%------------------------------------------------------------------------------ % File : LisaST---0.9 % Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % Computer : n016.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 06:58:43 AM UTC 2026 % Result : Theorem 70.06s 41.53s % Output : CNFRefutation 70.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.04 % Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.09/5.38 % Computer : n016.cluster.edu % 0.09/5.38 % Model : x86_64 x86_64 % 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/5.38 % Memory : 8046.5625MB % 0.09/5.38 % OS : Linux 6.8.0-71-generic % 0.14/25.85 % CPULimit : 300 % 0.14/25.85 % WCLimit : 300 % 0.14/25.85 % DateTime : Sat Sep 26 23:21:42 UTC 2026 % 0.14/25.85 % CPUTime : % 0.14/25.85 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 70.06/41.53 % SZS status Theorem for theBenchmark.p % 70.06/41.53 % SZS output start CNFRefutation for theBenchmark.p % 70.06/41.53 fof(mReduct, axiom, ! [X0] : ! [X1] : (((aElement0(X0) & aRewritingSystem0(X1)) => ! [X2] : ((aReductOfIn0(X2,X0,X1) => aElement0(X2)))))). % 70.06/41.53 fof(mTCDef, definition, ! [X0] : ! [X1] : ! [X2] : (((aElement0(X0) & (aRewritingSystem0(X1) & aElement0(X2))) => (sdtmndtplgtdt0(X0,X1,X2) <=> (aReductOfIn0(X2,X0,X1) | ? [X3] : ((aElement0(X3) & (aReductOfIn0(X3,X0,X1) & sdtmndtplgtdt0(X3,X1,X2))))))))). % 70.06/41.53 fof(mTCRDef, definition, ! [X0] : ! [X1] : ! [X2] : (((aElement0(X0) & (aRewritingSystem0(X1) & aElement0(X2))) => (sdtmndtasgtdt0(X0,X1,X2) <=> (X0 = X2 | sdtmndtplgtdt0(X0,X1,X2)))))). % 70.06/41.53 fof(mTCRTrans, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : (((aElement0(X0) & (aRewritingSystem0(X1) & (aElement0(X2) & aElement0(X3)))) => ((sdtmndtasgtdt0(X0,X1,X2) & sdtmndtasgtdt0(X2,X1,X3)) => sdtmndtasgtdt0(X0,X1,X3))))). % 70.06/41.53 fof(mTermin, definition, ! [X0] : ((aRewritingSystem0(X0) => (isTerminating0(X0) <=> ! [X1] : ! [X2] : (((aElement0(X1) & aElement0(X2)) => (sdtmndtplgtdt0(X1,X0,X2) => iLess0(X2,X1)))))))). % 70.06/41.53 fof(mNFRDef, definition, ! [X0] : ! [X1] : (((aElement0(X0) & aRewritingSystem0(X1)) => ! [X2] : ((aNormalFormOfIn0(X2,X0,X1) <=> (aElement0(X2) & (sdtmndtasgtdt0(X0,X1,X2) & ~? [X3] : aReductOfIn0(X3,X2,X1)))))))). % 70.06/41.53 fof(m__587, hypothesis, (aRewritingSystem0(xR) & isTerminating0(xR))). % 70.06/41.53 fof(m__, conjecture, ! [X0] : ((aElement0(X0) => (! [X1] : ((aElement0(X1) => (iLess0(X1,X0) => ? [X2] : aNormalFormOfIn0(X2,X1,xR)))) => ? [X1] : aNormalFormOfIn0(X1,X0,xR))))). % 70.06/41.53 fof(negated_conjecture, negated_conjecture, ~! [X0] : ((aElement0(X0) => (! [X1] : ((aElement0(X1) => (iLess0(X1,X0) => ? [X2] : aNormalFormOfIn0(X2,X1,xR)))) => ? [X1] : aNormalFormOfIn0(X1,X0,xR)))), inference(negate_conjecture, [status(cth)], [m__])). % 