%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET931+1 : 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 : n014.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 08:33:35 AM UTC 2026
% Result : Theorem 12.31s 3.39s
% Output : CNFRefutation 12.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:26:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.31/3.39 % SZS status Theorem for theBenchmark.p
% 12.31/3.39 % SZS output start CNFRefutation for theBenchmark.p
% 12.31/3.39 fof(l46_zfmisc_1, axiom, ! [X0] : ! [X1] : ! [X2] : ((subset(X0,'unordered$upair'(X1,X2)) <=> ~((X0 != 'empty$uset' & (X0 != singleton(X1) & (X0 != singleton(X2) & X0 != 'unordered$upair'(X1,X2)))))))).
% 12.31/3.39 fof(reflexivity_r1_tarski, axiom, ! [X0] : ! [X1] : subset(X0,X0)).
% 12.31/3.39 fof(t37_xboole_1, axiom, ! [X0] : ! [X1] : (('set$udifference'(X0,X1) = 'empty$uset' <=> subset(X0,X1)))).
% 12.31/3.39 fof(t75_zfmisc_1, conjecture, ! [X0] : ! [X1] : ! [X2] : (('set$udifference'(X0,'unordered$upair'(X1,X2)) = 'empty$uset' <=> ~((X0 != 'empty$uset' & (X0 != singleton(X1) & (X0 != singleton(X2) & X0 != 'unordered$upair'(X1,X2)))))))).
% 12.31/3.39 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ! [X2] : (('set$udifference'(X0,'unordered$upair'(X1,X2)) = 'empty$uset' <=> ~((X0 != 'empty$uset' & (X0 != singleton(X1) & (X0 != singleton(X2) & X0 != 'unordered$upair'(X1,X2))))))), inference(negate_conjecture, [status(cth)], [t75_zfmisc_1])).
% 12.31/3.39 cnf(c2, plain, ~subset(X0,'unordered$upair'(X1,X2)) | X3(X0,X1,X2), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c3, plain, subset(X0,'unordered$upair'(X1,X2)) | ~X3(X0,X1,X2), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c4, plain, X0 = singleton(X1) | X0 = 'unordered$upair'(X2,X1) | ~X3(X0,X2,X1) | X0 = 'empty$uset' | X0 = singleton(X2), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c5, plain, X0(X1,X2,X3) | X1 != 'empty$uset', inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c6, plain, X0(X1,X2,X3) | X1 != singleton(X2), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c7, plain, X0(X1,X2,X3) | X1 != singleton(X3), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c8, plain, X0(X1,X2,X3) | X1 != 'unordered$upair'(X2,X3), inference(clausification, [status(esa)], [l46_zfmisc_1])).
% 12.31/3.39 cnf(c11, plain, subset(X0,X0), inference(clausification, [status(esa)], [reflexivity_r1_tarski])).
% 12.31/3.39 cnf(c12, plain, 'set$udifference'(X0,X1) != 'empty$uset' | subset(X0,X1), inference(clausification, [status(esa)], [t37_xboole_1])).
% 12.31/3.39 cnf(c13, plain, 'set$udifference'(X0,X1) = 'empty$uset' | ~subset(X0,X1), inference(clausification, [status(esa)], [t37_xboole_1])).
% 12.31/3.39 cnf(c15, plain, 'set$udifference'(sK13,'unordered$upair'(sK14,sK15)) = 'empty$uset' | X0(sK13,sK14,sK15), inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c16, plain, ~X0(sK13,sK14,sK15) | 'set$udifference'(sK13,'unordered$upair'(sK14,sK15)) != 'empty$uset', inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c18, plain, X0 = singleton(X1) | X0 = 'unordered$upair'(X2,X1) | X0 = singleton(X2) | ~X3(X0,X2,X1) | X0 = 'empty$uset', inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c19, plain, X0(X1,X2,X3) | X1 != 'empty$uset', inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c20, plain, X0(X1,X2,X3) | X1 != singleton(X2), inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c21, plain, X0(X1,X2,X3) | X1 != singleton(X3), inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(c22, plain, X0(X1,X2,X3) | X1 != 'unordered$upair'(X2,X3), inference(clausification, [status(esa)], [negated_conjecture])).
