, ! [X0] : 'ilf$utype'(X0,'set$utype')).
% 21.30/3.61 fof(prove_relset_1_28, conjecture, ! [X0] : (('ilf$utype'(X0,'set$utype') => subset('identity$urelation$uof'(X0),'cross$uproduct'(X0,X0))))).
% 21.30/3.61 fof(negated_conjecture, negated_conjecture, ~! [X0] : (('ilf$utype'(X0,'set$utype') => subset('identity$urelation$uof'(X0),'cross$uproduct'(X0,X0)))), inference(negate_conjecture, [status(cth)], [prove_relset_1_28])).
% 21.30/3.61 cnf(c2, plain, member('ordered$upair'(X0,X1),X2) | ~member('ordered$upair'(X0,X1),X3) | ~'ilf$utype'(X1,'set$utype') | ~X4(X3,X2) | ~'ilf$utype'(X0,'set$utype'), inference(clausification, [status(esa)], [p1])).
% 21.30/3.61 cnf(c5, plain, X0(X1,X2) | member('ordered$upair'(sK5(X1,X2),sK6(X1,X2)),X1), inference(clausification, [status(esa)], [p1])).
% 21.30/3.61 cnf(c6, plain, X0(X1,X2) | ~member('ordered$upair'(sK5(X1,X2),sK6(X1,X2)),X2), inference(clausification, [status(esa)], [p1])).
% 21.30/3.61 cnf(c7, plain, ~'ilf$utype'(X0,'set$utype') | member(X0,X1) | ~member('ordered$upair'(X0,X2),'identity$urelation$uof'(X1)) | ~'ilf$utype'(X2,'set$utype') | ~'ilf$utype'(X1,'set$utype'), inference(clausification, [status(esa)], [p2])).
% 21.30/3.61 cnf(c8, plain, ~'ilf$utype'(X0,'set$utype') | X0 = X1 | ~member('ordered$upair'(X0,X1),'identity$urelation$uof'(X2)) | ~'ilf$utype'(X1,'set$utype') | ~'ilf$utype'(X2,'set$utype'), inference(clausification, [status(esa)], [p2])).
% 21.30/3.61 cnf(c15, plain, member(X0,'cross$uproduct'(X1,X2)) | ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X2,'set$utype') | ~X3(X1,X2,X0) | ~'ilf$utype'(X1,'set$utype'), inference(clausification, [status(esa)], [p5])).
% 21.30/3.61 cnf(c21, plain, X0(X1,X2,X3) | ~'ilf$utype'(X4,'set$utype') | ~member(X4,X2) | ~'ilf$utype'(X5,'set$utype') | ~member(X5,X1) | X3 != 'ordered$upair'(X5,X4), inference(clausification, [status(esa)], [p5])).
% 21.30/3.61 cnf(c26, plain, ~'ilf$utype'(X0,'set$utype') | 'ilf$utype'('identity$urelation$uof'(X0),'binary$urelation$utype'), inference(clausification, [status(esa)], [p8])).
% 21.30/3.61 cnf(c29, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | subset(X0,X1) | member(sK33(X0,X1),X0), inference(clausification, [status(esa)], [p9])).
% 21.30/3.61 cnf(c30, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | subset(X0,X1) | ~member(sK33(X0,X1),X1), inference(clausification, [status(esa)], [p9])).
% 21.30/3.61 cnf(c32, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X0,'binary$urelation$utype') | 'relation$ulike'(X0), inference(clausification, [status(esa)], [p11])).
% 21.30/3.61 cnf(c44, plain, ~'ilf$utype'(X0,'set$utype') | ~'relation$ulike'(X0) | X1(X0), inference(clausification, [status(esa)], [p19])).
% 21.30/3.61 cnf(c48, plain, ~X0(X1) | ~'ilf$utype'(X2,'set$utype') | ~member(X2,X1) | X2 = 'ordered$upair'(sK54(X2),sK55(X2)), inference(clausification, [status(esa)], [p19])).
% 21.30/3.61 cnf(c66, plain, 'ilf$utype'(X0,'set$utype'), inference(clausification, [status(esa)], [p27])).
% 21.30/3.61 cnf(c68, plain, ~subset('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(clausification, [status(esa)], [negated_conjecture])).
% 21.30/3.61 cnf(d0, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | member(X0,X1) | ~member('ordered$upair'(X0,X2),'identity$urelation$uof'(X1)), inference(resolution, [status(thm)], [c66,c7])).
% 21.30/3.61 cnf(d1, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(sK5('identity$urelation$uof'(X0),X1),'set$utype') | member(sK5('identity$urelation$uof'(X0),X1),X0) | 'Ts0'('identity$urelation$uof'(X0),X1), inference(resolution, [status(thm)], [d0,c5])).
% 21.30/3.61 cnf(d2, plain, ~'ilf$utype'(sK5('identity$urelation$uof'(X0),X1),'set$utype') | 'Ts0'('identity$urelation$uof'(X0),X1) | member(sK5('identity$urelation$uof'(X0),X1),X0), inference(resolution, [status(thm)], [c66,d1])).
