%------------------------------------------------------------------------------ % File : LisaST---0.9 % Problem : SWC109+1 : TPTP v9.3.1. Released v2.4.0. % 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 08:54:18 AM UTC 2026 % Result : Theorem 17.00s 12.95s % Output : CNFRefutation 17.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : SWC109+1 : TPTP v9.3.1. Released v2.4.0. % 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p % 0.15/10.44 % Computer : n002.cluster.edu % 0.15/10.44 % Model : x86_64 x86_64 % 0.15/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/10.44 % Memory : 8046.5625MB % 0.15/10.44 % OS : Linux 6.8.0-71-generic % 0.15/10.44 % CPULimit : 300 % 0.15/10.44 % WCLimit : 300 % 0.15/10.44 % DateTime : Sat Sep 26 12:19:02 UTC 2026 % 0.15/10.45 % CPUTime : % 0.15/10.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p % 17.00/12.95 % SZS status Theorem for theBenchmark.p % 17.00/12.95 % SZS output start CNFRefutation for theBenchmark.p % 17.00/12.95 fof(ax4, axiom, ! [X0] : ((ssList(X0) => (singletonP(X0) <=> ? [X1] : ((ssItem(X1) & cons(X1,nil) = X0)))))). % 17.00/12.95 fof(ax7, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => (segmentP(X0,X1) <=> ? [X2] : ((ssList(X2) & ? [X3] : ((ssList(X3) & app(app(X2,X1),X3) = X0)))))))))). % 17.00/12.95 fof(ax15, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => (neq(X0,X1) <=> X0 != X1)))))). % 17.00/12.95 fof(ax17, axiom, ssList(nil)). % 17.00/12.95 fof(ax39, axiom, ~singletonP(nil)). % 17.00/12.95 fof(ax57, axiom, ! [X0] : ((ssList(X0) => segmentP(X0,nil)))). % 17.00/12.95 fof(ax58, axiom, ! [X0] : ((ssList(X0) => (segmentP(nil,X0) <=> nil = X0)))). % 17.00/12.95 fof(co1, conjecture, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => ! [X2] : ((ssList(X2) => ! [X3] : ((~ssList(X3) | (X1 != X3 | (X0 != X2 | ((! [X4] : ((ssItem(X4) => ! [X5] : ((ssList(X5) => ! [X6] : ((~ssList(X6) | (cons(X4,nil) != X2 | (app(app(X5,X2),X6) != X3 | (? [X7] : ((ssItem(X7) & (memberP(X5,X7) & lt(X4,X7)))) | ? [X8] : ((ssItem(X8) & (memberP(X6,X8) & lt(X8,X4))))))))))))) & (nil != X3 | nil != X2)) | ((nil != X1 | nil = X0) & (~neq(X1,nil) | (neq(X0,nil) & segmentP(X1,X0)))))))))))))))). % 17.00/12.95 fof(negated_conjecture, negated_conjecture, ~! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => ! [X2] : ((ssList(X2) => ! [X3] : ((~ssList(X3) | (X1 != X3 | (X0 != X2 | ((! [X4] : ((ssItem(X4) => ! [X5] : ((ssList(X5) => ! [X6] : ((~ssList(X6) | (cons(X4,nil) != X2 | (app(app(X5,X2),X6) != X3 | (? [X7] : ((ssItem(X7) & (memberP(X5,X7) & lt(X4,X7)))) | ? [X8] : ((ssItem(X8) & (memberP(X6,X8) & lt(X8,X4))))))))))))) & (nil != X3 | nil != X2)) | ((nil != X1 | nil = X0) & (~neq(X1,nil) | (neq(X0,nil) & segmentP(X1,X0))))))))))))))), inference(negate_conjecture, [status(cth)], [co1])). % 17.00/12.95 cnf(c11, plain, ~ssList(X0) | singletonP(X0) | ~ssItem(X1) | cons(X1,nil) != X0, inference(clausification, [status(esa)], [ax4])). % 17.00/12.95 cnf(c21, plain, segmentP(X0,X1) | ~ssList(X1) | app(app(X2,X1),X3) != X0 | ~ssList(X3) | ~ssList(X0) | ~ssList(X2), inference(clausification, [status(esa)], [ax7])). % 17.00/12.95 