TSTP Solution File: SWC098+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC098+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 : Tue Jul 19 22:01:42 EDT 2022
% Result : Theorem 31.59s 31.77s
% Output : Refutation 37.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC098+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 11:06:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 31.59/31.77
% 31.59/31.77 SPASS V 3.9
% 31.59/31.77 SPASS beiseite: Proof found.
% 31.59/31.77 % SZS status Theorem
% 31.59/31.77 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.59/31.77 SPASS derived 21997 clauses, backtracked 2846 clauses, performed 48 splits and kept 8287 clauses.
% 31.59/31.77 SPASS allocated 130597 KBytes.
% 31.59/31.77 SPASS spent 0:0:31.39 on the problem.
% 31.59/31.77 0:00:00.04 for the input.
% 31.59/31.77 0:00:00.07 for the FLOTTER CNF translation.
% 31.59/31.77 0:00:00.36 for inferences.
% 31.59/31.77 0:00:01.86 for the backtracking.
% 31.59/31.77 0:0:28.74 for the reduction.
% 31.59/31.77
% 31.59/31.77
% 31.59/31.77 Here is a proof with depth 5, length 110 :
% 31.59/31.77 % SZS output start Refutation
% 31.59/31.77 1[0:Inp] || -> ssList(skc5)*.
% 31.59/31.77 2[0:Inp] || -> ssList(skc4)*.
% 31.59/31.77 4[0:Inp] || -> ssItem(skc6)*.
% 31.59/31.77 5[0:Inp] || -> ssList(nil)*.
% 31.59/31.77 6[0:Inp] || -> cyclefreeP(nil)*.
% 31.59/31.77 7[0:Inp] || -> totalorderP(nil)*.
% 31.59/31.77 8[0:Inp] || -> strictorderP(nil)*.
% 31.59/31.77 9[0:Inp] || -> totalorderedP(nil)*.
% 31.59/31.77 10[0:Inp] || -> strictorderedP(nil)*.
% 31.59/31.77 11[0:Inp] || -> duplicatefreeP(nil)*.
% 31.59/31.77 12[0:Inp] || -> equalelemsP(nil)*.
% 31.59/31.77 13[0:Inp] || -> ssItem(skf45(u))*.
% 31.59/31.77 52[0:Inp] || -> ssItem(skf46(u,v))*.
% 31.59/31.77 68[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc5).
% 31.59/31.77 69[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc4).
% 31.59/31.77 70[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 31.59/31.77 79[0:Inp] || equal(nil,skc4) equal(nil,skc5)** -> .
% 31.59/31.77 80[0:Inp] || -> SkP0(u,v) memberP(u,skf46(u,v))*.
% 31.59/31.77 81[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 31.59/31.77 87[0:Inp] || -> SkP0(u,v) equal(cons(skf46(u,v),nil),v)**.
% 31.59/31.77 91[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 31.59/31.77 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 31.59/31.77 111[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 31.59/31.77 128[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 31.59/31.77 133[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 31.59/31.77 136[0:Inp] ssItem(u) || memberP(skc5,u) equal(cons(u,nil),skc4) -> memberP(skc5,skf45(u))*.
% 31.59/31.77 137[0:Inp] ssItem(u) || memberP(skc5,u) equal(cons(u,nil),skc4) -> leq(u,skf45(u))*.
% 31.59/31.77 145[0:Inp] ssItem(u) || memberP(skc5,u) equal(skf45(u),u) equal(cons(u,nil),skc4)** -> .
% 31.59/31.77 183[0:Inp] ssItem(u) || memberP(v,u) leq(skf46(v,w),u)* -> SkP0(v,w) equal(skf46(v,w),u).
% 31.59/31.77 191[0:Inp] ssList(u) ssList(v) || equal(tl(u),tl(v))* equal(hd(u),hd(v)) -> equal(u,v) equal(nil,v) equal(nil,u).
% 31.59/31.77 200[0:Rew:69.1,68.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4).
% 31.59/31.77 248[0:Res:2.0,133.0] ssList(u) || -> equal(nil,skc4) equal(hd(app(skc4,u)),hd(skc4))**.
% 31.59/31.77 257[0:Res:2.0,109.0] ssItem(u) || equal(cons(u,skc4),skc4)** -> .
% 31.59/31.77 259[0:Res:2.0,111.0] ssItem(u) || -> equal(hd(cons(u,skc4)),u)**.
% 31.59/31.77 289[0:Res:2.0,191.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(nil,skc4).
% 31.59/31.77 420[0:Res:1.0,128.0] ssItem(u) || -> equal(app(cons(u,nil),skc5),cons(u,skc5))**.
% 31.59/31.77 428[0:Res:1.0,109.0] ssItem(u) || equal(cons(u,skc5),skc5)** -> .
% 31.59/31.77 430[0:Res:1.0,111.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 31.59/31.77 442[0:Res:1.0,91.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 31.59/31.77 452[0:Res:1.0,81.0] || -> equal(app(nil,skc5),skc5)**.
