%------------------------------------------------------------------------------ % File : LisaST---0.9 % Problem : SWC416+1 : TPTP v9.3.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % Computer : n026.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 08:55:19 AM UTC 2026 % Result : Theorem 60.23s 10.44s % Output : CNFRefutation 60.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : SWC416+1 : TPTP v9.3.1. Released v2.4.0. % 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.09/0.37 % Computer : n026.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 26 13:03:13 UTC 2026 % 0.09/0.38 % CPUTime : % 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 60.23/10.44 % SZS status Theorem for theBenchmark.p % 60.23/10.44 % SZS output start CNFRefutation for theBenchmark.p % 60.23/10.44 fof(ax5, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => (frontsegP(X0,X1) <=> ? [X2] : ((ssList(X2) & app(X1,X2) = X0)))))))). % 60.23/10.44 fof(ax15, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => (neq(X0,X1) <=> X0 != X1)))))). % 60.23/10.44 fof(ax16, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssItem(X1) => ssList(cons(X1,X0))))))). % 60.23/10.44 fof(ax17, axiom, ssList(nil)). % 60.23/10.44 fof(ax21, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssItem(X1) => nil != cons(X1,X0)))))). % 60.23/10.44 fof(ax23, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssItem(X1) => hd(cons(X1,X0)) = X1))))). % 60.23/10.44 fof(ax28, axiom, ! [X0] : ((ssList(X0) => app(nil,X0) = X0))). % 60.23/10.44 fof(ax42, axiom, ! [X0] : ((ssList(X0) => frontsegP(X0,X0)))). % 60.23/10.44 fof(ax43, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => ! [X2] : ((ssList(X2) => (frontsegP(X0,X1) => frontsegP(app(X0,X2),X1))))))))). % 60.23/10.44 fof(ax45, axiom, ! [X0] : ((ssList(X0) => frontsegP(X0,nil)))). % 60.23/10.44 fof(ax81, axiom, ! [X0] : ((ssList(X0) => ! [X1] : ((ssItem(X1) => cons(X1,X0) = app(cons(X1,nil),X0)))))). % 60.23/10.44 fof(co1, conjecture, ! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => ! [X2] : ((ssList(X2) => ! [X3] : ((ssList(X3) => (X1 != X3 | (X0 != X2 | ((~neq(X1,nil) | (? [X4] : ((ssList(X4) & (X1 = X4 & ? [X5] : ((ssList(X5) & (app(X5,X0) = X4 & ? [X6] : ((ssItem(X6) & (cons(X6,nil) = X5 & (hd(X1) = X6 & neq(nil,X1))))))))))) | ! [X7] : ((ssItem(X7) => app(cons(X7,nil),X2) != X3)))) & (~neq(X1,nil) | neq(X3,nil)))))))))))))). % 60.23/10.44 fof(negated_conjecture, negated_conjecture, ~! [X0] : ((ssList(X0) => ! [X1] : ((ssList(X1) => ! [X2] : ((ssList(X2) => ! [X3] : ((ssList(X3) => (X1 != X3 | (X0 != X2 | ((~neq(X1,nil) | (? [X4] : ((ssList(X4) & (X1 = X4 & ? [X5] : ((ssList(X5) & (app(X5,X0) = X4 & ? [X6] : ((ssItem(X6) & (cons(X6,nil) = X5 & (hd(X1) = X6 & neq(nil,X1))))))))))) | ! [X7] : ((ssItem(X7) => app(cons(X7,nil),X2) != X3)))) & (~neq(X1,nil) | neq(X3,nil))))))))))))), inference(negate_conjecture, [status(cth)], [co1])). % 60.23/10.44 cnf(c13, plain, ~ssList(X0) | ~ssList(X1) | ~frontsegP(X0,X1) | app(X1,sK15(X0,X1)) = X0, inference(clausification, [status(esa)], [ax5])). % 60.23/10.44 cnf(c88, plain, ~ssList(X0) | ~ssList(X1) | neq(X0,X1) | X1 = X0, inference(clausification, [status(esa)], [ax15])). % 60.23/10.44 cnf(c89, plain, ~ssList(X0) | ~ssItem(X1) | ssList(cons(X1,X0)), inference(clausification, [status(esa)], [ax16])). % 60.23/10.44 cnf(c90, plain, ssList(nil), inference(clausification, [status(esa)], [ax17])). % 60.23/10.44 cnf(c97, plain, ~ssList(X0) | ~ssItem(X1) | cons(X1,X0) != nil, inference(clausification, [status(esa)], [ax21])). % 60.23/10.44 