% 21.30/3.61 cnf(d3, plain, 'Ts0'('identity$urelation$uof'(X0),X1) | member(sK5('identity$urelation$uof'(X0),X1),X0), inference(resolution, [status(thm)], [d2,c66])).
% 21.30/3.61 cnf(d4, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | member(X0,'cross$uproduct'(X1,X2)) | ~'Ts16'(X1,X2,X0), inference(resolution, [status(thm)], [c66,c15])).
% 21.30/3.61 cnf(d5, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'('ordered$upair'(sK5(X1,'cross$uproduct'(X0,X2)),sK6(X1,'cross$uproduct'(X0,X2))),'set$utype') | ~'Ts16'(X0,X2,'ordered$upair'(sK5(X1,'cross$uproduct'(X0,X2)),sK6(X1,'cross$uproduct'(X0,X2)))) | 'Ts0'(X1,'cross$uproduct'(X0,X2)), inference(resolution, [status(thm)], [d4,c6])).
% 21.30/3.61 cnf(d6, plain, ~'ilf$utype'('ordered$upair'(sK5(X0,'cross$uproduct'(X1,X2)),sK6(X0,'cross$uproduct'(X1,X2))),'set$utype') | 'Ts0'(X0,'cross$uproduct'(X1,X2)) | ~'Ts16'(X1,X2,'ordered$upair'(sK5(X0,'cross$uproduct'(X1,X2)),sK6(X0,'cross$uproduct'(X1,X2)))), inference(resolution, [status(thm)], [c66,d5])).
% 21.30/3.61 cnf(d7, plain, X0 != 'ordered$upair'(X1,X2) | ~'ilf$utype'(X2,'set$utype') | ~member(X1,X3) | ~member(X2,X4) | 'Ts16'(X3,X4,X0), inference(resolution, [status(thm)], [c66,c21])).
% 21.30/3.61 cnf(d8, plain, ~'ilf$utype'(X0,'set$utype') | ~member(X0,X1) | ~member(X2,X3) | 'Ts16'(X3,X1,'ordered$upair'(X2,X0)), inference(equality_resolution, [status(thm)], [d7])).
% 21.30/3.61 cnf(d9, plain, ~member(X0,X1) | ~member(X2,X3) | 'Ts16'(X1,X3,'ordered$upair'(X0,X2)), inference(resolution, [status(thm)], [c66,d8])).
% 21.30/3.61 cnf(d10, plain, ~member(sK6(X0,'cross$uproduct'(X1,X2)),X2) | ~member(sK5(X0,'cross$uproduct'(X1,X2)),X1) | ~'ilf$utype'('ordered$upair'(sK5(X0,'cross$uproduct'(X1,X2)),sK6(X0,'cross$uproduct'(X1,X2))),'set$utype') | 'Ts0'(X0,'cross$uproduct'(X1,X2)), inference(resolution, [status(thm)], [d9,d6])).
% 21.30/3.61 cnf(d11, plain, 'Ts0'(X0,'cross$uproduct'(X1,X2)) | ~member(sK5(X0,'cross$uproduct'(X1,X2)),X1) | ~member(sK6(X0,'cross$uproduct'(X1,X2)),X2), inference(resolution, [status(thm)], [c66,d10])).
% 21.30/3.61 cnf(d12, plain, X0 = X1 | ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X2,'set$utype') | ~member('ordered$upair'(X0,X1),'identity$urelation$uof'(X2)), inference(resolution, [status(thm)], [c66,c8])).
% 21.30/3.61 cnf(d13, plain, sK5('identity$urelation$uof'(X0),X1) = sK6('identity$urelation$uof'(X0),X1) | ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(sK5('identity$urelation$uof'(X0),X1),'set$utype') | 'Ts0'('identity$urelation$uof'(X0),X1), inference(resolution, [status(thm)], [d12,c5])).
% 21.30/3.61 cnf(d14, plain, sK5('identity$urelation$uof'(X0),X1) = sK6('identity$urelation$uof'(X0),X1) | ~'ilf$utype'(sK5('identity$urelation$uof'(X0),X1),'set$utype') | 'Ts0'('identity$urelation$uof'(X0),X1), inference(resolution, [status(thm)], [c66,d13])).
% 21.30/3.61 cnf(d15, plain, sK5('identity$urelation$uof'(X0),X1) = sK6('identity$urelation$uof'(X0),X1) | 'Ts0'('identity$urelation$uof'(X0),X1), inference(resolution, [status(thm)], [d14,c66])).
% 21.30/3.61 cnf(d16, plain, ~'ilf$utype'(X0,'set$utype') | subset(X0,X1) | ~member(sK33(X0,X1),X1), inference(resolution, [status(thm)], [c66,c30])).
% 21.30/3.61 cnf(d17, plain, ~'ilf$utype'(X0,'set$utype') | subset(X1,X0) | member(sK33(X1,X0),X1), inference(resolution, [status(thm)], [c66,c29])).
% 21.30/3.61 cnf(d18, plain, X0 = 'ordered$upair'(sK54(X0),sK55(X0)) | ~member(X0,X1) | ~'Ts51'(X1), inference(resolution, [status(thm)], [c66,c48])).