70.06/41.53 cnf(c0, plain, ~aRewritingSystem0(X0) | ~aElement0(X1) | ~aReductOfIn0(X2,X1,X0) | aElement0(X2), inference(clausification, [status(esa)], [mReduct])). % 70.06/41.53 cnf(c1, plain, ~aRewritingSystem0(X0) | ~aElement0(X1) | ~aElement0(X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [mTCDef])). % 70.06/41.53 cnf(c5, plain, ~X0(X1,X2,X3) | sdtmndtplgtdt0(X1,X2,X3) | ~aReductOfIn0(X3,X1,X2), inference(clausification, [status(esa)], [mTCDef])). % 70.06/41.53 cnf(c9, plain, sdtmndtasgtdt0(X0,X1,X2) | ~aRewritingSystem0(X1) | X2 != X0 | ~aElement0(X0) | ~aElement0(X2), inference(clausification, [status(esa)], [mTCRDef])). % 70.06/41.53 cnf(c10, plain, sdtmndtasgtdt0(X0,X1,X2) | ~aElement0(X0) | ~aElement0(X2) | ~sdtmndtplgtdt0(X0,X1,X2) | ~aRewritingSystem0(X1), inference(clausification, [status(esa)], [mTCRDef])). % 70.06/41.53 cnf(c11, plain, ~aRewritingSystem0(X0) | sdtmndtasgtdt0(X1,X0,X2) | ~sdtmndtasgtdt0(X1,X0,X3) | ~aElement0(X3) | ~sdtmndtasgtdt0(X3,X0,X2) | ~aElement0(X1) | ~aElement0(X2), inference(clausification, [status(esa)], [mTCRTrans])). % 70.06/41.53 cnf(c32, plain, ~aRewritingSystem0(X0) | X1(X0), inference(clausification, [status(esa)], [mTermin])). % 70.06/41.53 cnf(c33, plain, iLess0(X0,X1) | ~sdtmndtplgtdt0(X1,X2,X0) | ~isTerminating0(X2) | ~X3(X2) | ~aElement0(X1) | ~aElement0(X0), inference(clausification, [status(esa)], [mTermin])). % 70.06/41.53 cnf(c38, plain, ~aRewritingSystem0(X0) | ~aElement0(X1) | ~aNormalFormOfIn0(X2,X1,X0) | aElement0(X2), inference(clausification, [status(esa)], [mNFRDef])). % 70.06/41.53 cnf(c39, plain, ~aRewritingSystem0(X0) | ~aElement0(X1) | ~aNormalFormOfIn0(X2,X1,X0) | ~aReductOfIn0(X3,X2,X0), inference(clausification, [status(esa)], [mNFRDef])). % 70.06/41.53 cnf(c40, plain, ~aRewritingSystem0(X0) | ~aElement0(X1) | ~aNormalFormOfIn0(X2,X1,X0) | sdtmndtasgtdt0(X1,X0,X2), inference(clausification, [status(esa)], [mNFRDef])). % 70.06/41.53 cnf(c41, plain, ~aElement0(X0) | ~sdtmndtasgtdt0(X1,X2,X0) | ~aElement0(X1) | aReductOfIn0(sK50(X2,X0),X0,X2) | ~aRewritingSystem0(X2) | aNormalFormOfIn0(X0,X1,X2), inference(clausification, [status(esa)], [mNFRDef])). % 70.06/41.53 cnf(c42, plain, aRewritingSystem0(xR), inference(clausification, [status(esa)], [m__587])). % 70.06/41.53 cnf(c43, plain, isTerminating0(xR), inference(clausification, [status(esa)], [m__587])). % 70.06/41.53 cnf(c44, plain, aElement0(sK51), inference(clausification, [status(esa)], [negated_conjecture])). % 70.06/41.53 cnf(c45, plain, ~aNormalFormOfIn0(X0,sK51,xR), inference(clausification, [status(esa)], [negated_conjecture])). % 70.06/41.53 