% 12.31/3.39 cnf(d0, plain, 'Ts2'('empty$uset',X0,X1), inference(equality_resolution, [status(thm)], [c5])).
% 12.31/3.39 cnf(d1, plain, 'set$udifference'(X0,'unordered$upair'(X1,X2)) = 'empty$uset' | ~'Ts2'(X0,X1,X2), inference(resolution, [status(thm)], [c13,c3])).
% 12.31/3.39 cnf(d2, plain, 'set$udifference'('empty$uset','unordered$upair'(X0,X1)) = 'empty$uset', inference(resolution, [status(thm)], [d1,d0])).
% 12.31/3.39 cnf(d3, plain, 'Ts12'(singleton(X0),X0,X1), inference(equality_resolution, [status(thm)], [c20])).
% 12.31/3.39 cnf(d4, plain, 'Ts12'(singleton(X0),X1,X0), inference(equality_resolution, [status(thm)], [c21])).
% 12.31/3.39 cnf(d5, plain, 'Ts12'('unordered$upair'(X0,X1),X0,X1), inference(equality_resolution, [status(thm)], [c22])).
% 12.31/3.39 cnf(d6, plain, sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK15) | sK13 = singleton(sK14) | 'set$udifference'(sK13,'unordered$upair'(sK14,sK15)) = 'empty$uset', inference(resolution, [status(thm)], [c18,c15])).
% 12.31/3.39 cnf(d7, plain, 'empty$uset' != 'empty$uset' | subset(sK13,'unordered$upair'(sK14,sK15)) | sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15), inference(superposition, [status(thm)], [d6,c12])).
% 12.31/3.39 cnf(d8, plain, sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | subset(sK13,'unordered$upair'(sK14,sK15)), inference(equality_resolution, [status(thm)], [d7])).
% 12.31/3.39 cnf(d9, plain, sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | 'Ts2'(sK13,sK14,sK15), inference(resolution, [status(thm)], [d8,c2])).
% 12.31/3.39 cnf(d10, plain, sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | sK13 = 'unordered$upair'(sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK15) | sK13 = singleton(sK14), inference(resolution, [status(thm)], [d9,c4])).
% 12.31/3.39 cnf(d11, plain, 'Ts12'(sK13,sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15), inference(superposition, [status(thm)], [d10,d5])).
% 12.31/3.39 cnf(d12, plain, 'set$udifference'(X0,X0) = 'empty$uset', inference(resolution, [status(thm)], [c13,c11])).
% 12.31/3.39 cnf(d13, plain, 'set$udifference'(sK13,sK13) != 'empty$uset' | ~'Ts12'(sK13,sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15), inference(superposition, [status(thm)], [d10,c16])).
% 12.31/3.39 cnf(d14, plain, 'empty$uset' != 'empty$uset' | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | ~'Ts12'(sK13,sK14,sK15), inference(demodulation, [status(thm)], [d13,d12])).
% 12.31/3.39 cnf(d15, plain, sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | ~'Ts12'(sK13,sK14,sK15), inference(equality_resolution, [status(thm)], [d14])).
% 12.31/3.39 cnf(d16, plain, sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = singleton(sK15), inference(resolution, [status(thm)], [d15,d11])).
% 12.31/3.39 cnf(d17, plain, 'Ts12'(sK13,X0,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14), inference(superposition, [status(thm)], [d16,d4])).
% 12.31/3.39 cnf(d18, plain, 'Ts2'(singleton(X0),X1,X0), inference(equality_resolution, [status(thm)], [c7])).
% 12.31/3.39 cnf(d19, plain, 'Ts2'(sK13,X0,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14), inference(superposition, [status(thm)], [d16,d18])).
% 12.31/3.39 cnf(d20, plain, sK13 = 'empty$uset' | sK13 = singleton(sK14) | 'set$udifference'(sK13,'unordered$upair'(X0,sK15)) = 'empty$uset', inference(resolution, [status(thm)], [d19,d1])).
