%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU156+2 : 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 : n005.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 08:41:04 AM UTC 2026
% Result : Theorem 81.81s 35.24s
% Output : CNFRefutation 81.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU156+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n005.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 08:41:52 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.81/35.24 % SZS status Theorem for theBenchmark.p
% 81.81/35.24 % SZS output start CNFRefutation for theBenchmark.p
% 81.81/35.24 fof(commutativity_k2_tarski, axiom, ! [X0] : ! [X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0)).
% 81.81/35.24 fof(commutativity_k2_xboole_0, axiom, ! [X0] : ! [X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0)).
% 81.81/35.24 fof(d10_xboole_0, axiom, ! [X0] : ! [X1] : ((X0 = X1 <=> (subset(X0,X1) & subset(X1,X0))))).
% 81.81/35.24 fof(d1_tarski, axiom, ! [X0] : ! [X1] : ((X1 = singleton(X0) <=> ! [X2] : ((in(X2,X1) <=> X2 = X0))))).
% 81.81/35.24 fof(d2_tarski, axiom, ! [X0] : ! [X1] : ! [X2] : ((X2 = 'unordered$upair'(X0,X1) <=> ! [X3] : ((in(X3,X2) <=> (X3 = X0 | X3 = X1)))))).
% 81.81/35.24 fof(d5_tarski, axiom, ! [X0] : ! [X1] : 'ordered$upair'(X0,X1) = 'unordered$upair'('unordered$upair'(X0,X1),singleton(X0))).
% 81.81/35.24 fof(idempotence_k2_xboole_0, axiom, ! [X0] : ! [X1] : 'set$uunion2'(X0,X0) = X0).
% 81.81/35.24 fof(l25_zfmisc_1, lemma, ! [X0] : ! [X1] : ~((disjoint(singleton(X0),X1) & in(X0,X1)))).
% 81.81/35.24 fof(l28_zfmisc_1, lemma, ! [X0] : ! [X1] : ((~in(X0,X1) => disjoint(singleton(X0),X1)))).
% 81.81/35.24 fof(l2_zfmisc_1, lemma, ! [X0] : ! [X1] : ((subset(singleton(X0),X1) <=> in(X0,X1)))).
% 81.81/35.24 fof(reflexivity_r1_tarski, axiom, ! [X0] : ! [X1] : subset(X0,X0)).
% 81.81/35.24 fof(symmetry_r1_xboole_0, axiom, ! [X0] : ! [X1] : ((disjoint(X0,X1) => disjoint(X1,X0)))).
% 81.81/35.24 fof(t69_enumset1, lemma, ! [X0] : 'unordered$upair'(X0,X0) = singleton(X0)).
% 81.81/35.24 fof(t7_xboole_1, lemma, ! [X0] : ! [X1] : subset(X0,'set$uunion2'(X0,X1))).
% 81.81/35.24 fof(t9_zfmisc_1, lemma, ! [X0] : ! [X1] : ! [X2] : ((singleton(X0) = 'unordered$upair'(X1,X2) => X1 = X2))).
% 81.81/35.24 fof(t33_zfmisc_1, conjecture, ! [X0] : ! [X1] : ! [X2] : ! [X3] : (('ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3) => (X0 = X2 & X1 = X3)))).
% 81.81/35.24 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ! [X2] : ! [X3] : (('ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3) => (X0 = X2 & X1 = X3))), inference(negate_conjecture, [status(cth)], [t33_zfmisc_1])).
% 81.81/35.24 cnf(c2, plain, 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0), inference(clausification, [status(esa)], [commutativity_k2_tarski])).
% 81.81/35.24 cnf(c3, plain, 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0), inference(clausification, [status(esa)], [commutativity_k2_xboole_0])).
% 81.81/35.24 cnf(c7, plain, X0 = X1 | ~subset(X0,X1) | ~subset(X1,X0), inference(clausification, [status(esa)], [d10_xboole_0])).