cnf(c46, plain, ~aElement0(X0) | aNormalFormOfIn0(sK54(X0),X0,xR) | ~iLess0(X0,sK51), inference(clausification, [status(esa)], [negated_conjecture])). % 70.06/41.53 cnf(d0, plain, aReductOfIn0(sK50(X0,sK51),sK51,X0) | ~aElement0(X1) | ~aRewritingSystem0(X0) | ~sdtmndtasgtdt0(X1,X0,sK51) | aNormalFormOfIn0(sK51,X1,X0), inference(resolution, [status(thm)], [c41,c44])). % 70.06/41.53 cnf(d1, plain, aReductOfIn0(sK50(X0,sK51),sK51,X0) | ~aRewritingSystem0(X0) | ~sdtmndtasgtdt0(sK51,X0,sK51) | aNormalFormOfIn0(sK51,sK51,X0), inference(resolution, [status(thm)], [d0,c44])). % 70.06/41.53 cnf(d2, plain, aReductOfIn0(sK50(xR,sK51),sK51,xR) | ~sdtmndtasgtdt0(sK51,xR,sK51) | aNormalFormOfIn0(sK51,sK51,xR), inference(resolution, [status(thm)], [d1,c42])). % 70.06/41.53 cnf(d3, plain, aReductOfIn0(sK50(xR,sK51),sK51,xR) | ~sdtmndtasgtdt0(sK51,xR,sK51), inference(resolution, [status(thm)], [c45,d2])). % 70.06/41.53 cnf(d4, plain, ~aElement0(X0) | ~aElement0(X0) | ~aRewritingSystem0(X1) | sdtmndtasgtdt0(X0,X1,X0), inference(equality_resolution, [status(thm)], [c9])). % 70.06/41.53 cnf(d5, plain, ~aRewritingSystem0(X0) | sdtmndtasgtdt0(sK51,X0,sK51), inference(resolution, [status(thm)], [d4,c44])). % 70.06/41.53 cnf(d6, plain, sdtmndtasgtdt0(sK51,xR,sK51), inference(resolution, [status(thm)], [d5,c42])). % 70.06/41.53 cnf(d7, plain, aReductOfIn0(sK50(xR,sK51),sK51,xR), inference(resolution, [status(thm)], [d6,d3])). % 70.06/41.53 cnf(d8, plain, ~aElement0(sK51) | aElement0(sK50(xR,sK51)) | ~aRewritingSystem0(xR), inference(resolution, [status(thm)], [d7,c0])). % 70.06/41.53 cnf(d9, plain, aElement0(sK50(xR,sK51)) | ~aRewritingSystem0(xR), inference(resolution, [status(thm)], [c44,d8])). % 70.06/41.53 cnf(d10, plain, aElement0(sK50(xR,sK51)), inference(resolution, [status(thm)], [c42,d9])). % 70.06/41.53 cnf(d11, plain, aElement0(X0) | ~aRewritingSystem0(X1) | ~aNormalFormOfIn0(X0,sK50(xR,sK51),X1), inference(resolution, [status(thm)], [d10,c38])). % 70.06/41.53 cnf(d12, plain, aElement0(X0) | ~aNormalFormOfIn0(X0,sK50(xR,sK51),xR), inference(resolution, [status(thm)], [d11,c42])). % 70.06/41.53 cnf(d13, plain, ~iLess0(sK50(xR,sK51),sK51) | aNormalFormOfIn0(sK54(sK50(xR,sK51)),sK50(xR,sK51),xR), inference(resolution, [status(thm)], [d10,c46])). % 70.06/41.53 cnf(d14, plain, ~'Ts3'(sK51,xR,sK50(xR,sK51)) | sdtmndtplgtdt0(sK51,xR,sK50(xR,sK51)), inference(resolution, [status(thm)], [d7,c5])). % 70.06/41.53 cnf(d15, plain, ~aElement0(X0) | ~aRewritingSystem0(X1) | 'Ts3'(sK51,X1,X0), inference(resolution, [status(thm)], [c1,c44])). % 70.06/41.53 cnf(d16, plain, ~aRewritingSystem0(X0) | 'Ts3'(sK51,X0,sK50(xR,sK51)), inference(resolution, [status(thm)], [d10,d15])). % 70.06/41.53 cnf(d17, plain, 