TSTP Solution File: SWC112+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC112+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:01:48 EDT 2022
% Result : Theorem 28.75s 28.97s
% Output : Refutation 35.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC112+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 15:55:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 28.75/28.97
% 28.75/28.97 SPASS V 3.9
% 28.75/28.97 SPASS beiseite: Proof found.
% 28.75/28.97 % SZS status Theorem
% 28.75/28.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.75/28.97 SPASS derived 26884 clauses, backtracked 7615 clauses, performed 97 splits and kept 14325 clauses.
% 28.75/28.97 SPASS allocated 129860 KBytes.
% 28.75/28.97 SPASS spent 0:0:28.58 on the problem.
% 28.75/28.97 0:00:00.04 for the input.
% 28.75/28.97 0:00:00.07 for the FLOTTER CNF translation.
% 28.75/28.97 0:00:00.35 for inferences.
% 28.75/28.97 0:00:00.66 for the backtracking.
% 28.75/28.97 0:0:27.04 for the reduction.
% 28.75/28.97
% 28.75/28.97
% 28.75/28.97 Here is a proof with depth 6, length 135 :
% 28.75/28.97 % SZS output start Refutation
% 28.75/28.97 1[0:Inp] || -> ssList(skc9)*.
% 28.75/28.97 2[0:Inp] || -> ssList(skc8)*.
% 28.75/28.97 3[0:Inp] || -> ssList(skc7)*.
% 28.75/28.97 4[0:Inp] || -> ssList(skc6)*.
% 28.75/28.97 5[0:Inp] || -> strictorderedP(skc6)*.
% 28.75/28.97 6[0:Inp] || -> ssItem(skc11)*.
% 28.75/28.97 7[0:Inp] || -> ssItem(skc10)*.
% 28.75/28.97 8[0:Inp] || -> ssList(nil)*.
% 28.75/28.97 9[0:Inp] || -> cyclefreeP(nil)*.
% 28.75/28.97 10[0:Inp] || -> totalorderP(nil)*.
% 28.75/28.97 11[0:Inp] || -> strictorderP(nil)*.
% 28.75/28.97 12[0:Inp] || -> totalorderedP(nil)*.
% 28.75/28.97 13[0:Inp] || -> strictorderedP(nil)*.
% 28.75/28.97 14[0:Inp] || -> duplicatefreeP(nil)*.
% 28.75/28.97 15[0:Inp] || -> equalelemsP(nil)*.
% 28.75/28.97 32[0:Inp] || -> ssList(skf69(u))*.
% 28.75/28.97 33[0:Inp] || -> ssList(skf68(u))*.
% 28.75/28.97 34[0:Inp] || -> ssList(skf67(u))*.
% 28.75/28.97 35[0:Inp] || -> ssItem(skf66(u))*.
% 28.75/28.97 36[0:Inp] || -> ssItem(skf65(u))*.
% 28.75/28.97 54[0:Inp] || equal(skc11,skc10)** -> .
% 28.75/28.97 61[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 28.75/28.97 67[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 28.75/28.97 68[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 28.75/28.97 70[0:Inp] || -> equal(app(app(skc8,skc6),skc9),skc7)**.
% 28.75/28.97 71[0:Inp] || equal(skc6,nil) -> equal(skc7,nil)**.
% 28.75/28.97 72[0:Inp] || SkP0(skc6,skc7) -> neq(skc7,nil)*.
% 28.75/28.97 73[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 28.75/28.97 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 28.75/28.97 84[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 28.75/28.97 92[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 28.75/28.97 93[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 28.75/28.97 96[0:Inp] ssList(u) || rearsegP(nil,u)* -> equal(nil,u).
% 28.75/28.97 104[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 28.75/28.97 107[0:Inp] || SkP0(skc6,skc7) segmentP(skc7,skc6)* neq(skc6,nil) -> .
% 28.75/28.97 110[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 28.75/28.97 113[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 28.75/28.97 121[0:Inp] ssItem(u) ssItem(v) || lt(v,u) -> leq(v,u)*.
% 28.75/28.97 124[0:Inp] ssList(u) ssList(v) || equal(v,u) neq(v,u)* -> .
% 28.75/28.97 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 28.75/28.97 146[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 28.75/28.97 154[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 28.75/28.97 155[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u)) -> lt(v,hd(u))* equal(nil,u).