% 21.30/3.61 cnf(d19, plain, sK33(X0,X1) = 'ordered$upair'(sK54(sK33(X0,X1)),sK55(sK33(X0,X1))) | ~'Ts51'(X0) | ~'ilf$utype'(X1,'set$utype') | subset(X0,X1), inference(resolution, [status(thm)], [d18,d17])).
% 21.30/3.61 cnf(d20, plain, sK33(X0,X1) = 'ordered$upair'(sK54(sK33(X0,X1)),sK55(sK33(X0,X1))) | subset(X0,X1) | ~'Ts51'(X0), inference(resolution, [status(thm)], [c66,d19])).
% 21.30/3.61 cnf(d21, plain, sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)) = 'ordered$upair'(sK54(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76))),sK55(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)))) | ~'Ts51'('identity$urelation$uof'(sK76)), inference(resolution, [status(thm)], [d20,c68])).
% 21.30/3.61 cnf(d22, plain, ~'relation$ulike'(X0) | 'Ts51'(X0), inference(resolution, [status(thm)], [c66,c44])).
% 21.30/3.61 cnf(d23, plain, 'ilf$utype'('identity$urelation$uof'(X0),'binary$urelation$utype'), inference(resolution, [status(thm)], [c66,c26])).
% 21.30/3.61 cnf(d24, plain, ~'ilf$utype'(X0,'binary$urelation$utype') | 'relation$ulike'(X0), inference(resolution, [status(thm)], [c66,c32])).
% 21.30/3.61 cnf(d25, plain, 'relation$ulike'('identity$urelation$uof'(X0)), inference(resolution, [status(thm)], [d24,d23])).
% 21.30/3.61 cnf(d26, plain, 'Ts51'('identity$urelation$uof'(X0)), inference(resolution, [status(thm)], [d25,d22])).
% 21.30/3.61 cnf(d27, plain, sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)) = 'ordered$upair'(sK54(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76))),sK55(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)))), inference(resolution, [status(thm)], [d26,d21])).
% 21.30/3.61 cnf(d28, plain, ~'ilf$utype'(X0,'set$utype') | ~'Ts0'(X1,X2) | member('ordered$upair'(X0,X3),X2) | ~member('ordered$upair'(X0,X3),X1), inference(resolution, [status(thm)], [c66,c2])).
% 21.30/3.61 cnf(d29, plain, ~'Ts0'(X0,X1) | member('ordered$upair'(X2,X3),X1) | ~member('ordered$upair'(X2,X3),X0), inference(resolution, [status(thm)], [c66,d28])).
% 21.30/3.61 cnf(d30, plain, ~member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X0) | ~'Ts0'(X0,X1) | member('ordered$upair'(sK54(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76))),sK55(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)))),X1), inference(superposition, [status(thm)], [d27,d29])).
% 21.30/3.61 cnf(d31, plain, ~'Ts0'(X0,X1) | member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X1) | ~member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X0), inference(demodulation, [status(thm)], [d30,d27])).
% 21.30/3.61 cnf(d32, plain, ~'Ts0'('identity$urelation$uof'(sK76),X0) | member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X0) | ~'ilf$utype'('cross$uproduct'(sK76,sK76),'set$utype') | subset('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [d31,d17])).
% 21.30/3.61 cnf(d33, plain, ~'ilf$utype'('cross$uproduct'(sK76,sK76),'set$utype') | ~'Ts0'('identity$urelation$uof'(sK76),X0) | member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X0), inference(resolution, [status(thm)], [c68,d32])).
% 21.30/3.61 cnf(d34, plain, ~'Ts0'('identity$urelation$uof'(sK76),X0) | member(sK33('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),X0), inference(resolution, [status(thm)], [c66,d33])).
% 21.30/3.61 cnf(d35, plain, ~'Ts0'('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)) | ~'ilf$utype'('identity$urelation$uof'(sK76),'set$utype') | subset('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [d34,d16])).
% 21.30/3.61 cnf(d36, plain, ~'ilf$utype'('identity$urelation$uof'(sK76),'set$utype') | ~'Ts0'('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [c68,d35])).
% 21.30/3.61 cnf(d37, plain, ~'Ts0'('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [c66,d36])).
% 21.30/3.61 cnf(d38, plain, sK5('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)) = sK6('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [d37,d15])).
% 21.30/3.61 cnf(d39, plain, ~member(sK5('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),sK76) | 'Ts0'('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)) | ~member(sK5('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),sK76), inference(superposition, [status(thm)], [d38,d11])).
% 21.30/3.61 cnf(d40, plain, ~member(sK5('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)),sK76), inference(resolution, [status(thm)], [d37,d39])).
% 21.30/3.61 cnf(d41, plain, 'Ts0'('identity$urelation$uof'(sK76),'cross$uproduct'(sK76,sK76)), inference(resolution, [status(thm)], [d40,d3])).
% 21.30/3.61 cnf(d42, plain, $false, inference(resolution, [status(thm)], [d37,d41])).
% 21.30/3.61 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------