%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:41:32 AM UTC 2026
% Result : Theorem 25.57s 9.68s
% Output : CNFRefutation 25.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n019.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 09:04:54 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.57/9.68 % SZS status Theorem for theBenchmark.p
% 25.57/9.68 % SZS output start CNFRefutation for theBenchmark.p
% 25.57/9.68 fof(s1_tarski__e16_22__wellord2__2, axiom, ! [X0] : ! [X1] : ((! [X2] : ! [X3] : ! [X4] : (((X2 = X3 & (? [X5] : ? [X6] : (('ordered$upair'(X5,X6) = X3 & (in(X5,X0) & X6 = singleton(X5)))) & (X2 = X4 & ? [X7] : ? [X8] : (('ordered$upair'(X7,X8) = X4 & (in(X7,X0) & X8 = singleton(X7))))))) => X3 = X4)) => ? [X2] : ! [X3] : ((in(X3,X2) <=> ? [X4] : ((in(X4,'cartesian$uproduct2'(X0,X1)) & (X4 = X3 & ? [X9] : ? [X10] : (('ordered$upair'(X9,X10) = X3 & (in(X9,X0) & X10 = singleton(X9)))))))))))).
% 25.57/9.68 fof(s1_xboole_0__e16_22__wellord2__1, conjecture, ! [X0] : ! [X1] : ? [X2] : ! [X3] : ((in(X3,X2) <=> (in(X3,'cartesian$uproduct2'(X0,X1)) & ? [X4] : ? [X5] : (('ordered$upair'(X4,X5) = X3 & (in(X4,X0) & X5 = singleton(X4)))))))).
% 25.57/9.68 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ? [X2] : ! [X3] : ((in(X3,X2) <=> (in(X3,'cartesian$uproduct2'(X0,X1)) & ? [X4] : ? [X5] : (('ordered$upair'(X4,X5) = X3 & (in(X4,X0) & X5 = singleton(X4))))))), inference(negate_conjecture, [status(cth)], [s1_xboole_0__e16_22__wellord2__1])).
% 25.57/9.68 cnf(c18, plain, X0(X1) | ~in(X2,sK16(X1,X3)) | X4(X1,X3,X2), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c19, plain, X0(X1) | 'ordered$upair'(X2,X3) != X4 | ~in(X2,X1) | X4 != X5 | singleton(X2) != X3 | ~in(X5,'cartesian$uproduct2'(X1,X6)) | in(X4,sK16(X1,X6)), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c20, plain, ~X0(X1,X2,X3) | in(sK21(X1,X2,X3),'cartesian$uproduct2'(X1,X2)), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c21, plain, ~X0(X1,X2,X3) | 'ordered$upair'(sK22(X1,X3),sK23(X1,X3)) = X3, inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c22, plain, ~X0(X1,X2,X3) | singleton(sK22(X1,X3)) = sK23(X1,X3), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c23, plain, ~X0(X1,X2,X3) | in(sK22(X1,X3),X1), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c24, plain, ~X0(X1,X2,X3) | X3 = sK21(X1,X2,X3), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c31, plain, ~X0(X1) | sK26(X1) = sK24(X1), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c32, plain, ~X0(X1) | sK25(X1) = sK24(X1), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c33, plain, ~X0(X1) | sK26(X1) != sK25(X1), inference(clausification, [status(esa)], [s1_tarski__e16_22__wellord2__2])).
% 25.57/9.68 cnf(c34, plain, in(sK35(X0),X0) | X1(sK32,sK33,X0,sK35(X0)), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c35, plain, ~in(X0,sK32) | 'ordered$upair'(X0,X1) != sK35(X2) | X3(sK32,sK33,X2,sK35(X2)) | ~in(sK35(X2),'cartesian$uproduct2'(sK32,sK33)) | singleton(X0) != X1, inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c36, plain, ~X0(X1,X2,X3,X4) | ~in(X4,X3), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c37, plain, ~X0(X1,X2,X3,X4) | 'ordered$upair'(sK38(X4,X1),sK39(X4,X1)) = X4, inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c38, plain, ~X0(X1,X2,X3,X4) | singleton(sK38(X4,X1)) = sK39(X4,X1), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c39, plain, ~X0(X1,X2,X3,X4) | in(sK38(X4,X1),X1), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(c40, plain, ~X0(X1,X2,X3,X4) | in(X4,'cartesian$uproduct2'(X1,X2)), inference(clausification, [status(esa)], [negated_conjecture])).
% 25.57/9.68 cnf(d0, plain, 'Ts12'(X0,X1,sK35(sK16(X0,X1))) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(resolution, [status(thm)], [c18,c34])).
% 25.57/9.68 cnf(d1, plain, 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | in(sK21(X0,X1,sK35(sK16(X0,X1))),'cartesian$uproduct2'(X0,X1)), inference(resolution, [status(thm)], [d0,c20])).