% 28.75/28.97 161[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 28.75/28.97 176[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 28.75/28.97 182[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(u,v) -> segmentP(app(app(w,u),x),v)*.
% 28.75/28.97 194[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) ssItem(y) ssItem(z) strictorderedP(u) || equal(app(app(x,cons(z,w)),cons(y,v)),u)* -> lt(z,y).
% 28.75/28.97 203[0:Rew:161.3,182.5] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(x,w) -> segmentP(app(v,app(x,u)),w)*.
% 28.75/28.97 227[0:Res:4.0,176.0] || -> totalorderedP(skc6) equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 28.75/28.97 259[0:Res:4.0,110.0] ssList(u) || -> neq(skc6,u)* equal(skc6,u).
% 28.75/28.97 262[0:Res:4.0,113.0] ssItem(u) || -> equal(hd(cons(u,skc6)),u)**.
% 28.75/28.97 268[0:Res:4.0,104.0] || leq(skf65(skc6),skf66(skc6))* -> totalorderedP(skc6).
% 28.75/28.97 274[0:Res:4.0,92.0] ssItem(u) || -> ssList(cons(u,skc6))*.
% 28.75/28.97 275[0:Res:4.0,93.0] ssList(u) || -> ssList(app(skc6,u))*.
% 28.75/28.97 278[0:Res:4.0,96.0] || rearsegP(nil,skc6)* -> equal(skc6,nil).
% 28.75/28.97 285[0:Res:4.0,84.0] || -> equal(app(skc6,nil),skc6)**.
% 28.75/28.97 290[0:Res:4.0,67.0] || -> segmentP(skc6,skc6)*.
% 28.75/28.97 291[0:Res:4.0,68.0] || -> segmentP(skc6,nil)*.
% 28.75/28.97 316[0:Res:4.0,154.1] ssItem(u) || totalorderedP(cons(u,skc6))* -> leq(u,hd(skc6)) equal(skc6,nil).
% 28.75/28.97 334[0:Res:4.0,93.1] ssList(u) || -> ssList(app(u,skc6))*.
% 28.75/28.97 426[0:Res:3.0,135.0] ssList(u) || -> equal(skc7,nil) equal(hd(app(skc7,u)),hd(skc7))**.
% 28.75/28.97 430[0:Res:3.0,124.0] ssList(u) || equal(skc7,u) neq(skc7,u)* -> .
% 28.75/28.97 492[0:Res:3.0,155.1] ssItem(u) || strictorderedP(cons(u,skc7)) -> lt(u,hd(skc7))* equal(skc7,nil).
% 28.75/28.97 565[1:Spt:426.0,426.2] ssList(u) || -> equal(hd(app(skc7,u)),hd(skc7))**.
% 28.75/28.97 569[2:Spt:316.3] || -> equal(skc6,nil)**.
% 28.75/28.97 572[2:Rew:569.0,107.0] || SkP0(nil,skc7) segmentP(skc7,skc6)* neq(skc6,nil) -> .
% 28.75/28.97 573[2:Rew:569.0,72.0] || SkP0(nil,skc7) -> neq(skc7,nil)*.
% 28.75/28.97 578[2:Rew:569.0,71.0] || equal(nil,nil) -> equal(skc7,nil)**.
% 28.75/28.97 677[2:Rew:569.0,291.0] || -> segmentP(nil,nil)*.
% 28.75/28.97 731[2:Obv:578.0] || -> equal(skc7,nil)**.
% 28.75/28.97 882[2:Rew:731.0,573.0] || SkP0(nil,nil) -> neq(skc7,nil)*.
% 28.75/28.97 904[2:Rew:731.0,882.1] || SkP0(nil,nil) -> neq(nil,nil)*.
% 28.75/28.97 939[2:Rew:569.0,572.2,731.0,572.1,569.0,572.1,731.0,572.0] || SkP0(nil,nil) segmentP(nil,nil)* neq(nil,nil) -> .
% 28.75/28.97 940[2:MRR:939.1,939.2,677.0,904.1] || SkP0(nil,nil)* -> .
% 28.75/28.97 1090[2:Res:73.1,940.0] || equal(nil,nil)* -> .
% 28.75/28.97 1091[2:Obv:1090.0] || -> .
% 28.75/28.97 1092[2:Spt:1091.0,316.3,569.0] || equal(skc6,nil)** -> .
% 28.75/28.97 1093[2:Spt:1091.0,316.0,316.1,316.2] ssItem(u) || totalorderedP(cons(u,skc6))* -> leq(u,hd(skc6)).