'Ts3'(sK51,xR,sK50(xR,sK51)), inference(resolution, [status(thm)], [d16,c42])). % 70.06/41.53 cnf(d18, plain, sdtmndtplgtdt0(sK51,xR,sK50(xR,sK51)), inference(resolution, [status(thm)], [d17,d14])). % 70.06/41.53 cnf(d19, plain, ~aElement0(X0) | ~sdtmndtplgtdt0(X0,X1,sK50(xR,sK51)) | ~'Ts40'(X1) | ~isTerminating0(X1) | iLess0(sK50(xR,sK51),X0), inference(resolution, [status(thm)], [d10,c33])). % 70.06/41.53 cnf(d20, plain, ~sdtmndtplgtdt0(sK51,X0,sK50(xR,sK51)) | ~'Ts40'(X0) | ~isTerminating0(X0) | iLess0(sK50(xR,sK51),sK51), inference(resolution, [status(thm)], [d19,c44])). % 70.06/41.53 cnf(d21, plain, ~'Ts40'(xR) | ~isTerminating0(xR) | iLess0(sK50(xR,sK51),sK51), inference(resolution, [status(thm)], [d20,d18])). % 70.06/41.53 cnf(d22, plain, ~'Ts40'(xR) | iLess0(sK50(xR,sK51),sK51), inference(resolution, [status(thm)], [c43,d21])). % 70.06/41.53 cnf(d23, plain, 'Ts40'(xR), inference(resolution, [status(thm)], [c32,c42])). % 70.06/41.53 cnf(d24, plain, iLess0(sK50(xR,sK51),sK51), inference(resolution, [status(thm)], [d23,d22])). % 70.06/41.53 cnf(d25, plain, aNormalFormOfIn0(sK54(sK50(xR,sK51)),sK50(xR,sK51),xR), inference(resolution, [status(thm)], [d24,d13])). % 70.06/41.53 cnf(d26, plain, aElement0(sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [d25,d12])). % 70.06/41.53 cnf(d27, plain, aReductOfIn0(sK50(X0,sK54(sK50(xR,sK51))),sK54(sK50(xR,sK51)),X0) | ~aElement0(X1) | ~aRewritingSystem0(X0) | ~sdtmndtasgtdt0(X1,X0,sK54(sK50(xR,sK51))) | aNormalFormOfIn0(sK54(sK50(xR,sK51)),X1,X0), inference(resolution, [status(thm)], [d26,c41])). % 70.06/41.53 cnf(d28, plain, aReductOfIn0(sK50(X0,sK54(sK50(xR,sK51))),sK54(sK50(xR,sK51)),X0) | ~aRewritingSystem0(X0) | ~sdtmndtasgtdt0(sK51,X0,sK54(sK50(xR,sK51))) | aNormalFormOfIn0(sK54(sK50(xR,sK51)),sK51,X0), inference(resolution, [status(thm)], [d27,c44])). % 70.06/41.53 cnf(d29, plain, aReductOfIn0(sK50(xR,sK54(sK50(xR,sK51))),sK54(sK50(xR,sK51)),xR) | ~sdtmndtasgtdt0(sK51,xR,sK54(sK50(xR,sK51))) | aNormalFormOfIn0(sK54(sK50(xR,sK51)),sK51,xR), inference(resolution, [status(thm)], [d28,c42])). % 70.06/41.53 cnf(d30, plain, aReductOfIn0(sK50(xR,sK54(sK50(xR,sK51))),sK54(sK50(xR,sK51)),xR) | ~sdtmndtasgtdt0(sK51,xR,sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [c45,d29])). % 70.06/41.53 cnf(d31, plain, ~aElement0(X0) | ~aElement0(X1) | ~aRewritingSystem0(X2) | ~sdtmndtasgtdt0(sK50(xR,sK51),X2,X0) | ~sdtmndtasgtdt0(X1,X2,sK50(xR,sK51)) | sdtmndtasgtdt0(X1,X2,X0), inference(resolution, [status(thm)], [d10,c11])). % 70.06/41.53 cnf(d32, plain, ~aElement0(X0) | ~aRewritingSystem0(X1) | sdtmndtasgtdt0(sK51,X1,X0) | ~sdtmndtasgtdt0(sK51,X1,sK50(xR,sK51)) | ~sdtmndtasgtdt0(sK50(xR,sK51),X1,X0), inference(resolution, [status(thm)], [d31,c44])). % 