% 12.31/3.39 cnf(d21, plain, 'empty$uset' != 'empty$uset' | ~'Ts12'(sK13,sK14,sK15) | sK13 = 'empty$uset' | sK13 = singleton(sK14), inference(superposition, [status(thm)], [d20,c16])).
% 12.31/3.39 cnf(d22, plain, 'Ts2'('unordered$upair'(X0,X1),X0,X1), inference(equality_resolution, [status(thm)], [c8])).
% 12.31/3.39 cnf(d23, plain, 'set$udifference'('unordered$upair'(X0,X1),'unordered$upair'(X0,X1)) = 'empty$uset', inference(resolution, [status(thm)], [d1,d22])).
% 12.31/3.39 cnf(d24, plain, 'empty$uset' = 'empty$uset', inference(demodulation, [status(thm)], [d23,d12])).
% 12.31/3.39 cnf(d25, plain, sK13 = 'empty$uset' | sK13 = singleton(sK14) | ~'Ts12'(sK13,sK14,sK15), inference(resolution, [status(thm)], [d24,d21])).
% 12.31/3.39 cnf(d26, plain, sK13 = 'empty$uset' | sK13 = singleton(sK14) | sK13 = 'empty$uset' | sK13 = singleton(sK14), inference(resolution, [status(thm)], [d25,d17])).
% 12.31/3.39 cnf(d27, plain, 'Ts12'(sK13,sK14,X0) | sK13 = 'empty$uset', inference(superposition, [status(thm)], [d26,d3])).
% 12.31/3.39 cnf(d28, plain, 'Ts2'(singleton(X0),X0,X1), inference(equality_resolution, [status(thm)], [c6])).
% 12.31/3.39 cnf(d29, plain, 'set$udifference'(singleton(X0),'unordered$upair'(X0,X1)) = 'empty$uset', inference(resolution, [status(thm)], [d1,d28])).
% 12.31/3.39 cnf(d30, plain, 'set$udifference'(sK13,'unordered$upair'(sK14,X0)) = 'empty$uset' | sK13 = 'empty$uset', inference(superposition, [status(thm)], [d26,d29])).
% 12.31/3.39 cnf(d31, plain, 'empty$uset' != 'empty$uset' | ~'Ts12'(sK13,sK14,sK15) | sK13 = 'empty$uset', inference(superposition, [status(thm)], [d30,c16])).
% 12.31/3.39 cnf(d32, plain, sK13 = 'empty$uset' | ~'Ts12'(sK13,sK14,sK15), inference(resolution, [status(thm)], [d24,d31])).
% 12.31/3.39 cnf(d33, plain, sK13 = 'empty$uset' | sK13 = 'empty$uset', inference(resolution, [status(thm)], [d32,d27])).
% 12.31/3.39 cnf(d34, plain, 'set$udifference'('empty$uset','unordered$upair'(sK14,sK15)) != 'empty$uset' | ~'Ts12'(sK13,sK14,sK15), inference(demodulation, [status(thm)], [c16,d33])).
% 12.31/3.39 cnf(d35, plain, 'set$udifference'('empty$uset','unordered$upair'(sK14,sK15)) != 'empty$uset' | ~'Ts12'('empty$uset',sK14,sK15), inference(demodulation, [status(thm)], [d34,d33])).
% 12.31/3.39 cnf(d36, plain, 'empty$uset' != 'empty$uset' | ~'Ts12'('empty$uset',sK14,sK15), inference(demodulation, [status(thm)], [d35,d2])).
% 12.31/3.39 cnf(d37, plain, 'Ts12'('empty$uset',X0,X1), inference(equality_resolution, [status(thm)], [c19])).
% 12.31/3.39 cnf(d38, plain, 'empty$uset' != 'empty$uset', inference(resolution, [status(thm)], [d37,d36])).
% 12.31/3.39 cnf(d39, plain, $false, inference(resolution, [status(thm)], [d24,d38])).
% 12.31/3.39 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------