TSTP Solution File: SWC029+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC029+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 22:01:12 EDT 2022
% Result : Theorem 1.20s 1.40s
% Output : Refutation 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC029+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 22:46:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.20/1.40
% 1.20/1.40 SPASS V 3.9
% 1.20/1.40 SPASS beiseite: Proof found.
% 1.20/1.40 % SZS status Theorem
% 1.20/1.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/1.40 SPASS derived 2211 clauses, backtracked 864 clauses, performed 31 splits and kept 2063 clauses.
% 1.20/1.40 SPASS allocated 100427 KBytes.
% 1.20/1.40 SPASS spent 0:00:01.03 on the problem.
% 1.20/1.40 0:00:00.04 for the input.
% 1.20/1.40 0:00:00.07 for the FLOTTER CNF translation.
% 1.20/1.40 0:00:00.01 for inferences.
% 1.20/1.40 0:00:00.01 for the backtracking.
% 1.20/1.40 0:00:00.66 for the reduction.
% 1.20/1.40
% 1.20/1.40
% 1.20/1.40 Here is a proof with depth 6, length 104 :
% 1.20/1.40 % SZS output start Refutation
% 1.20/1.40 1[0:Inp] || -> ssList(skc9)*.
% 1.20/1.40 2[0:Inp] || -> ssItem(skc8)*.
% 1.20/1.40 3[0:Inp] || -> ssList(skc7)*.
% 1.20/1.40 4[0:Inp] || -> ssList(skc6)*.
% 1.20/1.40 5[0:Inp] || -> ssItem(skc11)*.
% 1.20/1.40 6[0:Inp] || -> ssItem(skc10)*.
% 1.20/1.40 7[0:Inp] || -> ssList(nil)*.
% 1.20/1.40 8[0:Inp] || -> cyclefreeP(nil)*.
% 1.20/1.40 9[0:Inp] || -> totalorderP(nil)*.
% 1.20/1.40 10[0:Inp] || -> strictorderP(nil)*.
% 1.20/1.40 11[0:Inp] || -> totalorderedP(nil)*.
% 1.20/1.40 12[0:Inp] || -> strictorderedP(nil)*.
% 1.20/1.40 13[0:Inp] || -> duplicatefreeP(nil)*.
% 1.20/1.40 14[0:Inp] || -> equalelemsP(nil)*.
% 1.20/1.40 53[0:Inp] || equal(skc11,skc10)** -> .
% 1.20/1.40 60[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 1.20/1.40 69[0:Inp] || equal(skc7,nil)** -> equal(skc6,nil).
% 1.20/1.40 70[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 1.20/1.40 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 1.20/1.40 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 1.20/1.40 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 1.20/1.40 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 1.20/1.40 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 1.20/1.40 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 1.20/1.40 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 1.20/1.40 80[0:Inp] || SkP0(skc7,skc6)* SkP0(skc6,skc7) -> .
% 1.20/1.40 81[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 1.20/1.40 90[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 1.20/1.40 98[0:Inp] || neq(skc7,nil) -> equal(app(cons(skc8,nil),skc9),skc7)**.
% 1.20/1.40 99[0:Inp] || neq(skc7,nil) -> equal(app(skc9,cons(skc8,nil)),skc6)**.
% 1.20/1.40 109[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 1.20/1.40 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 1.20/1.40 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 1.20/1.40 129[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 1.20/1.40 131[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 1.20/1.40 134[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 1.20/1.40 188[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).
% 1.20/1.40 244[0:Res:4.0,134.0] ssList(u) || -> equal(skc6,nil) equal(hd(app(skc6,u)),hd(skc6))**.
% 1.20/1.40 245[0:Res:4.0,129.0] ssItem(u) || -> equal(app(cons(u,nil),skc6),cons(u,skc6))**.
% 1.20/1.40 267[0:Res:4.0,90.0] ssItem(u) || -> ssList(cons(u,skc6))*.
% 1.20/1.40 285[0:Res:4.0,188.1] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u) equal(skc6,nil).