cnf(c99, plain, ~ssList(X0) | ~ssItem(X1) | hd(cons(X1,X0)) = X1, inference(clausification, [status(esa)], [ax23])). % 60.23/10.44 cnf(c104, plain, ~ssList(X0) | app(nil,X0) = X0, inference(clausification, [status(esa)], [ax28])). % 60.23/10.44 cnf(c124, plain, ~ssList(X0) | frontsegP(X0,X0), inference(clausification, [status(esa)], [ax42])). % 60.23/10.44 cnf(c125, plain, ~frontsegP(X0,X1) | ~ssList(X1) | ~ssList(X0) | frontsegP(app(X0,X2),X1) | ~ssList(X2), inference(clausification, [status(esa)], [ax43])). % 60.23/10.44 cnf(c129, plain, ~ssList(X0) | frontsegP(X0,nil), inference(clausification, [status(esa)], [ax45])). % 60.23/10.44 cnf(c180, plain, ~ssList(X0) | ~ssItem(X1) | app(cons(X1,nil),X0) = cons(X1,X0), inference(clausification, [status(esa)], [ax81])). % 60.23/10.44 cnf(c199, plain, ssList(sK254), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c200, plain, ssList(sK255), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c203, plain, sK256 = sK254, inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c204, plain, X0(sK254,sK255,sK256,sK257) | neq(sK255,nil), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c205, plain, X0(sK254,sK255,sK256,sK257) | ~neq(sK257,nil), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c206, plain, sK257 = sK255, inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c207, plain, ~X0(X1,X2,X3,X4) | neq(X2,nil), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c208, plain, ~X0(X1,X2,X3,X4) | ssItem(sK258(X3,X4)), inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c209, plain, ~X0(X1,X2,X3,X4) | app(cons(sK258(X3,X4),nil),X3) = X4, inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(c210, plain, cons(X0,nil) != X1 | ~X2(X3,X4,X5,X6) | X7 != X4 | ~ssItem(X0) | ~neq(nil,X4) | hd(X4) != X0 | ~ssList(X1) | ~ssList(X7) | app(X1,X3) != X7, inference(clausification, [status(esa)], [negated_conjecture])). % 60.23/10.44 cnf(d0, plain, ~neq(sK255,nil) | 'Ts253'(sK254,sK255,sK256,sK257), inference(demodulation, [status(thm)], [c205,c206])). % 60.23/10.44 cnf(d1, plain, ~neq(sK255,nil) | 'Ts253'(sK254,sK255,sK254,sK257), inference(demodulation, [status(thm)], [d0,c203])). % 60.23/10.44 cnf(d2, plain, ~neq(sK255,nil) | 'Ts253'(sK254,sK255,sK254,sK255), inference(demodulation, [status(thm)], [d1,c206])). % 60.23/10.44 cnf(d3, plain, neq(sK255,nil) | 'Ts253'(sK254,sK255,sK254,sK257), inference(demodulation, [status(thm)], [c204,c203])). % 60.23/10.44 cnf(d4, plain, neq(sK255,nil) | 'Ts253'(sK254,sK255,sK254,sK255), inference(demodulation, [status(thm)], [d3,c206])). % 60.23/10.44 cnf(d5, plain, neq(sK255,nil) | neq(sK255,nil), inference(resolution, [status(thm)], [c207,d4])). % 60.23/10.44 cnf(d6, plain, 'Ts253'(sK254,sK255,sK254,sK255), inference(resolution, [status(thm)], [d5,d2])). % 60.23/10.44 cnf(d7, plain, app(cons(sK258(sK254,sK255),nil),sK254) = sK255, inference(resolution, [status(thm)], [c209,d6])). % 60.23/10.44 cnf(d8, plain, ssItem(sK258(sK254,sK255)), inference(resolution, [status(thm)], [c208,d6])). % 60.23/10.44 cnf(d9, plain, app(cons(X0,nil),sK254) = cons(X0,sK254) | ~ssItem(X0), inference(resolution, [status(thm)], [c180,c199])). % 60.23/10.44 cnf(d10, plain, app(cons(sK258(sK254,sK255),nil),sK254) = cons(sK258(sK254,sK255),sK254), inference(resolution, [status(thm)], [d9,d8])). % 60.23/10.44 cnf(d11, plain, sK255 = cons(sK258(sK254,sK255),sK254), inference(demodulation, [status(thm)], [d10,d7])). % 60.23/10.44 cnf(d12, plain, hd(cons(X0,sK254)) = X0 | ~ssItem(X0), inference(resolution, [status(thm)], [c99,c199])). % 60.23/10.44 cnf(d13, plain, hd(cons(sK258(sK254,sK255),sK254)) = sK258(sK254,sK255), inference(resolution, [status(thm)], [d12,d8])). % 