TSTP Solution File: COM013+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:44:17 EDT 2022
% Result : Theorem 0.41s 0.57s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 17:03:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.41/0.57
% 0.41/0.57 SPASS V 3.9
% 0.41/0.57 SPASS beiseite: Proof found.
% 0.41/0.57 % SZS status Theorem
% 0.41/0.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.57 SPASS derived 523 clauses, backtracked 43 clauses, performed 6 splits and kept 389 clauses.
% 0.41/0.57 SPASS allocated 104830 KBytes.
% 0.41/0.57 SPASS spent 0:00:00.22 on the problem.
% 0.41/0.57 0:00:00.04 for the input.
% 0.41/0.57 0:00:00.07 for the FLOTTER CNF translation.
% 0.41/0.57 0:00:00.01 for inferences.
% 0.41/0.57 0:00:00.00 for the backtracking.
% 0.41/0.57 0:00:00.07 for the reduction.
% 0.41/0.57
% 0.41/0.57
% 0.41/0.57 Here is a proof with depth 7, length 87 :
% 0.41/0.57 % SZS output start Refutation
% 0.41/0.57 1[0:Inp] || -> aElement0(skc1)*.
% 0.41/0.57 2[0:Inp] || -> aRewritingSystem0(xR)*.
% 0.41/0.57 3[0:Inp] || -> isTerminating0(xR)*.
% 0.41/0.57 5[0:Inp] || -> aElement0(skf15(u))*.
% 0.41/0.57 6[0:Inp] || -> aElement0(skf24(u))*.
% 0.41/0.57 7[0:Inp] || -> aElement0(skf23(u))*.
% 0.41/0.57 8[0:Inp] || -> aElement0(skf21(u))*.
% 0.41/0.57 18[0:Inp] aRewritingSystem0(u) || -> isConfluent0(u) sdtmndtasgtdt0(skf24(u),u,skf23(u))*.
% 0.41/0.57 19[0:Inp] aRewritingSystem0(u) || -> isConfluent0(u) sdtmndtasgtdt0(skf24(u),u,skf21(u))*.
% 0.41/0.57 26[0:Inp] aElement0(u) || equal(skc1,u) -> aReductOfIn0(skf17(u),u,xR)*.
% 0.41/0.57 27[0:Inp] aElement0(u) || iLess0(u,skc1) aReductOfIn0(v,skf15(u),xR)* -> .
% 0.41/0.57 28[0:Inp] aElement0(u) || aReductOfIn0(u,skc1,xR) -> aReductOfIn0(skf17(u),u,xR)*.
% 0.41/0.57 29[0:Inp] aElement0(u) || sdtmndtplgtdt0(skc1,xR,u) -> aReductOfIn0(skf17(u),u,xR)*.
% 0.41/0.57 31[0:Inp] aRewritingSystem0(u) aElement0(v) || aReductOfIn0(w,v,u)* -> aElement0(w).
% 0.41/0.57 33[0:Inp] aElement0(u) aElement0(v) || aReductOfIn0(u,v,xR)* -> iLess0(u,v).
% 0.41/0.57 34[0:Inp] aElement0(u) aElement0(v) || sdtmndtplgtdt0(v,xR,u)* -> iLess0(u,v).
% 0.41/0.57 36[0:Inp] aElement0(u) || iLess0(u,skc1) -> equal(skf15(u),u) sdtmndtplgtdt0(u,xR,skf15(u))*.
% 0.41/0.57 38[0:Inp] aElement0(u) aRewritingSystem0(v) aElement0(w) || equal(w,u) -> sdtmndtasgtdt0(w,v,u)*.
% 0.41/0.57 43[0:Inp] aRewritingSystem0(u) aElement0(v) || sdtmndtasgtdt0(skf23(u),u,v)* sdtmndtasgtdt0(skf21(u),u,v) -> isConfluent0(u).
% 0.41/0.57 44[0:Inp] aElement0(u) aRewritingSystem0(v) aElement0(w) || sdtmndtasgtdt0(w,v,u)* -> equal(w,u) sdtmndtplgtdt0(w,v,u).