% 81.81/35.24 cnf(c8, plain, X0 != singleton(X1) | ~in(X2,X0) | X2 = X1, inference(clausification, [status(esa)], [d1_tarski])).
% 81.81/35.24 cnf(c22, plain, X0 != 'unordered$upair'(X1,X2) | X3(X1,X2,X0), inference(clausification, [status(esa)], [d2_tarski])).
% 81.81/35.24 cnf(c23, plain, X0 = 'unordered$upair'(X1,X2) | ~X3(X1,X2,X0), inference(clausification, [status(esa)], [d2_tarski])).
% 81.81/35.24 cnf(c24, plain, ~X0(X1,X2,X3) | ~in(X4,X3) | X4 = X1 | X4 = X2, inference(clausification, [status(esa)], [d2_tarski])).
% 81.81/35.24 cnf(c25, plain, ~X0(X1,X2,X3) | in(X4,X3) | X4 != X1, inference(clausification, [status(esa)], [d2_tarski])).
% 81.81/35.24 cnf(c80, plain, 'ordered$upair'(X0,X1) = 'unordered$upair'('unordered$upair'(X0,X1),singleton(X0)), inference(clausification, [status(esa)], [d5_tarski])).
% 81.81/35.24 cnf(c90, plain, 'set$uunion2'(X0,X0) = X0, inference(clausification, [status(esa)], [idempotence_k2_xboole_0])).
% 81.81/35.24 cnf(c95, plain, ~disjoint(singleton(X0),X1) | ~in(X0,X1), inference(clausification, [status(esa)], [l25_zfmisc_1])).
% 81.81/35.24 cnf(c96, plain, in(X0,X1) | disjoint(singleton(X0),X1), inference(clausification, [status(esa)], [l28_zfmisc_1])).
% 81.81/35.24 cnf(c97, plain, ~subset(singleton(X0),X1) | in(X0,X1), inference(clausification, [status(esa)], [l2_zfmisc_1])).
% 81.81/35.24 cnf(c108, plain, subset(X0,X0), inference(clausification, [status(esa)], [reflexivity_r1_tarski])).
% 81.81/35.24 cnf(c109, plain, ~disjoint(X0,X1) | disjoint(X1,X0), inference(clausification, [status(esa)], [symmetry_r1_xboole_0])).
% 81.81/35.24 cnf(c143, plain, 'unordered$upair'(X0,X0) = singleton(X0), inference(clausification, [status(esa)], [t69_enumset1])).
% 81.81/35.24 cnf(c147, plain, subset(X0,'set$uunion2'(X0,X1)), inference(clausification, [status(esa)], [t7_xboole_1])).
% 81.81/35.24 cnf(c153, plain, singleton(X0) != 'unordered$upair'(X1,X2) | X1 = X2, inference(clausification, [status(esa)], [t9_zfmisc_1])).
% 81.81/35.24 cnf(c154, plain, 'ordered$upair'(sK179,sK180) = 'ordered$upair'(sK181,sK182), inference(clausification, [status(esa)], [negated_conjecture])).
% 81.81/35.24 cnf(c155, plain, sK179 != sK181 | sK180 != sK182, inference(clausification, [status(esa)], [negated_conjecture])).
% 81.81/35.24 cnf(d0, plain, X0 = X1 | ~in(X0,singleton(X1)), inference(equality_resolution, [status(thm)], [c8])).
% 81.81/35.24 cnf(d1, plain, 'Ts23'(X0,X1,'unordered$upair'(X0,X1)), inference(equality_resolution, [status(thm)], [c22])).
% 81.81/35.24 cnf(d2, plain, 'Ts23'(X0,X1,'unordered$upair'(X1,X0)), inference(superposition, [status(thm)], [c2,d1])).
% 81.81/35.24 cnf(d3, plain, in(X0,X1) | ~'Ts23'(X0,X2,X1), inference(equality_resolution, [status(thm)], [c25])).
% 81.81/35.24 cnf(d4, plain, in(X0,'unordered$upair'(X1,X0)), inference(resolution, [status(thm)], [d3,d2])).