% 25.57/9.68 cnf(d2, plain, 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | sK35(sK16(X0,X1)) = sK21(X0,X1,sK35(sK16(X0,X1))), inference(resolution, [status(thm)], [d0,c24])).
% 25.57/9.68 cnf(d3, plain, in(sK35(sK16(X0,X1)),'cartesian$uproduct2'(X0,X1)) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(superposition, [status(thm)], [d2,d1])).
% 25.57/9.68 cnf(d4, plain, 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | in(sK22(X0,sK35(sK16(X0,X1))),X0), inference(resolution, [status(thm)], [d0,c23])).
% 25.57/9.68 cnf(d5, plain, 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | 'ordered$upair'(sK22(X0,sK35(sK16(X0,X1))),sK23(X0,sK35(sK16(X0,X1)))) = sK35(sK16(X0,X1)), inference(resolution, [status(thm)], [d0,c21])).
% 25.57/9.68 cnf(d6, plain, sK35(sK16(X0,X1)) != sK35(X2) | singleton(sK22(X0,sK35(sK16(X0,X1)))) != sK23(X0,sK35(sK16(X0,X1))) | ~in(sK22(X0,sK35(sK16(X0,X1))),sK32) | ~in(sK35(X2),'cartesian$uproduct2'(sK32,sK33)) | 'Ts31'(sK32,sK33,X2,sK35(X2)) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(superposition, [status(thm)], [d5,c35])).
% 25.57/9.68 cnf(d7, plain, 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | singleton(sK22(X0,sK35(sK16(X0,X1)))) = sK23(X0,sK35(sK16(X0,X1))), inference(resolution, [status(thm)], [d0,c22])).
% 25.57/9.68 cnf(d8, plain, sK23(X0,sK35(sK16(X0,X1))) != sK23(X0,sK35(sK16(X0,X1))) | sK35(sK16(X0,X1)) != sK35(X2) | ~in(sK22(X0,sK35(sK16(X0,X1))),sK32) | ~in(sK35(X2),'cartesian$uproduct2'(sK32,sK33)) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,X2,sK35(X2)) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(superposition, [status(thm)], [d7,d6])).
% 25.57/9.68 cnf(d9, plain, sK35(sK16(X0,X1)) != sK35(X2) | ~in(sK22(X0,sK35(sK16(X0,X1))),sK32) | ~in(sK35(X2),'cartesian$uproduct2'(sK32,sK33)) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,X2,sK35(X2)) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(equality_resolution, [status(thm)], [d8])).
% 25.57/9.68 cnf(d10, plain, ~in(sK22(X0,sK35(sK16(X0,X1))),sK32) | ~in(sK35(sK16(X0,X1)),'cartesian$uproduct2'(sK32,sK33)) | 'Ts13'(X0) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))) | 'Ts31'(sK32,sK33,sK16(X0,X1),sK35(sK16(X0,X1))), inference(equality_resolution, [status(thm)], [d9])).
% 25.57/9.68 cnf(d11, plain, ~in(sK35(sK16(sK32,X0)),'cartesian$uproduct2'(sK32,sK33)) | 'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,X0),sK35(sK16(sK32,X0))) | 'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,X0),sK35(sK16(sK32,X0))), inference(resolution, [status(thm)], [d10,d4])).
% 25.57/9.68 cnf(d12, plain, 'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))) | 'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(resolution, [status(thm)], [d11,d3])).
% 25.57/9.68 cnf(d13, plain, 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))) | sK26(sK32) = sK24(sK32), inference(resolution, [status(thm)], [d12,c31])).
% 25.57/9.68 cnf(d14, plain, 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))) | sK25(sK32) = sK24(sK32), inference(resolution, [status(thm)], [d12,c32])).
% 25.57/9.68 cnf(d15, plain, sK26(sK32) = sK25(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(superposition, [status(thm)], [d14,d13])).
% 25.57/9.68 cnf(d16, plain, sK25(sK32) != sK25(sK32) | ~'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(superposition, [status(thm)], [d15,c33])).
% 25.57/9.68 cnf(d17, plain, ~'Ts13'(sK32) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(equality_resolution, [status(thm)], [d16])).
% 25.57/9.68 cnf(d18, plain, 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))) | 'Ts31'(sK32,sK33,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(resolution, [status(thm)], [d17,d12])).
% 25.57/9.68 cnf(d19, plain, in(sK35(sK16(sK32,sK33)),'cartesian$uproduct2'(sK32,sK33)), inference(resolution, [status(thm)], [d18,c40])).
% 25.57/9.68 cnf(d20, plain, 'ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),sK39(sK35(sK16(sK32,sK33)),sK32)) = sK35(sK16(sK32,sK33)), inference(resolution, [status(thm)], [d18,c37])).
