TSTP Solution File: SWC165+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC165+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 22:02:11 EDT 2022

% Result   : Theorem 13.93s 14.12s
% Output   : Refutation 14.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWC165+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 12 12:41:43 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 13.93/14.12  
% 13.93/14.12  SPASS V 3.9 
% 13.93/14.12  SPASS beiseite: Proof found.
% 13.93/14.12  % SZS status Theorem
% 13.93/14.12  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 13.93/14.12  SPASS derived 10173 clauses, backtracked 5533 clauses, performed 48 splits and kept 8623 clauses.
% 13.93/14.12  SPASS allocated 113635 KBytes.
% 13.93/14.12  SPASS spent	0:0:13.76 on the problem.
% 13.93/14.12  		0:00:00.04 for the input.
% 13.93/14.12  		0:00:00.07 for the FLOTTER CNF translation.
% 13.93/14.12  		0:00:00.12 for inferences.
% 13.93/14.12  		0:00:00.47 for the backtracking.
% 13.93/14.12  		0:0:12.85 for the reduction.
% 13.93/14.12  
% 13.93/14.12  
% 13.93/14.12  Here is a proof with depth 6, length 130 :
% 13.93/14.12  % SZS output start Refutation
% 13.93/14.12  1[0:Inp] ||  -> ssList(skc13)*.
% 13.93/14.12  2[0:Inp] ||  -> ssList(skc12)*.
% 13.93/14.12  3[0:Inp] ||  -> ssItem(skc11)*.
% 13.93/14.12  4[0:Inp] ||  -> ssItem(skc10)*.
% 13.93/14.12  5[0:Inp] ||  -> ssList(skc9)*.
% 13.93/14.12  6[0:Inp] ||  -> ssList(skc8)*.
% 13.93/14.12  7[0:Inp] ||  -> ssItem(skc15)*.
% 13.93/14.12  8[0:Inp] ||  -> ssItem(skc14)*.
% 13.93/14.12  9[0:Inp] ||  -> ssList(nil)*.
% 13.93/14.12  10[0:Inp] ||  -> cyclefreeP(nil)*.
% 13.93/14.12  11[0:Inp] ||  -> totalorderP(nil)*.
% 13.93/14.12  12[0:Inp] ||  -> strictorderP(nil)*.
% 13.93/14.12  13[0:Inp] ||  -> totalorderedP(nil)*.
% 13.93/14.12  14[0:Inp] ||  -> strictorderedP(nil)*.
% 13.93/14.12  15[0:Inp] ||  -> duplicatefreeP(nil)*.
% 13.93/14.12  16[0:Inp] ||  -> equalelemsP(nil)*.
% 13.93/14.12  17[0:Inp] ||  -> ssItem(skf51(u))*.
% 13.93/14.12  57[0:Inp] ||  -> ssItem(skf46(u,v))*.
% 13.93/14.12  58[0:Inp] || neq(skc10,skc11)* -> .
% 13.93/14.12  59[0:Inp] || equal(skc15,skc14)** -> .
% 13.93/14.12  74[0:Inp] || SkP0(skc9,skc8)* -> equal(nil,skc9).
% 13.93/14.12  75[0:Inp] || SkP0(skc9,skc8)* -> equal(nil,skc8).
% 13.93/14.12  77[0:Inp] ssItem(u) ||  -> cyclefreeP(cons(u,nil))*.
% 13.93/14.12  78[0:Inp] ssItem(u) ||  -> totalorderP(cons(u,nil))*.
% 13.93/14.12  79[0:Inp] ssItem(u) ||  -> strictorderP(cons(u,nil))*.
% 13.93/14.12  80[0:Inp] ssItem(u) ||  -> totalorderedP(cons(u,nil))*.
% 13.93/14.12  81[0:Inp] ssItem(u) ||  -> strictorderedP(cons(u,nil))*.
% 13.93/14.12  82[0:Inp] ssItem(u) ||  -> duplicatefreeP(cons(u,nil))*.
% 13.93/14.12  83[0:Inp] ssItem(u) ||  -> equalelemsP(cons(u,nil))*.
% 13.93/14.12  85[0:Inp] ssList(u) ||  -> equal(app(nil,u),u)**.
% 13.93/14.12  91[0:Inp] ||  -> SkP0(u,v) equal(cons(skf46(u,v),nil),v)**.
% 13.93/14.12  95[0:Inp] ssItem(u) ssList(v) ||  -> ssList(cons(u,v))*.
% 13.93/14.12  96[0:Inp] ssList(u) ssList(v) ||  -> ssList(app(v,u))*.
