%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:41:07 AM UTC 2026
% Result : Theorem 25.83s 4.22s
% Output : CNFRefutation 25.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 08:43:14 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.83/4.22 % SZS status Theorem for theBenchmark.p
% 25.83/4.22 % SZS output start CNFRefutation for theBenchmark.p
% 25.83/4.22 fof(d2_zfmisc_1, axiom, ! [X0] : ! [X1] : ! [X2] : ((X2 = 'cartesian$uproduct2'(X0,X1) <=> ! [X3] : ((in(X3,X2) <=> ? [X4] : ? [X5] : ((in(X4,X0) & (in(X5,X1) & X3 = 'ordered$upair'(X4,X5))))))))).
% 25.83/4.22 fof(d3_tarski, axiom, ! [X0] : ! [X1] : ((subset(X0,X1) <=> ! [X2] : ((in(X2,X0) => in(X2,X1)))))).
% 25.83/4.22 fof(t118_zfmisc_1, conjecture, ! [X0] : ! [X1] : ! [X2] : ((subset(X0,X1) => (subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)) & subset('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X2,X1)))))).
% 25.83/4.22 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ! [X2] : ((subset(X0,X1) => (subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)) & subset('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X2,X1))))), inference(negate_conjecture, [status(cth)], [t118_zfmisc_1])).
% 25.83/4.22 cnf(c2, plain, X0 != 'cartesian$uproduct2'(X1,X2) | X3(X1,X2,X0), inference(clausification, [status(esa)], [d2_zfmisc_1])).
% 25.83/4.22 cnf(c4, plain, ~X0(X1,X2,X3) | ~in(X4,X3) | in(sK9(X1,X2,X4),X1), inference(clausification, [status(esa)], [d2_zfmisc_1])).
% 25.83/4.22 cnf(c5, plain, ~X0(X1,X2,X3) | ~in(X4,X3) | in(sK10(X1,X2,X4),X2), inference(clausification, [status(esa)], [d2_zfmisc_1])).
% 25.83/4.22 cnf(c6, plain, ~X0(X1,X2,X3) | ~in(X4,X3) | X4 = 'ordered$upair'(sK9(X1,X2,X4),sK10(X1,X2,X4)), inference(clausification, [status(esa)], [d2_zfmisc_1])).
% 25.83/4.22 cnf(c7, plain, ~in(X0,X1) | ~in(X2,X3) | ~X4(X1,X3,X5) | in(X6,X5) | X6 != 'ordered$upair'(X0,X2), inference(clausification, [status(esa)], [d2_zfmisc_1])).
% 25.83/4.22 cnf(c16, plain, ~subset(X0,X1) | ~in(X2,X0) | in(X2,X1), inference(clausification, [status(esa)], [d3_tarski])).
% 25.83/4.22 cnf(c17, plain, subset(X0,X1) | in(sK21(X0,X1),X0), inference(clausification, [status(esa)], [d3_tarski])).
% 25.83/4.22 cnf(c18, plain, subset(X0,X1) | ~in(sK21(X0,X1),X1), inference(clausification, [status(esa)], [d3_tarski])).
% 25.83/4.22 cnf(c24, plain, subset(sK30,sK31), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.83/4.22 cnf(c25, plain, ~subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)) | ~subset('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.83/4.22 cnf(d0, plain, in(X0,sK31) | ~in(X0,sK30), inference(resolution, [status(thm)], [c16,c24])).
% 25.83/4.22 cnf(d1, plain, 'Ts4'(X0,X1,'cartesian$uproduct2'(X0,X1)), inference(equality_resolution, [status(thm)], [c2])).
% 25.83/4.22 cnf(d2, plain, ~in(X0,'cartesian$uproduct2'(X1,X2)) | in(sK9(X1,X2,X0),X1), inference(resolution, [status(thm)], [d1,c4])).
% 25.83/4.22 cnf(d3, plain, ~in(X0,'cartesian$uproduct2'(sK30,X1)) | in(sK9(sK30,X1,X0),sK31), inference(resolution, [status(thm)], [d2,d0])).
% 25.83/4.22 cnf(d4, plain, ~in(X0,'cartesian$uproduct2'(X1,X2)) | in(sK10(X1,X2,X0),X2), inference(resolution, [status(thm)], [d1,c5])).
% 25.83/4.22 cnf(d5, plain, in('ordered$upair'(X0,X1),X2) | ~in(X1,X3) | ~in(X0,X4) | ~'Ts4'(X4,X3,X2), inference(equality_resolution, [status(thm)], [c7])).