% 0.41/0.57 47[0:Inp] aElement0(u) aElement0(v) aElement0(w) || aReductOfIn0(w,v,xR)*+ sdtmndtplgtdt0(w,xR,u)* -> iLess0(u,v)*.
% 0.41/0.57 54[0:Inp] aElement0(u) aElement0(v) aRewritingSystem0(w) aElement0(x) || sdtmndtplgtdt0(u,w,x)* aReductOfIn0(u,v,w)* -> sdtmndtplgtdt0(v,w,x)*.
% 0.41/0.57 60[0:MRR:54.0,31.3] aElement0(u) aRewritingSystem0(v) aElement0(w) || aReductOfIn0(x,w,v)*+ sdtmndtplgtdt0(x,v,u)* -> sdtmndtplgtdt0(w,v,u)*.
% 0.41/0.57 82[0:Res:1.0,33.0] aElement0(u) || aReductOfIn0(u,skc1,xR)* -> iLess0(u,skc1).
% 0.41/0.57 88[0:Res:1.0,31.0] aRewritingSystem0(u) || aReductOfIn0(v,skc1,u)* -> aElement0(v).
% 0.41/0.57 92[0:Res:1.0,26.0] || equal(skc1,skc1) -> aReductOfIn0(skf17(skc1),skc1,xR)*.
% 0.41/0.57 176[0:Obv:92.0] || -> aReductOfIn0(skf17(skc1),skc1,xR)*.
% 0.41/0.57 211[0:Res:176.0,88.1] aRewritingSystem0(xR) || -> aElement0(skf17(skc1))*.
% 0.41/0.57 212[0:SSi:211.0,3.0,2.0] || -> aElement0(skf17(skc1))*.
% 0.41/0.57 213[0:Res:176.0,82.1] aElement0(skf17(skc1)) || -> iLess0(skf17(skc1),skc1)*.
% 0.41/0.57 214[0:SSi:213.0,212.0] || -> iLess0(skf17(skc1),skc1)*.
% 0.41/0.57 241[0:Res:28.2,27.2] aElement0(skf15(u)) aElement0(u) || aReductOfIn0(skf15(u),skc1,xR)* iLess0(u,skc1) -> .
% 0.41/0.57 243[0:Res:29.2,27.2] aElement0(skf15(u)) aElement0(u) || sdtmndtplgtdt0(skc1,xR,skf15(u))* iLess0(u,skc1) -> .
% 0.41/0.57 246[0:SSi:241.0,5.0] aElement0(u) || aReductOfIn0(skf15(u),skc1,xR)* iLess0(u,skc1) -> .
% 0.41/0.57 248[0:SSi:243.0,5.0] aElement0(u) || sdtmndtplgtdt0(skc1,xR,skf15(u))* iLess0(u,skc1) -> .
% 0.41/0.57 565[0:Res:18.2,44.3] aRewritingSystem0(u) aElement0(skf23(u)) aRewritingSystem0(u) aElement0(skf24(u)) || -> isConfluent0(u) equal(skf24(u),skf23(u)) sdtmndtplgtdt0(skf24(u),u,skf23(u))*.
% 0.41/0.57 576[0:Obv:565.0] aElement0(skf23(u)) aRewritingSystem0(u) aElement0(skf24(u)) || -> isConfluent0(u) equal(skf24(u),skf23(u)) sdtmndtplgtdt0(skf24(u),u,skf23(u))*.
% 0.41/0.57 577[0:SSi:576.2,576.0,6.0,7.0] aRewritingSystem0(u) || -> isConfluent0(u) equal(skf24(u),skf23(u)) sdtmndtplgtdt0(skf24(u),u,skf23(u))*.
% 0.41/0.57 581[0:Res:577.3,34.2] aRewritingSystem0(xR) aElement0(skf23(xR)) aElement0(skf24(xR)) || -> isConfluent0(xR) equal(skf24(xR),skf23(xR)) iLess0(skf23(xR),skf24(xR))*.