% 1.20/1.40 423[0:Res:3.0,109.0] ssList(u) || -> neq(skc7,u)* equal(skc7,u).
% 1.20/1.40 426[0:Res:3.0,112.0] ssItem(u) || -> equal(hd(cons(u,skc7)),u)**.
% 1.20/1.40 438[0:Res:3.0,90.0] ssItem(u) || -> ssList(cons(u,skc7))*.
% 1.20/1.40 448[0:Res:3.0,81.0] || -> equal(app(nil,skc7),skc7)**.
% 1.20/1.40 456[0:Res:3.0,188.1] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u) equal(skc7,nil).
% 1.20/1.40 548[1:Spt:244.0,244.2] ssList(u) || -> equal(hd(app(skc6,u)),hd(skc6))**.
% 1.20/1.40 552[2:Spt:456.5] || -> equal(skc7,nil)**.
% 1.20/1.40 559[2:Rew:552.0,69.0] || equal(nil,nil) -> equal(skc6,nil)**.
% 1.20/1.40 667[2:Rew:552.0,80.0] || SkP0(nil,skc6) SkP0(skc6,skc7)* -> .
% 1.20/1.40 707[2:Obv:559.0] || -> equal(skc6,nil)**.
% 1.20/1.40 885[2:Rew:707.0,667.1,552.0,667.1,707.0,667.0] || SkP0(nil,nil)* SkP0(nil,nil)* -> .
% 1.20/1.40 886[2:Obv:885.0] || SkP0(nil,nil)* -> .
% 1.20/1.40 1060[2:Res:70.1,886.0] || equal(nil,nil)* -> .
% 1.20/1.40 1061[2:Obv:1060.0] || -> .
% 1.20/1.40 1062[2:Spt:1061.0,456.5,552.0] || equal(skc7,nil)** -> .
% 1.20/1.40 1063[2:Spt:1061.0,456.0,456.1,456.2,456.3,456.4] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u).
% 1.20/1.40 1078[3:Spt:285.5] || -> equal(skc6,nil)**.
% 1.20/1.40 1107[3:Rew:1078.0,548.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 1.20/1.40 1249[3:Rew:81.1,1107.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 1.20/1.40 1412[3:SpR:426.1,1249.1] ssItem(u) ssList(cons(u,skc7)) || -> equal(u,hd(nil))*.
% 1.20/1.40 1415[3:SSi:1412.1,438.1] ssItem(u) || -> equal(u,hd(nil))*.
% 1.20/1.40 1503[3:SpR:1415.1,1415.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 1.20/1.40 1606[3:EmS:1503.0,2.0] ssItem(u) || -> equal(u,skc8)*.
% 1.20/1.40 1633[3:EmS:1606.0,5.0] || -> equal(skc11,skc8)**.
% 1.20/1.40 1634[3:EmS:1606.0,6.0] || -> equal(skc10,skc8)**.
% 1.20/1.40 1636[3:Rew:1633.0,53.0] || equal(skc10,skc8)** -> .
% 1.20/1.40 1790[3:Rew:1634.0,1636.0] || equal(skc8,skc8)* -> .
% 1.20/1.40 1791[3:Obv:1790.0] || -> .
% 1.20/1.40 1843[3:Spt:1791.0,285.5,1078.0] || equal(skc6,nil)** -> .
% 1.20/1.40 1844[3:Spt:1791.0,285.0,285.1,285.2,285.3,285.4] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u).
% 1.20/1.40 1891[0:Res:70.1,80.0] || equal(skc7,nil) SkP0(skc6,skc7)* -> .
% 1.20/1.40 1892[0:Res:60.0,80.0] || SkP0(skc6,skc7)* -> equal(skc6,nil).
% 1.20/1.40 1893[3:MRR:1892.1,1843.0] || SkP0(skc6,skc7)* -> .
% 1.20/1.40 1895[3:Res:60.0,1893.0] || -> equal(skc7,nil)**.
% 1.20/1.40 1896[3:MRR:1895.0,1062.0] || -> .