% 25.57/9.68 cnf(d21, plain, singleton(sK38(sK35(sK16(sK32,sK33)),sK32)) = sK39(sK35(sK16(sK32,sK33)),sK32), inference(resolution, [status(thm)], [d18,c38])).
% 25.57/9.68 cnf(d22, plain, 'ordered$upair'(X0,X1) != X2 | singleton(X0) != X1 | ~in(X2,'cartesian$uproduct2'(X3,X4)) | in(X2,sK16(X3,X4)) | ~in(X0,X3) | 'Ts13'(X3), inference(equality_resolution, [status(thm)], [c19])).
% 25.57/9.68 cnf(d23, plain, singleton(X0) != X1 | in('ordered$upair'(X0,X1),sK16(X2,X3)) | ~in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) | ~in(X0,X2) | 'Ts13'(X2), inference(equality_resolution, [status(thm)], [d22])).
% 25.57/9.68 cnf(d24, plain, ~in(X0,X1) | in('ordered$upair'(X0,singleton(X0)),sK16(X1,X2)) | ~in('ordered$upair'(X0,singleton(X0)),'cartesian$uproduct2'(X1,X2)) | 'Ts13'(X1), inference(equality_resolution, [status(thm)], [d23])).
% 25.57/9.68 cnf(d25, plain, in(sK38(sK35(sK16(sK32,sK33)),sK32),sK32), inference(resolution, [status(thm)], [d18,c39])).
% 25.57/9.68 cnf(d26, plain, in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),singleton(sK38(sK35(sK16(sK32,sK33)),sK32))),sK16(sK32,X0)) | ~in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),singleton(sK38(sK35(sK16(sK32,sK33)),sK32))),'cartesian$uproduct2'(sK32,X0)) | 'Ts13'(sK32), inference(resolution, [status(thm)], [d25,d24])).
% 25.57/9.68 cnf(d27, plain, in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),sK39(sK35(sK16(sK32,sK33)),sK32)),sK16(sK32,X0)) | ~in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),singleton(sK38(sK35(sK16(sK32,sK33)),sK32))),'cartesian$uproduct2'(sK32,X0)) | 'Ts13'(sK32), inference(demodulation, [status(thm)], [d26,d21])).
% 25.57/9.68 cnf(d28, plain, in(sK35(sK16(sK32,sK33)),sK16(sK32,X0)) | ~in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),singleton(sK38(sK35(sK16(sK32,sK33)),sK32))),'cartesian$uproduct2'(sK32,X0)) | 'Ts13'(sK32), inference(demodulation, [status(thm)], [d27,d20])).
% 25.57/9.68 cnf(d29, plain, in(sK35(sK16(sK32,sK33)),sK16(sK32,X0)) | ~in('ordered$upair'(sK38(sK35(sK16(sK32,sK33)),sK32),sK39(sK35(sK16(sK32,sK33)),sK32)),'cartesian$uproduct2'(sK32,X0)) | 'Ts13'(sK32), inference(demodulation, [status(thm)], [d28,d21])).
% 25.57/9.68 cnf(d30, plain, in(sK35(sK16(sK32,sK33)),sK16(sK32,X0)) | ~in(sK35(sK16(sK32,sK33)),'cartesian$uproduct2'(sK32,X0)) | 'Ts13'(sK32), inference(demodulation, [status(thm)], [d29,d20])).
% 25.57/9.68 cnf(d31, plain, in(sK35(sK16(sK32,sK33)),sK16(sK32,sK33)) | 'Ts13'(sK32), inference(resolution, [status(thm)], [d30,d19])).
% 25.57/9.68 cnf(d32, plain, 'Ts13'(sK32) | ~'Ts31'(X0,X1,sK16(sK32,sK33),sK35(sK16(sK32,sK33))), inference(resolution, [status(thm)], [d31,c36])).
% 25.57/9.68 cnf(d33, plain, 'Ts13'(sK32), inference(resolution, [status(thm)], [d32,d18])).
% 25.57/9.68 cnf(d34, plain, sK25(sK32) = sK24(sK32), inference(resolution, [status(thm)], [d33,c32])).
% 25.57/9.68 cnf(d35, plain, sK26(sK32) = sK24(sK32), inference(resolution, [status(thm)], [d33,c31])).
% 25.57/9.68 cnf(d36, plain, sK26(sK32) = sK25(sK32), inference(demodulation, [status(thm)], [d35,d34])).
% 25.57/9.68 cnf(d37, plain, sK25(sK32) != sK25(sK32) | ~'Ts13'(sK32), inference(superposition, [status(thm)], [d36,c33])).
% 25.57/9.68 cnf(d38, plain, sK25(sK32) != sK25(sK32), inference(resolution, [status(thm)], [d33,d37])).
% 25.57/9.68 cnf(d39, plain, $false, inference(equality_resolution, [status(thm)], [d38])).
% 25.57/9.68 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------