% 0.41/0.57 583[0:SSi:581.2,581.1,581.0,6.0,3.0,2.0,7.0,3.0,2.0,3.0,2.0] || -> isConfluent0(xR) equal(skf24(xR),skf23(xR)) iLess0(skf23(xR),skf24(xR))*.
% 0.41/0.57 587[1:Spt:583.0] || -> isConfluent0(xR)*.
% 0.41/0.57 607[0:Res:176.0,47.3] aElement0(u) aElement0(skc1) aElement0(skf17(skc1)) || sdtmndtplgtdt0(skf17(skc1),xR,u)* -> iLess0(u,skc1).
% 0.41/0.57 615[0:SSi:607.2,607.1,212.0,1.0] aElement0(u) || sdtmndtplgtdt0(skf17(skc1),xR,u)* -> iLess0(u,skc1).
% 0.41/0.57 628[0:Res:36.3,615.1] aElement0(skf17(skc1)) aElement0(skf15(skf17(skc1))) || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) iLess0(skf15(skf17(skc1)),skc1)*.
% 0.41/0.57 631[0:SSi:628.1,628.0,5.0,212.0,212.0] || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) iLess0(skf15(skf17(skc1)),skc1)*.
% 0.41/0.57 632[0:MRR:631.0,214.0] || -> equal(skf15(skf17(skc1)),skf17(skc1)) iLess0(skf15(skf17(skc1)),skc1)*.
% 0.41/0.57 649[0:Res:176.0,60.3] aElement0(u) aRewritingSystem0(xR) aElement0(skc1) || sdtmndtplgtdt0(skf17(skc1),xR,u)* -> sdtmndtplgtdt0(skc1,xR,u).
% 0.41/0.57 657[1:SSi:649.2,649.1,1.0,3.0,2.0,587.0] aElement0(u) || sdtmndtplgtdt0(skf17(skc1),xR,u)* -> sdtmndtplgtdt0(skc1,xR,u).
% 0.41/0.57 672[1:Res:36.3,657.1] aElement0(skf17(skc1)) aElement0(skf15(skf17(skc1))) || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.57 675[1:SSi:672.1,672.0,5.0,212.0,212.0] || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.57 676[1:MRR:675.0,214.0] || -> equal(skf15(skf17(skc1)),skf17(skc1)) sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.57 677[2:Spt:676.0] || -> equal(skf15(skf17(skc1)),skf17(skc1))**.
% 0.41/0.57 693[2:SpL:677.0,246.1] aElement0(skf17(skc1)) || aReductOfIn0(skf17(skc1),skc1,xR)* iLess0(skf17(skc1),skc1) -> .
% 0.41/0.57 720[2:SSi:693.0,212.0] || aReductOfIn0(skf17(skc1),skc1,xR)* iLess0(skf17(skc1),skc1) -> .
% 0.41/0.57 721[2:MRR:720.0,720.1,176.0,214.0] || -> .
% 0.41/0.57 730[2:Spt:721.0,676.0,677.0] || equal(skf15(skf17(skc1)),skf17(skc1))** -> .
% 0.41/0.57 731[2:Spt:721.0,676.1] || -> sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.57 739[2:Res:731.0,248.1] aElement0(skf17(skc1)) || iLess0(skf17(skc1),skc1)* -> .
% 0.41/0.57 745[2:SSi:739.0,212.0] || iLess0(skf17(skc1),skc1)* -> .
% 0.41/0.57 746[2:MRR:745.0,214.0] || -> .
% 0.41/0.57 749[1:Spt:746.0,583.0,587.0] || isConfluent0(xR)* -> .
% 0.41/0.57 750[1:Spt:746.0,583.1,583.2] || -> equal(skf24(xR),skf23(xR)) iLess0(skf23(xR),skf24(xR))*.
% 0.41/0.57 756[0:SSi:649.2,649.1,1.0,3.0,2.0] aElement0(u) || sdtmndtplgtdt0(skf17(skc1),xR,u)* -> sdtmndtplgtdt0(skc1,xR,u).