% 25.83/4.22 cnf(d6, plain, ~in(X0,X1) | ~in(X2,X3) | in('ordered$upair'(X2,X0),'cartesian$uproduct2'(X3,X1)), inference(resolution, [status(thm)], [d5,d1])).
% 25.83/4.22 cnf(d7, plain, X0 = 'ordered$upair'(sK9(X1,X2,X0),sK10(X1,X2,X0)) | ~in(X0,'cartesian$uproduct2'(X1,X2)), inference(resolution, [status(thm)], [c6,d1])).
% 25.83/4.22 cnf(d8, plain, sK21('cartesian$uproduct2'(X0,X1),X2) = 'ordered$upair'(sK9(X0,X1,sK21('cartesian$uproduct2'(X0,X1),X2)),sK10(X0,X1,sK21('cartesian$uproduct2'(X0,X1),X2))) | subset('cartesian$uproduct2'(X0,X1),X2), inference(resolution, [status(thm)], [d7,c17])).
% 25.83/4.22 cnf(d9, plain, ~in(X0,'cartesian$uproduct2'(X1,sK30)) | in(sK10(X1,sK30,X0),sK31), inference(resolution, [status(thm)], [d4,d0])).
% 25.83/4.22 cnf(d10, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | ~subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d8,c25])).
% 25.83/4.22 cnf(d11, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)) = 'ordered$upair'(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),sK10(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)))), inference(resolution, [status(thm)], [d10,d8])).
% 25.83/4.22 cnf(d12, plain, in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(X0,X1)) | ~in(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X0) | ~in(sK10(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X1) | sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))), inference(superposition, [status(thm)], [d11,d6])).
% 25.83/4.22 cnf(d13, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | ~in(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X0) | in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(X0,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)), inference(resolution, [status(thm)], [d12,d4])).
% 25.83/4.22 cnf(d14, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK31,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)), inference(resolution, [status(thm)], [d13,d3])).
% 25.83/4.22 cnf(d15, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK31,sK32)) | subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d14,c17])).
% 25.83/4.22 cnf(d16, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)) | subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d15,c18])).
% 25.83/4.22 cnf(d17, plain, sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))) | sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) = 'ordered$upair'(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)))), inference(resolution, [status(thm)], [d16,d10])).
% 25.83/4.22 cnf(d18, plain, in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(X0,X1)) | ~in(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),X0) | ~in(sK10(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),X1), inference(superposition, [status(thm)], [d17,d6])).
% 25.83/4.22 cnf(d19, plain, ~in(sK9(sK32,sK30,sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31))),X0) | in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(X0,sK31)) | ~in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(sK32,sK30)), inference(resolution, [status(thm)], [d18,d9])).
% 25.83/4.22 cnf(d20, plain, in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(sK32,sK31)) | ~in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(sK32,sK30)) | ~in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(sK32,sK30)), inference(resolution, [status(thm)], [d19,d2])).
% 25.83/4.22 cnf(d21, plain, in(sK21('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)),'cartesian$uproduct2'(sK32,sK31)) | subset('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)), inference(resolution, [status(thm)], [d20,c17])).
% 25.83/4.22 cnf(d22, plain, subset('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)) | subset('cartesian$uproduct2'(sK32,sK30),'cartesian$uproduct2'(sK32,sK31)), inference(resolution, [status(thm)], [d21,c18])).
% 25.83/4.22 cnf(d23, plain, ~subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d22,c25])).
% 25.83/4.22 cnf(d24, plain, sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)) = 'ordered$upair'(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),sK10(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)))), inference(resolution, [status(thm)], [d23,d8])).
% 25.83/4.22 cnf(d25, plain, in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(X0,X1)) | ~in(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X0) | ~in(sK10(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X1), inference(superposition, [status(thm)], [d24,d6])).
% 25.83/4.22 cnf(d26, plain, ~in(sK9(sK30,sK32,sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32))),X0) | in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(X0,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)), inference(resolution, [status(thm)], [d25,d4])).
% 25.83/4.22 cnf(d27, plain, in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK31,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)) | ~in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK30,sK32)), inference(resolution, [status(thm)], [d26,d3])).
% 25.83/4.22 cnf(d28, plain, in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK31,sK32)) | subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d27,c17])).
% 25.83/4.22 cnf(d29, plain, in(sK21('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d23,d28])).
% 25.83/4.22 cnf(d30, plain, subset('cartesian$uproduct2'(sK30,sK32),'cartesian$uproduct2'(sK31,sK32)), inference(resolution, [status(thm)], [d29,c18])).
% 25.83/4.22 cnf(d31, plain, $false, inference(resolution, [status(thm)], [d23,d30])).
% 25.83/4.22 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------