60.23/10.44 cnf(d14, plain, hd(sK255) = sK258(sK254,sK255), inference(demodulation, [status(thm)], [d13,d11])). % 60.23/10.44 cnf(d15, plain, sK255 = cons(hd(sK255),sK254), inference(demodulation, [status(thm)], [d11,d14])). % 60.23/10.44 cnf(d16, plain, X0 != X1 | app(cons(X2,nil),X3) != X0 | hd(X1) != X2 | ~ssItem(X2) | ~neq(nil,X1) | ~ssList(cons(X2,nil)) | ~ssList(X0) | ~'Ts253'(X3,X1,X4,X5), inference(equality_resolution, [status(thm)], [c210])). % 60.23/10.44 cnf(d17, plain, app(cons(X0,nil),X1) != X2 | hd(X2) != X0 | ~ssItem(X0) | ~neq(nil,X2) | ~ssList(app(cons(X0,nil),X1)) | ~ssList(cons(X0,nil)) | ~'Ts253'(X1,X2,X3,X4), inference(equality_resolution, [status(thm)], [d16])). % 60.23/10.44 cnf(d18, plain, sK255 != X0 | hd(X0) != sK258(sK254,sK255) | ~ssItem(sK258(sK254,sK255)) | ~neq(nil,X0) | ~ssList(app(cons(sK258(sK254,sK255),nil),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,X0,X1,X2), inference(superposition, [status(thm)], [d7,d17])). % 60.23/10.44 cnf(d19, plain, hd(X0) != sK258(sK254,sK255) | sK255 != X0 | ~ssItem(sK258(sK254,sK255)) | ~neq(nil,X0) | ~ssList(sK255) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,X0,X1,X2), inference(demodulation, [status(thm)], [d18,d7])). % 60.23/10.44 cnf(d20, plain, hd(X0) != sK258(sK254,sK255) | sK255 != X0 | ~ssItem(sK258(sK254,sK255)) | ~neq(nil,X0) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,X0,X1,X2), inference(resolution, [status(thm)], [c200,d19])). % 60.23/10.44 cnf(d21, plain, hd(X0) != sK258(sK254,sK255) | sK255 != X0 | ~neq(nil,X0) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,X0,X1,X2), inference(resolution, [status(thm)], [d8,d20])). % 60.23/10.44 cnf(d22, plain, sK258(sK254,sK255) != sK258(sK254,sK255) | sK255 != cons(sK258(sK254,sK255),sK254) | ~neq(nil,cons(sK258(sK254,sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(superposition, [status(thm)], [d13,d21])). % 60.23/10.44 cnf(d23, plain, sK255 != cons(hd(sK255),sK254) | sK258(sK254,sK255) != sK258(sK254,sK255) | ~neq(nil,cons(sK258(sK254,sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d22,d14])). % 60.23/10.44 cnf(d24, plain, sK255 != sK255 | sK258(sK254,sK255) != sK258(sK254,sK255) | ~neq(nil,cons(sK258(sK254,sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d23,d15])). % 60.23/10.44 cnf(d25, plain, sK255 != sK255 | hd(sK255) != sK258(sK254,sK255) | ~neq(nil,cons(sK258(sK254,sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d24,d14])). % 60.23/10.44 cnf(d26, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,cons(sK258(sK254,sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d25,d14])). % 60.23/10.44 cnf(d27, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,cons(hd(sK255),sK254)) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d26,d14])). % 60.23/10.44 cnf(d28, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,sK255) | ~ssList(cons(sK258(sK254,sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d27,d15])). % 60.23/10.44 cnf(d29, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)) | ~'Ts253'(sK254,cons(sK258(sK254,sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d28,d14])). % 60.23/10.44 cnf(d30, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)) | ~'Ts253'(sK254,cons(hd(sK255),sK254),X0,X1), inference(demodulation, [status(thm)], [d29,d14])). % 60.23/10.44 cnf(d31, plain, sK255 != sK255 | hd(sK255) != hd(sK255) | ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)) | ~'Ts253'(sK254,sK255,X0,X1), inference(demodulation, [status(thm)], [d30,d15])). % 60.23/10.44 cnf(d32, plain, app(nil,sK15(X0,nil)) = X0 | ~ssList(nil) | ~ssList(X0) | ~ssList(X0), inference(resolution, [status(thm)], [c13,c129])). % 