% 81.81/35.24 cnf(d5, plain, 'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)), inference(demodulation, [status(thm)], [c80,c2])).
% 81.81/35.24 cnf(d6, plain, singleton(X0) = 'unordered$upair'(X0,X0), inference(superposition, [status(thm)], [c143,c2])).
% 81.81/35.24 cnf(d7, plain, 'ordered$upair'(X0,X0) = 'unordered$upair'(singleton(X0),singleton(X0)), inference(superposition, [status(thm)], [d6,d5])).
% 81.81/35.24 cnf(d8, plain, 'ordered$upair'(X0,X0) = singleton(singleton(X0)), inference(demodulation, [status(thm)], [d7,c143])).
% 81.81/35.24 cnf(d9, plain, X0 = X1 | X0 = X2 | ~in(X0,'unordered$upair'(X2,X1)), inference(resolution, [status(thm)], [c24,d1])).
% 81.81/35.24 cnf(d10, plain, in(X0,X1) | disjoint(X1,singleton(X0)), inference(resolution, [status(thm)], [c96,c109])).
% 81.81/35.24 cnf(d11, plain, in(X0,singleton(X1)) | ~in(X1,singleton(X0)), inference(resolution, [status(thm)], [d10,c95])).
% 81.81/35.24 cnf(d12, plain, in(X0,singleton(X0)), inference(resolution, [status(thm)], [c97,c108])).
% 81.81/35.24 cnf(d13, plain, in(X0,'unordered$upair'(X0,X1)), inference(resolution, [status(thm)], [d3,d1])).
% 81.81/35.24 cnf(d14, plain, in(singleton(X0),'ordered$upair'(X0,X1)), inference(superposition, [status(thm)], [d5,d13])).
% 81.81/35.24 cnf(d15, plain, in(singleton(sK181),'ordered$upair'(sK179,sK180)), inference(superposition, [status(thm)], [c154,d14])).
% 81.81/35.24 cnf(d16, plain, ~in(X2,'ordered$upair'(X0,X1)) | X2 = singleton(X0) | X2 = 'unordered$upair'(X0,X1), inference(superposition, [status(thm)], [d5,d9])).
% 81.81/35.24 cnf(d17, plain, singleton(sK181) = 'unordered$upair'(sK179,sK180) | singleton(sK181) = singleton(sK179), inference(resolution, [status(thm)], [d16,d15])).
% 81.81/35.24 cnf(d18, plain, in(sK179,singleton(sK181)) | singleton(sK181) = singleton(sK179), inference(superposition, [status(thm)], [d17,d13])).
% 81.81/35.24 cnf(d19, plain, in(sK181,singleton(sK179)) | in(sK179,singleton(sK181)), inference(superposition, [status(thm)], [d18,d12])).
% 81.81/35.24 cnf(d20, plain, in(sK179,singleton(sK181)) | in(sK179,singleton(sK181)), inference(resolution, [status(thm)], [d19,d11])).
% 81.81/35.24 cnf(d21, plain, sK179 = sK181, inference(resolution, [status(thm)], [d20,d0])).
% 81.81/35.24 cnf(d22, plain, singleton(X2) != 'unordered$upair'(X1,X0) | X0 = X1, inference(superposition, [status(thm)], [c2,c153])).
% 81.81/35.24 cnf(d23, plain, in('unordered$upair'(X0,X1),'ordered$upair'(X0,X1)), inference(superposition, [status(thm)], [d5,d4])).
% 81.81/35.24 cnf(d24, plain, singleton(X0) = X1 | ~'Ts23'(X0,X0,X1), inference(superposition, [status(thm)], [c23,d6])).
% 81.81/35.24 cnf(d25, plain, 'Ts23'(singleton(X0),'unordered$upair'(X0,X1),'ordered$upair'(X0,X1)), inference(superposition, [status(thm)], [d5,d1])).