% 28.75/28.97 1106[3:Spt:492.3] || -> equal(skc7,nil)**.
% 28.75/28.97 1138[3:Rew:1106.0,565.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 28.75/28.97 1282[3:Rew:83.1,1138.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 28.75/28.97 1427[3:SpR:262.1,1282.1] ssItem(u) ssList(cons(u,skc6)) || -> equal(u,hd(nil))*.
% 28.75/28.97 1430[3:SSi:1427.1,274.1] ssItem(u) || -> equal(u,hd(nil))*.
% 28.75/28.97 1524[3:SpR:1430.1,1430.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 28.75/28.97 1656[3:EmS:1524.0,6.0] ssItem(u) || -> equal(u,skc11)*.
% 28.75/28.97 1678[3:EmS:1656.0,7.0] || -> equal(skc11,skc10)**.
% 28.75/28.97 1679[3:MRR:1678.0,54.0] || -> .
% 28.75/28.97 1903[3:Spt:1679.0,492.3,1106.0] || equal(skc7,nil)** -> .
% 28.75/28.97 1904[3:Spt:1679.0,492.0,492.1,492.2] ssItem(u) || strictorderedP(cons(u,skc7)) -> lt(u,hd(skc7))*.
% 28.75/28.97 1921[4:Spt:227.0] || -> totalorderedP(skc6)*.
% 28.75/28.97 1993[0:Res:72.1,430.2] ssList(nil) || SkP0(skc6,skc7)* equal(skc7,nil) -> .
% 28.75/28.97 4047[0:EqR:146.3] ssList(u) ssList(app(v,u)) ssList(v) || -> rearsegP(app(v,u),u)*.
% 28.75/28.97 4058[0:SpL:70.0,146.3] ssList(skc9) ssList(u) ssList(app(skc8,skc6)) || equal(skc7,u) -> rearsegP(u,skc9)*.
% 28.75/28.97 4062[0:SSi:4047.1,93.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 28.75/28.97 4065[0:SSi:4058.2,4058.0,334.0,2.0,1.1] ssList(u) || equal(skc7,u) -> rearsegP(u,skc9)*.
% 28.75/28.97 4098[0:Res:4065.2,96.1] ssList(nil) ssList(skc9) || equal(skc7,nil) -> equal(skc9,nil)**.
% 28.75/28.97 4473[0:SpR:161.3,70.0] ssList(skc9) ssList(skc6) ssList(skc8) || -> equal(app(skc8,app(skc6,skc9)),skc7)**.
% 28.75/28.97 15868[4:SSi:4473.2,4473.1,4473.0,2.0,4.0,5.0,1921.0,1.0] || -> equal(app(skc8,app(skc6,skc9)),skc7)**.
% 28.75/28.97 16473[4:SpR:15868.0,203.5] ssList(skc9) ssList(skc8) ssList(u) ssList(skc6) || segmentP(skc6,u) -> segmentP(skc7,u)*.
% 28.75/28.97 23455[4:SSi:16473.3,16473.1,16473.0,4.0,5.0,1921.0,2.0,1.0] ssList(u) || segmentP(skc6,u) -> segmentP(skc7,u)*.
% 28.75/28.97 27089[4:Res:23455.2,107.1] ssList(skc6) || segmentP(skc6,skc6)* SkP0(skc6,skc7) neq(skc6,nil) -> .
% 28.75/28.97 27110[4:SSi:27089.0,4.0,5.0,1921.0] || segmentP(skc6,skc6)* SkP0(skc6,skc7) neq(skc6,nil) -> .
% 28.75/28.97 27111[4:MRR:27110.0,290.0] || SkP0(skc6,skc7) neq(skc6,nil)* -> .
% 28.75/28.97 27757[4:Res:259.1,27111.1] ssList(nil) || SkP0(skc6,skc7)* -> equal(skc6,nil).
% 28.75/28.97 27760[4:SSi:27757.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0] || SkP0(skc6,skc7)* -> equal(skc6,nil).
% 28.75/28.97 27761[4:MRR:27760.1,1092.0] || SkP0(skc6,skc7)* -> .
% 28.75/28.97 27771[4:Res:61.0,27761.0] || -> equal(skc7,nil)**.
% 28.75/28.97 27772[4:MRR:27771.0,1903.0] || -> .