60.23/10.44 cnf(d33, plain, app(nil,sK15(X0,nil)) = X0 | ~ssList(X0), inference(resolution, [status(thm)], [c90,d32])). % 60.23/10.44 cnf(d34, plain, app(nil,sK15(sK255,nil)) = sK255, inference(resolution, [status(thm)], [d33,c200])). % 60.23/10.44 cnf(d35, plain, app(nil,sK255) = sK255, inference(resolution, [status(thm)], [c104,c200])). % 60.23/10.44 cnf(d36, plain, frontsegP(sK255,X0) | ~ssList(sK255) | ~ssList(nil) | ~ssList(X0) | ~frontsegP(nil,X0), inference(superposition, [status(thm)], [d35,c125])). % 60.23/10.44 cnf(d37, plain, ~ssList(X0) | ~ssList(nil) | ~frontsegP(nil,X0) | frontsegP(sK255,X0), inference(resolution, [status(thm)], [c200,d36])). % 60.23/10.44 cnf(d38, plain, ~ssList(X0) | ~frontsegP(nil,X0) | frontsegP(sK255,X0), inference(resolution, [status(thm)], [c90,d37])). % 60.23/10.44 cnf(d39, plain, ~ssList(nil) | frontsegP(sK255,nil) | ~ssList(nil), inference(resolution, [status(thm)], [d38,c124])). % 60.23/10.44 cnf(d40, plain, frontsegP(sK255,nil), inference(resolution, [status(thm)], [c90,d39])). % 60.23/10.44 cnf(d41, plain, app(nil,sK15(sK255,nil)) = sK255 | ~ssList(nil) | ~ssList(sK255), inference(resolution, [status(thm)], [d40,c13])). % 60.23/10.44 cnf(d42, plain, sK255 = sK255 | ~ssList(nil) | ~ssList(sK255), inference(demodulation, [status(thm)], [d41,d34])). % 60.23/10.44 cnf(d43, plain, sK255 = sK255 | ~ssList(nil), inference(resolution, [status(thm)], [c200,d42])). % 60.23/10.44 cnf(d44, plain, sK255 = sK255, inference(resolution, [status(thm)], [c90,d43])). % 60.23/10.44 cnf(d45, plain, hd(sK255) != hd(sK255) | ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)) | ~'Ts253'(sK254,sK255,X0,X1), inference(resolution, [status(thm)], [d44,d31])). % 60.23/10.44 cnf(d46, plain, ssItem(hd(sK255)), inference(demodulation, [status(thm)], [d8,d14])). % 60.23/10.44 cnf(d47, plain, hd(cons(hd(sK255),sK254)) = hd(sK255), inference(resolution, [status(thm)], [d46,d12])). % 60.23/10.44 cnf(d48, plain, hd(sK255) = hd(sK255), inference(demodulation, [status(thm)], [d47,d15])). % 60.23/10.44 cnf(d49, plain, ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)) | ~'Ts253'(sK254,sK255,X0,X1), inference(resolution, [status(thm)], [d48,d45])). % 60.23/10.44 cnf(d50, plain, ~neq(nil,sK255) | ~ssList(cons(hd(sK255),nil)), inference(resolution, [status(thm)], [d49,d6])). % 60.23/10.44 cnf(d51, plain, ~neq(nil,sK255) | ~ssItem(hd(sK255)) | ~ssList(nil), inference(resolution, [status(thm)], [d50,c89])). % 60.23/10.44 cnf(d52, plain, ~ssItem(hd(sK255)) | ~neq(nil,sK255), inference(resolution, [status(thm)], [c90,d51])). % 60.23/10.44 cnf(d53, plain, ~neq(nil,sK255), inference(resolution, [status(thm)], [d46,d52])). % 60.23/10.44 cnf(d54, plain, sK255 = nil | ~ssList(sK255) | ~ssList(nil), inference(resolution, [status(thm)], [d53,c88])). % 60.23/10.44 cnf(d55, plain, sK255 = nil | ~ssList(nil), inference(resolution, [status(thm)], [c200,d54])). % 60.23/10.44 cnf(d56, plain, sK255 = nil, inference(resolution, [status(thm)], [c90,d55])). % 60.23/10.44 cnf(d57, plain, sK255 != nil | ~ssItem(hd(sK255)) | ~ssList(sK254), inference(superposition, [status(thm)], [d15,c97])). % 60.23/10.44 cnf(d58, plain, sK255 != nil | ~ssItem(hd(sK255)), inference(resolution, [status(thm)], [c199,d57])). % 60.23/10.44 cnf(d59, plain, sK255 != nil, inference(resolution, [status(thm)], [d46,d58])). % 60.23/10.44 cnf(d60, plain, $false, inference(resolution, [status(thm)], [d59,d56])). % 60.23/10.44 % SZS output end CNFRefutation for theBenchmark.p %------------------------------------------------------------------------------