% 81.81/35.24 cnf(d26, plain, 'Ts23'(singleton(sK181),'unordered$upair'(sK181,sK182),'ordered$upair'(sK179,sK180)), inference(superposition, [status(thm)], [c154,d25])).
% 81.81/35.24 cnf(d27, plain, 'Ts23'(singleton(sK181),X0,'ordered$upair'(sK179,sK180)) | ~'Ts23'(sK181,sK182,X0), inference(superposition, [status(thm)], [c23,d26])).
% 81.81/35.24 cnf(d28, plain, ~'Ts23'(sK181,sK182,singleton(sK181)) | singleton(singleton(sK181)) = 'ordered$upair'(sK179,sK180), inference(resolution, [status(thm)], [d27,d24])).
% 81.81/35.24 cnf(d29, plain, in('unordered$upair'(sK179,sK180),singleton(singleton(sK181))) | ~'Ts23'(sK181,sK182,singleton(sK181)), inference(superposition, [status(thm)], [d28,d23])).
% 81.81/35.24 cnf(d30, plain, ~'Ts23'(sK181,sK182,singleton(sK181)) | in(singleton(sK181),singleton('unordered$upair'(sK179,sK180))), inference(resolution, [status(thm)], [d29,d11])).
% 81.81/35.24 cnf(d31, plain, ~'Ts23'(sK181,sK182,singleton(sK181)) | singleton(sK181) = 'unordered$upair'(sK179,sK180), inference(resolution, [status(thm)], [d30,d0])).
% 81.81/35.24 cnf(d32, plain, singleton(X0) != singleton(sK181) | sK180 = sK179 | ~'Ts23'(sK181,sK182,singleton(sK181)), inference(superposition, [status(thm)], [d31,d22])).
% 81.81/35.24 cnf(d33, plain, singleton(X0) != singleton(sK179) | sK180 = sK179 | ~'Ts23'(sK181,sK182,singleton(sK181)), inference(demodulation, [status(thm)], [d32,d21])).
% 81.81/35.24 cnf(d34, plain, singleton(X0) != singleton(sK179) | sK180 = sK179 | ~'Ts23'(sK179,sK182,singleton(sK181)), inference(demodulation, [status(thm)], [d33,d21])).
% 81.81/35.24 cnf(d35, plain, singleton(X0) != singleton(sK179) | sK180 = sK179 | ~'Ts23'(sK179,sK182,singleton(sK179)), inference(demodulation, [status(thm)], [d34,d21])).
% 81.81/35.24 cnf(d36, plain, sK180 = sK179 | ~'Ts23'(sK179,sK182,singleton(sK179)), inference(equality_resolution, [status(thm)], [d35])).
% 81.81/35.24 cnf(d37, plain, in('unordered$upair'(sK181,sK182),'ordered$upair'(sK179,sK180)), inference(superposition, [status(thm)], [c154,d23])).
% 81.81/35.24 cnf(d38, plain, X2 = 'unordered$upair'(X1,X0) | ~'Ts23'(X0,X1,X2), inference(superposition, [status(thm)], [c23,c2])).
% 81.81/35.24 cnf(d39, plain, in(X0,'ordered$upair'(sK179,sK180)) | ~'Ts23'(sK182,sK181,X0), inference(superposition, [status(thm)], [d38,d37])).
% 81.81/35.24 cnf(d40, plain, X0 = 'unordered$upair'(sK179,sK180) | X0 = singleton(sK179) | ~'Ts23'(sK182,sK181,X0), inference(resolution, [status(thm)], [d16,d39])).
% 81.81/35.24 cnf(d41, plain, X0 = 'unordered$upair'(sK179,sK180) | X0 = singleton(sK179) | ~'Ts23'(sK182,sK179,X0), inference(demodulation, [status(thm)], [d40,d21])).
% 81.81/35.24 cnf(d42, plain, in(sK180,X0) | X0 = singleton(sK179) | ~'Ts23'(sK182,sK179,X0), inference(superposition, [status(thm)], [d41,d4])).