% 0.41/0.57 774[2:Spt:750.0] || -> equal(skf24(xR),skf23(xR))**.
% 0.41/0.57 780[2:SpR:774.0,19.2] aRewritingSystem0(xR) || -> isConfluent0(xR) sdtmndtasgtdt0(skf23(xR),xR,skf21(xR))*.
% 0.41/0.57 785[2:SSi:780.0,3.0,2.0] || -> isConfluent0(xR) sdtmndtasgtdt0(skf23(xR),xR,skf21(xR))*.
% 0.41/0.57 786[2:MRR:785.0,749.0] || -> sdtmndtasgtdt0(skf23(xR),xR,skf21(xR))*.
% 0.41/0.57 792[2:Res:786.0,43.2] aRewritingSystem0(xR) aElement0(skf21(xR)) || sdtmndtasgtdt0(skf21(xR),xR,skf21(xR))* -> isConfluent0(xR).
% 0.41/0.57 794[2:SSi:792.1,792.0,8.0,3.0,2.0,3.0,2.0] || sdtmndtasgtdt0(skf21(xR),xR,skf21(xR))* -> isConfluent0(xR).
% 0.41/0.57 795[2:MRR:794.1,749.0] || sdtmndtasgtdt0(skf21(xR),xR,skf21(xR))* -> .
% 0.41/0.57 801[2:Res:38.4,795.0] aElement0(skf21(xR)) aRewritingSystem0(xR) aElement0(skf21(xR)) || equal(skf21(xR),skf21(xR))* -> .
% 0.41/0.57 802[2:Obv:801.3] aRewritingSystem0(xR) aElement0(skf21(xR)) || -> .
% 0.41/0.57 803[2:SSi:802.1,802.0,8.0,3.0,2.0,3.0,2.0] || -> .
% 0.41/0.57 806[2:Spt:803.0,750.0,774.0] || equal(skf24(xR),skf23(xR))** -> .
% 0.41/0.57 807[2:Spt:803.0,750.1] || -> iLess0(skf23(xR),skf24(xR))*.
% 0.41/0.57 867[3:Spt:632.0] || -> equal(skf15(skf17(skc1)),skf17(skc1))**.
% 0.41/0.57 883[3:SpL:867.0,246.1] aElement0(skf17(skc1)) || aReductOfIn0(skf17(skc1),skc1,xR)* iLess0(skf17(skc1),skc1) -> .
% 0.41/0.57 910[3:SSi:883.0,212.0] || aReductOfIn0(skf17(skc1),skc1,xR)* iLess0(skf17(skc1),skc1) -> .
% 0.41/0.57 911[3:MRR:910.0,910.1,176.0,214.0] || -> .
% 0.41/0.57 920[3:Spt:911.0,632.0,867.0] || equal(skf15(skf17(skc1)),skf17(skc1))** -> .
% 0.41/0.57 921[3:Spt:911.0,632.1] || -> iLess0(skf15(skf17(skc1)),skc1)*.
% 0.41/0.57 1034[0:Res:36.3,756.1] aElement0(skf17(skc1)) aElement0(skf15(skf17(skc1))) || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.57 1037[0:SSi:1034.1,1034.0,5.0,212.0,212.0] || iLess0(skf17(skc1),skc1) -> equal(skf15(skf17(skc1)),skf17(skc1)) sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.58 1038[3:MRR:1037.0,1037.1,214.0,920.0] || -> sdtmndtplgtdt0(skc1,xR,skf15(skf17(skc1)))*.
% 0.41/0.58 1043[3:Res:1038.0,248.1] aElement0(skf17(skc1)) || iLess0(skf17(skc1),skc1)* -> .
% 0.41/0.58 1050[3:SSi:1043.0,212.0] || iLess0(skf17(skc1),skc1)* -> .
% 0.41/0.58 1051[3:MRR:1050.0,214.0] || -> .
% 0.41/0.58 % SZS output end Refutation
% 0.41/0.58 Formulae used in the proof : m__ m__587 mCRDef mReduct mTCRDef mTCDef
% 0.41/0.58
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