70.06/41.53 cnf(d33, plain, ~aRewritingSystem0(X0) | ~sdtmndtasgtdt0(sK50(xR,sK51),X0,sK54(sK50(xR,sK51))) | sdtmndtasgtdt0(sK51,X0,sK54(sK50(xR,sK51))) | ~sdtmndtasgtdt0(sK51,X0,sK50(xR,sK51)), inference(resolution, [status(thm)], [d32,d26])). % 70.06/41.53 cnf(d34, plain, ~sdtmndtasgtdt0(sK50(xR,sK51),xR,sK54(sK50(xR,sK51))) | ~sdtmndtasgtdt0(sK51,xR,sK50(xR,sK51)) | sdtmndtasgtdt0(sK51,xR,sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [d33,c42])). % 70.06/41.53 cnf(d35, plain, ~aElement0(X0) | ~aRewritingSystem0(X1) | ~sdtmndtplgtdt0(X0,X1,sK50(xR,sK51)) | sdtmndtasgtdt0(X0,X1,sK50(xR,sK51)), inference(resolution, [status(thm)], [d10,c10])). % 70.06/41.53 cnf(d36, plain, ~aRewritingSystem0(X0) | ~sdtmndtplgtdt0(sK51,X0,sK50(xR,sK51)) | sdtmndtasgtdt0(sK51,X0,sK50(xR,sK51)), inference(resolution, [status(thm)], [d35,c44])). % 70.06/41.53 cnf(d37, plain, ~sdtmndtplgtdt0(sK51,xR,sK50(xR,sK51)) | sdtmndtasgtdt0(sK51,xR,sK50(xR,sK51)), inference(resolution, [status(thm)], [d36,c42])). % 70.06/41.53 cnf(d38, plain, sdtmndtasgtdt0(sK51,xR,sK50(xR,sK51)), inference(resolution, [status(thm)], [d18,d37])). % 70.06/41.53 cnf(d39, plain, ~sdtmndtasgtdt0(sK50(xR,sK51),xR,sK54(sK50(xR,sK51))) | sdtmndtasgtdt0(sK51,xR,sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [d38,d34])). % 70.06/41.53 cnf(d40, plain, ~aRewritingSystem0(X0) | sdtmndtasgtdt0(sK50(xR,sK51),X0,X1) | ~aNormalFormOfIn0(X1,sK50(xR,sK51),X0), inference(resolution, [status(thm)], [d10,c40])). % 70.06/41.53 cnf(d41, plain, sdtmndtasgtdt0(sK50(xR,sK51),xR,X0) | ~aNormalFormOfIn0(X0,sK50(xR,sK51),xR), inference(resolution, [status(thm)], [d40,c42])). % 70.06/41.53 cnf(d42, plain, sdtmndtasgtdt0(sK50(xR,sK51),xR,sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [d25,d41])). % 70.06/41.53 cnf(d43, plain, sdtmndtasgtdt0(sK51,xR,sK54(sK50(xR,sK51))), inference(resolution, [status(thm)], [d42,d39])). % 70.06/41.53 cnf(d44, plain, aReductOfIn0(sK50(xR,sK54(sK50(xR,sK51))),sK54(sK50(xR,sK51)),xR), inference(resolution, [status(thm)], [d43,d30])). % 70.06/41.53 cnf(d45, plain, ~aElement0(X0) | ~aRewritingSystem0(xR) | ~aNormalFormOfIn0(sK54(sK50(xR,sK51)),X0,xR), inference(resolution, [status(thm)], [d44,c39])). % 70.06/41.53 cnf(d46, plain, ~aElement0(X0) | ~aNormalFormOfIn0(sK54(sK50(xR,sK51)),X0,xR), inference(resolution, [status(thm)], [c42,d45])). % 70.06/41.53 cnf(d47, plain, ~aNormalFormOfIn0(sK54(sK50(xR,sK51)),sK50(xR,sK51),xR), inference(resolution, [status(thm)], [d46,d10])). % 70.06/41.53 cnf(d48, plain, $false, inference(resolution, [status(thm)], [d25,d47])). % 70.06/41.53 % SZS output end CNFRefutation for theBenchmark.p %------------------------------------------------------------------------------