% 28.75/28.97 27773[4:Spt:27772.0,227.0,1921.0] || totalorderedP(skc6)* -> .
% 28.75/28.97 27774[4:Spt:27772.0,227.1] || -> equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 28.75/28.97 27775[4:MRR:268.1,27773.0] || leq(skf65(skc6),skf66(skc6))* -> .
% 28.75/28.97 27805[0:SSi:4473.2,4473.1,4473.0,2.0,4.0,5.0,1.0] || -> equal(app(skc8,app(skc6,skc9)),skc7)**.
% 28.75/28.97 27935[4:SpL:27774.0,194.7] ssList(u) ssList(skf69(skc6)) ssList(skf68(skc6)) ssList(skf67(skc6)) ssItem(skf66(skc6)) ssItem(skf65(skc6)) strictorderedP(u) || equal(skc6,u)* -> lt(skf65(skc6),skf66(skc6))*.
% 28.75/28.97 27947[4:SSi:27935.5,27935.4,27935.3,27935.2,27935.1,36.0,4.0,5.0,35.0,4.0,5.0,34.0,4.0,5.0,33.0,4.0,5.0,32.0,4.0,5.0] ssList(u) strictorderedP(u) || equal(skc6,u)* -> lt(skf65(skc6),skf66(skc6))*.
% 35.16/35.36 28016[4:Res:121.3,27775.0] ssItem(skf66(skc6)) ssItem(skf65(skc6)) || lt(skf65(skc6),skf66(skc6))* -> .
% 35.16/35.36 28217[0:SpR:27805.0,4062.2] ssList(app(skc6,skc9)) ssList(skc8) || -> rearsegP(skc7,app(skc6,skc9))*.
% 35.16/35.36 28237[0:SSi:28217.1,28217.0,2.0,275.1,1.0] || -> rearsegP(skc7,app(skc6,skc9))*.
% 35.16/35.36 35270[4:SSi:28016.1,28016.0,36.0,4.0,5.0,35.0,4.0,5.0] || lt(skf65(skc6),skf66(skc6))* -> .
% 35.16/35.36 35272[4:MRR:27947.3,35270.0] ssList(u) strictorderedP(u) || equal(skc6,u)* -> .
% 35.16/35.36 38553[4:EmS:35272.0,35272.1,4.0,5.0] || equal(skc6,skc6)* -> .
% 35.16/35.36 38560[4:Obv:38553.0] || -> .
% 35.16/35.36 38568[1:Spt:38560.0,426.1] || -> equal(skc7,nil)**.
% 35.16/35.36 38633[1:Rew:38568.0,28237.0] || -> rearsegP(nil,app(skc6,skc9))*.
% 35.16/35.36 38934[1:Rew:38568.0,1993.2,38568.0,1993.1] ssList(nil) || SkP0(skc6,nil)* equal(nil,nil) -> .
% 35.16/35.36 38935[1:Obv:38934.2] ssList(nil) || SkP0(skc6,nil)* -> .
% 35.16/35.36 38936[1:SSi:38935.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0] || SkP0(skc6,nil)* -> .
% 35.16/35.36 38981[1:Rew:38568.0,4098.2] ssList(nil) ssList(skc9) || equal(nil,nil) -> equal(skc9,nil)**.
% 35.16/35.36 38982[1:Obv:38981.2] ssList(nil) ssList(skc9) || -> equal(skc9,nil)**.
% 35.16/35.36 38983[1:SSi:38982.1,38982.0,1.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0] || -> equal(skc9,nil)**.
% 35.16/35.36 39007[1:Rew:38983.0,38633.0] || -> rearsegP(nil,app(skc6,nil))*.
% 35.16/35.36 39024[1:Rew:285.0,39007.0] || -> rearsegP(nil,skc6)*.
% 35.16/35.36 39025[1:MRR:278.0,39024.0] || -> equal(skc6,nil)**.
% 35.16/35.36 39334[1:Rew:39025.0,38936.0] || SkP0(nil,nil)* -> .
% 35.16/35.36 40863[1:Res:73.1,39334.0] || equal(nil,nil)* -> .
% 35.16/35.36 40865[1:Obv:40863.0] || -> .
% 35.16/35.36 % SZS output end Refutation
% 35.16/35.36 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax11 ax55 ax57 ax28 ax84 ax16 ax26 ax52 ax15 ax23 ax93 ax85 ax6 ax67 ax70 ax82 ax56 ax12
% 35.16/35.36
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