cnf(c95, plain, ~ssList(X0) | ~ssList(X1) | neq(X0,X1) | X0 = X1, inference(clausification, [status(esa)], [ax15])). % 17.00/12.95 cnf(c97, plain, ssList(nil), inference(clausification, [status(esa)], [ax17])). % 17.00/12.95 cnf(c128, plain, ~singletonP(nil), inference(clausification, [status(esa)], [ax39])). % 17.00/12.95 cnf(c150, plain, ~ssList(X0) | segmentP(X0,nil), inference(clausification, [status(esa)], [ax57])). % 17.00/12.95 cnf(c151, plain, ~ssList(X0) | ~segmentP(nil,X0) | nil = X0, inference(clausification, [status(esa)], [ax58])). % 17.00/12.95 cnf(c208, plain, ssList(sK254), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c209, plain, ssList(sK255), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c212, plain, sK255 = sK257, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c213, plain, sK254 = sK256, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c214, plain, ~X0(sK256,sK257) | nil = sK257, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c215, plain, ~X0(sK256,sK257) | nil = sK256, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c217, plain, nil = sK255 | ~neq(sK254,nil) | ~segmentP(sK255,sK254), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c218, plain, nil != sK254 | neq(sK255,nil), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c219, plain, nil != sK254 | ~neq(sK254,nil) | ~segmentP(sK255,sK254), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c220, plain, X0(X1,X2) | ssItem(sK258(X1,X2)), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c221, plain, X0(X1,X2) | ssList(sK259(X1,X2)), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c222, plain, X0(X1,X2) | ssList(sK260(X1,X2)), inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c223, plain, X0(X1,X2) | cons(sK258(X1,X2),nil) = X1, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(c224, plain, X0(X1,X2) | app(app(sK259(X1,X2),X1),sK260(X1,X2)) = X2, inference(clausification, [status(esa)], [negated_conjecture])). % 17.00/12.95 cnf(d0, plain, nil = sK254 | ~'Ts253'(sK256,sK257), inference(demodulation, [status(thm)], [c215,c213])). % 17.00/12.95 cnf(d1, plain, nil = sK254 | ~'Ts253'(sK254,sK257), inference(demodulation, [status(thm)], [d0,c213])). % 17.00/12.95 cnf(d2, plain, nil = sK254 | ~'Ts253'(sK254,sK255), inference(demodulation, [status(thm)], [d1,c212])). % 17.00/12.95 cnf(d3, plain, cons(sK258(sK254,sK255),nil) = sK254 | nil = sK254, inference(resolution, [status(thm)], [c223,d2])). % 17.00/12.95 cnf(d4, plain, sK254 != X0 | ~ssItem(sK258(sK254,sK255)) | ~ssList(X0) | singletonP(X0) | nil = sK254, inference(superposition, [status(thm)], [d3,c11])). % 17.00/12.95 cnf(d5, plain, nil = sK254 | ~ssItem(sK258(sK254,sK255)) | ~ssList(sK254) | singletonP(sK254), inference(equality_resolution, [status(thm)], [d4])). % 17.00/12.95 cnf(d6, plain, nil = sK254 | ~ssItem(sK258(sK254,sK255)) | singletonP(sK254), inference(resolution, [status(thm)], [c208,d5])). % 17.00/12.95 cnf(d7, plain, nil = sK254 | singletonP(sK254) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d6,c220])). % 17.00/12.95 cnf(d8, plain, nil = sK254 | singletonP(sK254) | nil = sK254, inference(resolution, [status(thm)], [d7,d2])). % 17.00/12.95 