% 81.81/35.24 cnf(d43, plain, 'unordered$upair'(sK182,sK179) = singleton(sK179) | in(sK180,'unordered$upair'(sK182,sK179)), inference(resolution, [status(thm)], [d42,d1])).
% 81.81/35.24 cnf(d44, plain, 'unordered$upair'(sK179,sK182) = singleton(sK179) | in(sK180,'unordered$upair'(sK182,sK179)), inference(demodulation, [status(thm)], [d43,c2])).
% 81.81/35.24 cnf(d45, plain, 'unordered$upair'(sK179,sK182) = singleton(sK179) | in(sK180,'unordered$upair'(sK179,sK182)), inference(demodulation, [status(thm)], [d44,c2])).
% 81.81/35.24 cnf(d46, plain, 'Ts23'(sK179,sK182,singleton(sK179)) | in(sK180,'unordered$upair'(sK179,sK182)), inference(superposition, [status(thm)], [d45,d1])).
% 81.81/35.24 cnf(d47, plain, in(sK180,'unordered$upair'(sK179,sK182)) | sK180 = sK179, inference(resolution, [status(thm)], [d46,d36])).
% 81.81/35.24 cnf(d48, plain, sK180 = sK179 | sK180 = sK179 | sK180 = sK182, inference(resolution, [status(thm)], [d47,d9])).
% 81.81/35.24 cnf(d49, plain, sK180 != sK182, inference(resolution, [status(thm)], [d21,c155])).
% 81.81/35.24 cnf(d50, plain, sK180 = sK179, inference(resolution, [status(thm)], [d49,d48])).
% 81.81/35.24 cnf(d51, plain, in('unordered$upair'(sK179,sK182),'ordered$upair'(sK179,sK180)), inference(demodulation, [status(thm)], [d37,d21])).
% 81.81/35.24 cnf(d52, plain, in('unordered$upair'(sK179,sK182),'ordered$upair'(sK179,sK179)), inference(demodulation, [status(thm)], [d51,d50])).
% 81.81/35.24 cnf(d53, plain, in('unordered$upair'(sK179,sK182),singleton(singleton(sK179))), inference(demodulation, [status(thm)], [d52,d8])).
% 81.81/35.24 cnf(d54, plain, 'unordered$upair'(sK179,sK182) = singleton(sK179), inference(resolution, [status(thm)], [d53,d0])).
% 81.81/35.24 cnf(d55, plain, in(sK182,singleton(sK179)), inference(superposition, [status(thm)], [d54,d4])).
% 81.81/35.24 cnf(d56, plain, sK182 = sK179, inference(resolution, [status(thm)], [d55,d0])).
% 81.81/35.24 cnf(d57, plain, sK179 != sK182, inference(demodulation, [status(thm)], [d49,d50])).
% 81.81/35.24 cnf(d58, plain, sK179 != sK179, inference(demodulation, [status(thm)], [d57,d56])).
% 81.81/35.24 cnf(d59, plain, subset(X0,'set$uunion2'(X1,X0)), inference(superposition, [status(thm)], [c3,c147])).
% 81.81/35.24 cnf(d60, plain, 'set$uunion2'(X0,X1) = X1 | ~subset('set$uunion2'(X0,X1),X1), inference(resolution, [status(thm)], [c7,d59])).
% 81.81/35.24 cnf(d61, plain, X0 = 'set$uunion2'(X0,X0), inference(superposition, [status(thm)], [c90,c3])).
% 81.81/35.24 cnf(d62, plain, ~subset(X0,X0) | 'set$uunion2'(X0,X0) = X0, inference(superposition, [status(thm)], [d61,d60])).
% 81.81/35.24 cnf(d63, plain, X0 = X0 | ~subset(X0,X0), inference(demodulation, [status(thm)], [d62,c90])).
% 81.81/35.24 cnf(d64, plain, X0 = X0, inference(resolution, [status(thm)], [c108,d63])).
% 81.81/35.24 cnf(d65, plain, $false, inference(resolution, [status(thm)], [d64,d58])).
% 81.81/35.24 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------