% 13.93/14.12  110[0:Inp] ssItem(u) ssItem(v) ||  -> neq(v,u)* equal(v,u).
% 13.93/14.12  111[0:Inp] ssList(u) singletonP(u) ||  -> equal(cons(skf51(u),nil),u)**.
% 13.93/14.12  113[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 13.93/14.12  115[0:Inp] ssItem(u) ssList(v) ||  -> equal(hd(cons(u,v)),u)**.
% 13.93/14.12  117[0:Inp] ||  -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8)**.
% 13.93/14.12  127[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 13.93/14.12  134[0:Inp] ssItem(u) ssList(v) ||  -> equal(app(cons(u,nil),v),cons(u,v))**.
% 13.93/14.12  139[0:Inp] ssList(u) ssList(v) ||  -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 13.93/14.12  167[0:Inp] ssList(u) ssList(v) ssList(w) ||  -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 13.93/14.12  195[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).
% 13.93/14.12  200[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) ssItem(y) ssItem(z) duplicatefreeP(u) || equal(z,y) equal(app(app(x,cons(z,w)),cons(y,v)),u)* -> .
% 13.93/14.12  204[0:Rew:75.1,74.1] || SkP0(skc9,skc8)* -> equal(skc9,skc8).
% 13.93/14.12  252[0:Res:6.0,139.0] ssList(u) ||  -> equal(nil,skc8) equal(hd(app(skc8,u)),hd(skc8))**.
% 13.93/14.12  261[0:Res:6.0,113.0] ssItem(u) || equal(cons(u,skc8),skc8)** -> .
% 13.93/14.12  263[0:Res:6.0,115.0] ssItem(u) ||  -> equal(hd(cons(u,skc8)),u)**.
% 13.93/14.12  275[0:Res:6.0,95.0] ssItem(u) ||  -> ssList(cons(u,skc8))*.
% 13.93/14.12  293[0:Res:6.0,195.1] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u) equal(nil,skc8).
% 13.93/14.12  423[0:Res:5.0,139.0] ssList(u) ||  -> equal(nil,skc9) equal(hd(app(skc9,u)),hd(skc9))**.
% 13.93/14.12  464[0:Res:5.0,195.1] ssList(u) || equal(tl(skc9),tl(u))* equal(hd(skc9),hd(u)) -> equal(nil,u) equal(skc9,u) equal(nil,skc9).
% 13.93/14.12  556[1:Spt:423.0,423.2] ssList(u) ||  -> equal(hd(app(skc9,u)),hd(skc9))**.
% 13.93/14.12  558[2:Spt:252.0,252.2] ssList(u) ||  -> equal(hd(app(skc8,u)),hd(skc8))**.
% 13.93/14.12  564[3:Spt:464.5] ||  -> equal(nil,skc9)**.
% 13.93/14.12  661[3:Rew:564.0,85.1] ssList(u) ||  -> equal(app(skc9,u),u)**.
% 13.93/14.12  720[3:Rew:661.1,556.1] ssList(u) ||  -> equal(hd(u),hd(skc9))*.
% 13.93/14.12  1509[3:SpR:720.1,263.1] ssList(cons(u,skc8)) ssItem(u) ||  -> equal(hd(skc9),u)*.
% 13.93/14.12  1514[3:SSi:1509.0,275.1] ssItem(u) ||  -> equal(hd(skc9),u)*.
% 13.93/14.12  1516[3:SpR:1514.1,1514.1] ssItem(u) ssItem(v) ||  -> equal(u,v)*.
% 13.93/14.12  1695[3:EmS:1516.0,8.0] ssItem(u) ||  -> equal(skc14,u)*.
% 13.93/14.12  1781[3:EmS:1695.0,7.0] ||  -> equal(skc15,skc14)**.
% 13.93/14.12  1784[3:MRR:1781.0,59.0] ||  -> .
% 13.93/14.12  2002[3:Spt:1784.0,464.5,564.0] || equal(nil,skc9)** -> .
% 13.93/14.12  2003[3:Spt:1784.0,464.0,464.1,464.2,464.3,464.4] ssList(u) || equal(tl(skc9),tl(u))* equal(hd(skc9),hd(u)) -> equal(nil,u) equal(skc9,u).
% 13.93/14.12  2027[4:Spt:293.5] ||  -> equal(nil,skc8)**.
% 13.93/14.12  2044[4:Rew:2027.0,2002.0] || equal(skc9,skc8)** -> .
% 13.93/14.12  2063[4:Rew:2027.0,77.1] ssItem(u) ||  -> cyclefreeP(cons(u,skc8))*.