cnf(d9, plain, app(app(sK259(sK254,sK255),sK254),sK260(sK254,sK255)) = sK255 | nil = sK254, inference(resolution, [status(thm)], [c224,d2])). % 17.00/12.95 cnf(d10, plain, sK255 != X0 | ~ssList(X0) | ~ssList(sK260(sK254,sK255)) | ~ssList(sK254) | ~ssList(sK259(sK254,sK255)) | segmentP(X0,sK254) | nil = sK254, inference(superposition, [status(thm)], [d9,c21])). % 17.00/12.95 cnf(d11, plain, nil = sK254 | sK255 != X0 | ~ssList(X0) | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(X0,sK254), inference(resolution, [status(thm)], [c208,d10])). % 17.00/12.95 cnf(d12, plain, nil = sK254 | ~ssList(sK255) | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(sK255,sK254), inference(equality_resolution, [status(thm)], [d11])). % 17.00/12.95 cnf(d13, plain, nil = sK254 | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(sK255,sK254), inference(resolution, [status(thm)], [c209,d12])). % 17.00/12.95 cnf(d14, plain, nil = sK254 | ~ssList(sK259(sK254,sK255)) | segmentP(sK255,sK254) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d13,c222])). % 17.00/12.95 cnf(d15, plain, nil = sK254 | segmentP(sK255,sK254) | 'Ts253'(sK254,sK255) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d14,c221])). % 17.00/12.95 cnf(d16, plain, nil = sK254 | segmentP(sK255,sK254) | nil = sK254, inference(resolution, [status(thm)], [d15,d2])). % 17.00/12.95 cnf(d17, plain, nil = sK255 | ~'Ts253'(sK256,sK257), inference(demodulation, [status(thm)], [c214,c212])). % 17.00/12.95 cnf(d18, plain, nil = sK255 | ~'Ts253'(sK254,sK257), inference(demodulation, [status(thm)], [d17,c213])). % 17.00/12.95 cnf(d19, plain, nil = sK255 | ~'Ts253'(sK254,sK255), inference(demodulation, [status(thm)], [d18,c212])). % 17.00/12.95 cnf(d20, plain, app(app(sK259(sK254,sK255),sK254),sK260(sK254,sK255)) = sK255 | nil = sK255, inference(resolution, [status(thm)], [c224,d19])). % 17.00/12.95 cnf(d21, plain, sK255 != X0 | ~ssList(X0) | ~ssList(sK260(sK254,sK255)) | ~ssList(sK254) | ~ssList(sK259(sK254,sK255)) | segmentP(X0,sK254) | nil = sK255, inference(superposition, [status(thm)], [d20,c21])). % 17.00/12.95 cnf(d22, plain, nil = sK255 | sK255 != X0 | ~ssList(X0) | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(X0,sK254), inference(resolution, [status(thm)], [c208,d21])). % 17.00/12.95 cnf(d23, plain, nil = sK255 | ~ssList(sK255) | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(sK255,sK254), inference(equality_resolution, [status(thm)], [d22])). % 17.00/12.95 cnf(d24, plain, nil = sK255 | ~ssList(sK259(sK254,sK255)) | ~ssList(sK260(sK254,sK255)) | segmentP(sK255,sK254), inference(resolution, [status(thm)], [c209,d23])). % 17.00/12.95 cnf(d25, plain, nil = sK255 | ~ssList(sK259(sK254,sK255)) | segmentP(sK255,sK254) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d24,c222])). % 17.00/12.95 cnf(d26, plain, nil = sK255 | segmentP(sK255,sK254) | 'Ts253'(sK254,sK255) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d25,c221])). % 17.00/12.95 cnf(d27, plain, nil = sK255 | segmentP(sK255,sK254) | nil = sK255, inference(resolution, [status(thm)], [d26,d19])). % 17.00/12.95 cnf(d28, plain, nil = sK255 | nil = sK255 | ~neq(sK254,nil), inference(resolution, [status(thm)], [d27,c217])). % 