% 31.59/31.77 460[0:Res:1.0,191.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 31.59/31.77 554[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 31.59/31.77 560[2:Spt:460.5] || -> equal(nil,skc5)**.
% 31.59/31.77 589[2:Rew:560.0,79.0] || equal(skc5,skc4) equal(nil,skc5)** -> .
% 31.59/31.77 637[2:Rew:560.0,12.0] || -> equalelemsP(skc5)*.
% 31.59/31.77 638[2:Rew:560.0,11.0] || -> duplicatefreeP(skc5)*.
% 31.59/31.77 639[2:Rew:560.0,10.0] || -> strictorderedP(skc5)*.
% 31.59/31.77 640[2:Rew:560.0,9.0] || -> totalorderedP(skc5)*.
% 31.59/31.77 641[2:Rew:560.0,8.0] || -> strictorderP(skc5)*.
% 31.59/31.77 642[2:Rew:560.0,7.0] || -> totalorderP(skc5)*.
% 31.59/31.77 643[2:Rew:560.0,6.0] || -> cyclefreeP(skc5)*.
% 31.59/31.77 659[2:Rew:560.0,70.1] ssItem(u) || memberP(skc5,u)* -> .
% 31.59/31.77 707[2:Rew:560.0,589.1] || equal(skc5,skc4) equal(skc5,skc5)* -> .
% 31.59/31.77 708[2:Obv:707.1] || equal(skc5,skc4)** -> .
% 31.59/31.77 709[2:MRR:200.1,708.0] || SkP0(skc5,skc4)* -> .
% 31.59/31.77 873[2:Res:80.1,659.1] ssItem(skf46(skc5,u)) || -> SkP0(skc5,u)*.
% 31.59/31.77 874[2:SSi:873.0,52.0,1.0,637.0,638.0,639.0,640.0,641.0,642.0,643.0] || -> SkP0(skc5,u)*.
% 31.59/31.77 875[2:UnC:874.0,709.0] || -> .
% 31.59/31.77 876[2:Spt:875.0,460.5,560.0] || equal(nil,skc5)** -> .
% 31.59/31.77 877[2:Spt:875.0,460.0,460.1,460.2,460.3,460.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 31.59/31.77 893[3:Spt:289.5] || -> equal(nil,skc4)**.
% 31.59/31.77 910[3:Rew:893.0,876.0] || equal(skc5,skc4)** -> .
% 31.59/31.77 944[3:Rew:893.0,81.1] ssList(u) || -> equal(app(skc4,u),u)**.
% 31.59/31.77 973[3:Rew:893.0,87.1] || -> SkP0(u,v) equal(cons(skf46(u,v),skc4),v)**.
% 31.59/31.77 993[3:MRR:200.1,910.0] || SkP0(skc5,skc4)* -> .
% 31.59/31.77 1018[3:Rew:944.1,554.1] ssList(u) || -> equal(hd(u),hd(skc4))*.
% 31.59/31.77 1129[3:SpR:430.1,1018.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(skc4))*.
% 31.59/31.77 1132[3:SSi:1129.1,442.1] ssItem(u) || -> equal(u,hd(skc4))*.
% 31.59/31.77 1306[3:SpR:973.1,259.1] ssItem(skf46(u,v)) || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 31.59/31.77 1321[3:SSi:1306.0,52.0] || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 31.59/31.77 1323[3:Rew:1321.1,973.1] || -> SkP0(u,v)* equal(cons(hd(v),skc4),v)**.
% 31.59/31.77 1355[3:SpR:1132.1,1323.1] ssItem(u) || -> SkP0(v,skc4)* equal(cons(u,skc4),skc4)**.
% 31.59/31.77 1361[3:MRR:1355.2,257.1] ssItem(u) || -> SkP0(v,skc4)*.
% 31.59/31.77 1384[3:EmS:1361.0,4.0] || -> SkP0(u,skc4)*.
% 31.59/31.77 1406[3:UnC:1384.0,993.0] || -> .
% 31.59/31.77 1407[3:Spt:1406.0,289.5,893.0] || equal(nil,skc4)** -> .
% 31.59/31.77 1408[3:Spt:1406.0,289.0,289.1,289.2,289.3,289.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 31.59/31.77 1414[3:MRR:69.1,1407.0] || SkP0(skc5,skc4)* -> .
% 31.59/31.77 1687[0:SpR:87.1,111.2] ssItem(skf46(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 31.59/31.77 1691[0:SSi:1687.1,1687.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0,52.0] || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 31.59/31.77 1692[0:Rew:1691.1,80.1] || -> SkP0(u,v) memberP(u,hd(v))*.
% 31.59/31.77 1693[0:Rew:1691.1,87.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 31.59/31.77 1694[0:Rew:1691.1,183.2] ssItem(u) || memberP(v,u)* leq(hd(w),u)* -> SkP0(v,w) equal(skf46(v,w),u)*.
% 31.59/31.77 1697[0:Rew:1691.1,1694.4] ssItem(u) || memberP(v,u)* leq(hd(w),u)*+ -> SkP0(v,w)* equal(hd(w),u).