% 1.20/1.40 1897[1:Spt:1896.0,244.1] || -> equal(skc6,nil)**.
% 1.20/1.40 1909[1:Rew:1897.0,267.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 1.20/1.40 1948[1:Rew:1897.0,99.1] || neq(skc7,nil) -> equal(app(skc9,cons(skc8,nil)),nil)**.
% 1.20/1.40 1949[1:Rew:1897.0,245.1] ssItem(u) || -> equal(app(cons(u,nil),nil),cons(u,nil))**.
% 1.20/1.40 2035[1:Rew:1897.0,1891.1] || equal(skc7,nil) SkP0(nil,skc7)* -> .
% 1.20/1.40 2143[2:Spt:456.5] || -> equal(skc7,nil)**.
% 1.20/1.40 2280[2:Rew:2143.0,2035.0] || equal(nil,nil) SkP0(nil,skc7)* -> .
% 1.20/1.40 2307[2:Obv:2280.0] || SkP0(nil,skc7)* -> .
% 1.20/1.40 2308[2:Rew:2143.0,2307.0] || SkP0(nil,nil)* -> .
% 1.20/1.40 2393[2:Res:70.1,2308.0] || equal(nil,nil)* -> .
% 1.20/1.40 2395[2:Obv:2393.0] || -> .
% 1.20/1.40 2396[2:Spt:2395.0,456.5,2143.0] || equal(skc7,nil)** -> .
% 1.20/1.40 2397[2:Spt:2395.0,456.0,456.1,456.2,456.3,456.4] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u).
% 1.20/1.40 3099[0:EqR:122.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.20/1.40 3103[1:SSi:3099.0,78.1,77.1,74.1,73.1,72.1,76.1,75.1,1909.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.20/1.40 3253[1:SpL:1948.1,131.2] ssList(cons(skc8,nil)) ssList(skc9) || neq(skc7,nil)* equal(nil,nil) -> equal(skc9,nil).
% 1.20/1.40 3255[1:Obv:3253.3] ssList(cons(skc8,nil)) ssList(skc9) || neq(skc7,nil)* -> equal(skc9,nil).
% 1.20/1.40 3256[1:SSi:3255.1,3255.0,1.0,78.1,2.0,77.1,2.0,74.1,2.0,73.1,2.0,72.1,2.0,76.1,2.0,75.1,2.0,1909.1,2.0,3103.1,2.0] || neq(skc7,nil)* -> equal(skc9,nil).
% 1.20/1.40 3257[1:Rew:3256.1,98.1] || neq(skc7,nil) -> equal(app(cons(skc8,nil),nil),skc7)**.
% 1.20/1.40 3258[1:Rew:3256.1,1948.1] || neq(skc7,nil) -> equal(app(nil,cons(skc8,nil)),nil)**.
% 1.20/1.40 3274[1:SpR:3257.1,1949.1] ssItem(skc8) || neq(skc7,nil) -> equal(cons(skc8,nil),skc7)**.
% 1.20/1.40 3280[1:SSi:3274.0,2.0] || neq(skc7,nil) -> equal(cons(skc8,nil),skc7)**.
% 1.20/1.40 3282[1:Rew:3280.1,3258.1] || neq(skc7,nil) -> equal(app(nil,skc7),nil)**.
% 1.20/1.40 3283[1:Rew:448.0,3282.1] || neq(skc7,nil)* -> equal(skc7,nil).
% 1.20/1.40 3284[2:MRR:3283.1,2396.0] || neq(skc7,nil)* -> .
% 1.20/1.40 3286[2:Res:423.1,3284.0] ssList(nil) || -> equal(skc7,nil)**.
% 1.20/1.40 3291[2:SSi:3286.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc7,nil)**.
% 1.20/1.40 3292[2:MRR:3291.0,2396.0] || -> .
% 1.20/1.40 % SZS output end Refutation
% 1.20/1.40 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax16 ax15 ax23 ax4 ax81 ax83 ax85 ax77
% 1.20/1.40
%------------------------------------------------------------------------------