17.00/12.95 cnf(d29, plain, sK254 = nil | ~ssList(nil) | ~ssList(sK254) | nil = sK255, inference(resolution, [status(thm)], [c95,d28])). % 17.00/12.95 cnf(d30, plain, nil = sK255 | sK254 = nil | ~ssList(nil), inference(resolution, [status(thm)], [c208,d29])). % 17.00/12.95 cnf(d31, plain, nil = sK255 | sK254 = nil, inference(resolution, [status(thm)], [c97,d30])). % 17.00/12.95 cnf(d32, plain, segmentP(nil,sK254) | nil = sK254 | sK254 = nil, inference(superposition, [status(thm)], [d31,d16])). % 17.00/12.95 cnf(d33, plain, nil = sK254 | ~ssList(sK254) | nil = sK254 | sK254 = nil, inference(resolution, [status(thm)], [c151,d32])). % 17.00/12.95 cnf(d34, plain, nil = sK254 | sK254 = nil, inference(resolution, [status(thm)], [c208,d33])). % 17.00/12.95 cnf(d35, plain, singletonP(nil) | nil = sK254 | nil = sK254, inference(superposition, [status(thm)], [d34,d8])). % 17.00/12.95 cnf(d36, plain, nil = sK254, inference(resolution, [status(thm)], [c128,d35])). % 17.00/12.95 cnf(d37, plain, cons(sK258(sK254,sK255),nil) = sK254 | nil = sK255, inference(resolution, [status(thm)], [c223,d19])). % 17.00/12.95 cnf(d38, plain, sK254 != X0 | ~ssItem(sK258(sK254,sK255)) | ~ssList(X0) | singletonP(X0) | nil = sK255, inference(superposition, [status(thm)], [d37,c11])). % 17.00/12.95 cnf(d39, plain, nil = sK255 | ~ssItem(sK258(sK254,sK255)) | ~ssList(sK254) | singletonP(sK254), inference(equality_resolution, [status(thm)], [d38])). % 17.00/12.95 cnf(d40, plain, nil = sK255 | ~ssItem(sK258(sK254,sK255)) | singletonP(sK254), inference(resolution, [status(thm)], [c208,d39])). % 17.00/12.95 cnf(d41, plain, nil = sK255 | singletonP(sK254) | 'Ts253'(sK254,sK255), inference(resolution, [status(thm)], [d40,c220])). % 17.00/12.95 cnf(d42, plain, nil = sK255 | singletonP(sK254) | nil = sK255, inference(resolution, [status(thm)], [d41,d19])). % 17.00/12.95 cnf(d43, plain, nil = sK255 | singletonP(nil), inference(demodulation, [status(thm)], [d42,d36])). % 17.00/12.95 cnf(d44, plain, nil = sK255, inference(resolution, [status(thm)], [c128,d43])). % 17.00/12.95 cnf(d45, plain, ~neq(sK254,nil) | ~segmentP(sK255,sK254), inference(resolution, [status(thm)], [d36,c219])). % 17.00/12.95 cnf(d46, plain, ~neq(nil,nil) | ~segmentP(sK255,sK254), inference(demodulation, [status(thm)], [d45,d36])). % 17.00/12.95 cnf(d47, plain, ~neq(nil,nil) | ~segmentP(nil,sK254), inference(demodulation, [status(thm)], [d46,d44])). % 17.00/12.95 cnf(d48, plain, ~neq(nil,nil) | ~segmentP(nil,nil), inference(demodulation, [status(thm)], [d47,d36])). % 17.00/12.95 cnf(d49, plain, neq(sK255,nil), inference(resolution, [status(thm)], [d36,c218])). % 17.00/12.95 cnf(d50, plain, neq(nil,nil), inference(demodulation, [status(thm)], [d49,d44])). % 17.00/12.95 cnf(d51, plain, ~segmentP(nil,nil), inference(resolution, [status(thm)], [d50,d48])). % 17.00/12.95 cnf(d52, plain, ~ssList(nil), inference(resolution, [status(thm)], [d51,c150])). % 17.00/12.95 cnf(d53, plain, $false, inference(resolution, [status(thm)], [c97,d52])). % 17.00/12.95 % SZS output end CNFRefutation for theBenchmark.p %------------------------------------------------------------------------------