% 31.59/31.77 1784[0:SpR:1691.1,52.0] || -> SkP0(u,v)* ssItem(hd(v)).
% 31.59/31.77 2009[0:SpR:1693.1,420.1] ssItem(hd(u)) || -> SkP0(v,u)* equal(cons(hd(u),skc5),app(u,skc5))**.
% 31.59/31.77 2013[0:MRR:2009.0,1784.1] || -> SkP0(u,v)* equal(cons(hd(v),skc5),app(v,skc5))**.
% 31.59/31.77 2124[0:SpL:2013.1,428.1] ssItem(hd(u)) || equal(app(u,skc5),skc5)** -> SkP0(v,u)*.
% 31.59/31.77 2132[0:MRR:2124.0,1784.1] || equal(app(u,skc5),skc5)**+ -> SkP0(v,u)*.
% 31.59/31.77 2280[0:SpL:452.0,2132.0] || equal(skc5,skc5) -> SkP0(u,nil)*.
% 31.59/31.77 2284[0:Obv:2280.0] || -> SkP0(u,nil)*.
% 31.59/31.77 3164[0:SpL:1693.1,145.3] ssItem(hd(u)) || memberP(skc5,hd(u))* equal(skf45(hd(u)),hd(u)) equal(u,skc4) -> SkP0(v,u)*.
% 31.59/31.77 3168[0:MRR:3164.0,1784.1] || memberP(skc5,hd(u))* equal(skf45(hd(u)),hd(u)) equal(u,skc4) -> SkP0(v,u)*.
% 31.59/31.77 4387[0:Res:137.3,1697.2] ssItem(hd(u)) ssItem(skf45(hd(u))) || memberP(skc5,hd(u)) equal(cons(hd(u),nil),skc4) memberP(v,skf45(hd(u)))* -> SkP0(v,u) equal(skf45(hd(u)),hd(u)).
% 31.59/31.77 4403[0:Rew:1693.1,4387.3] ssItem(hd(u)) ssItem(skf45(hd(u))) || memberP(skc5,hd(u)) equal(u,skc4) memberP(v,skf45(hd(u)))* -> SkP0(v,u) equal(skf45(hd(u)),hd(u)).
% 31.59/31.77 4404[0:SSi:4403.1,13.0] ssItem(hd(u)) || memberP(skc5,hd(u)) equal(u,skc4) memberP(v,skf45(hd(u)))* -> SkP0(v,u) equal(skf45(hd(u)),hd(u)).
% 31.59/31.77 4405[0:MRR:4404.0,1784.1] || memberP(skc5,hd(u)) equal(u,skc4) memberP(v,skf45(hd(u)))* -> SkP0(v,u) equal(skf45(hd(u)),hd(u)).
% 31.59/31.77 4406[0:MRR:4405.4,3168.1] || memberP(skc5,hd(u)) equal(u,skc4) memberP(v,skf45(hd(u)))* -> SkP0(v,u).
% 31.59/31.77 31156[0:Res:136.3,4406.2] ssItem(hd(u)) || memberP(skc5,hd(u)) equal(cons(hd(u),nil),skc4)** memberP(skc5,hd(u)) equal(u,skc4) -> SkP0(skc5,u).
% 31.59/31.77 31197[0:Obv:31156.1] ssItem(hd(u)) || equal(cons(hd(u),nil),skc4)** memberP(skc5,hd(u)) equal(u,skc4) -> SkP0(skc5,u).
% 31.59/31.77 31198[0:Rew:1693.1,31197.1] ssItem(hd(u)) || equal(u,skc4) memberP(skc5,hd(u))* equal(u,skc4) -> SkP0(skc5,u).
% 31.59/31.77 31199[0:Obv:31198.1] ssItem(hd(u)) || memberP(skc5,hd(u))* equal(u,skc4) -> SkP0(skc5,u).
% 31.59/31.77 31200[0:MRR:31199.0,31199.1,1784.1,1692.1] || equal(u,skc4) -> SkP0(skc5,u)*.
% 31.59/31.77 31217[3:Res:31200.1,1414.0] || equal(skc4,skc4)* -> .
% 31.59/31.77 31218[3:Obv:31217.0] || -> .
% 31.59/31.77 31219[1:Spt:31218.0,248.1] || -> equal(nil,skc4)**.
% 31.59/31.77 31846[1:Rew:31219.0,2284.0] || -> SkP0(u,skc4)*.
% 31.59/31.77 31906[1:MRR:200.0,31846.0] || -> equal(skc5,skc4)**.
% 31.59/31.77 32411[1:Rew:31219.0,79.1,31906.0,79.1,31219.0,79.0] || equal(skc4,skc4)* equal(skc4,skc4)* -> .
% 31.59/31.77 32412[1:Obv:32411.1] || -> .
% 37.26/37.46 % SZS output end Refutation
% 37.26/37.46 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax28 ax16 ax18 ax23 ax81 ax85 ax77
% 37.26/37.46
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