% 13.93/14.12  2064[4:Rew:2027.0,78.1] ssItem(u) ||  -> totalorderP(cons(u,skc8))*.
% 13.93/14.12  2065[4:Rew:2027.0,79.1] ssItem(u) ||  -> strictorderP(cons(u,skc8))*.
% 13.93/14.12  2066[4:Rew:2027.0,80.1] ssItem(u) ||  -> totalorderedP(cons(u,skc8))*.
% 13.93/14.12  2067[4:Rew:2027.0,81.1] ssItem(u) ||  -> strictorderedP(cons(u,skc8))*.
% 13.93/14.12  2068[4:Rew:2027.0,82.1] ssItem(u) ||  -> duplicatefreeP(cons(u,skc8))*.
% 13.93/14.12  2069[4:Rew:2027.0,83.1] ssItem(u) ||  -> equalelemsP(cons(u,skc8))*.
% 13.93/14.12  2075[4:Rew:2027.0,85.1] ssList(u) ||  -> equal(app(skc8,u),u)**.
% 13.93/14.12  2104[4:Rew:2027.0,91.1] ||  -> SkP0(u,v) equal(cons(skf46(u,v),skc8),v)**.
% 13.93/14.12  2125[4:MRR:204.1,2044.0] || SkP0(skc9,skc8)* -> .
% 13.93/14.12  2161[4:Rew:2075.1,558.1] ssList(u) ||  -> equal(hd(u),hd(skc8))*.
% 13.93/14.12  2232[4:SpR:2161.1,263.1] ssList(cons(u,skc8)) ssItem(u) ||  -> equal(hd(skc8),u)*.
% 13.93/14.12  2242[4:SSi:2232.0,275.1,2063.1,2064.1,2065.1,2066.1,2067.1,2068.1,2069.1] ssItem(u) ||  -> equal(hd(skc8),u)*.
% 13.93/14.12  2412[4:SpR:2104.1,263.1] ssItem(skf46(u,v)) ||  -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 13.93/14.12  2434[4:SSi:2412.0,57.0] ||  -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 13.93/14.12  2435[4:Rew:2434.1,2104.1] ||  -> SkP0(u,v)* equal(cons(hd(v),skc8),v)**.
% 13.93/14.12  2458[4:SpR:2242.1,2435.1] ssItem(u) ||  -> SkP0(v,skc8)* equal(cons(u,skc8),skc8)**.
% 13.93/14.12  2462[4:MRR:2458.2,261.1] ssItem(u) ||  -> SkP0(v,skc8)*.
% 13.93/14.12  2492[4:EmS:2462.0,4.0] ||  -> SkP0(u,skc8)*.
% 13.93/14.12  2515[4:UnC:2492.0,2125.0] ||  -> .
% 13.93/14.12  2516[4:Spt:2515.0,293.5,2027.0] || equal(nil,skc8)** -> .
% 13.93/14.12  2517[4:Spt:2515.0,293.0,293.1,293.2,293.3,293.4] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u).
% 13.93/14.12  2523[4:MRR:75.1,2516.0] || SkP0(skc9,skc8)* -> .
% 13.93/14.12  2633[0:SpR:91.1,83.1] ssItem(skf46(u,v)) ||  -> SkP0(u,v)* equalelemsP(v).
% 13.93/14.12  2641[0:SSi:2633.0,57.0] ||  -> SkP0(u,v)* equalelemsP(v).
% 13.93/14.12  2649[4:Res:2641.0,2523.0] ||  -> equalelemsP(skc8)*.
% 13.93/14.12  2717[0:SpR:111.2,82.1] ssList(u) singletonP(u) ssItem(skf51(u)) ||  -> duplicatefreeP(u)*.
% 13.93/14.12  2728[0:SSi:2717.2,17.0] ssList(u) singletonP(u) ||  -> duplicatefreeP(u)*.
% 13.93/14.12  2791[0:SpR:91.1,115.2] ssItem(skf46(u,v)) ssList(nil) ||  -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 13.93/14.12  2795[0:SSi:2791.1,2791.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,57.0] ||  -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 13.93/14.12  2796[0:Rew:2795.1,91.1] ||  -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 13.93/14.12  2880[0:SpR:2795.1,57.0] ||  -> SkP0(u,v)* ssItem(hd(v)).
% 13.93/14.12  2927[0:Res:110.2,58.0] ssItem(skc11) ssItem(skc10) ||  -> equal(skc11,skc10)**.
% 13.93/14.12  2928[0:SSi:2927.1,2927.0,4.0,3.0] ||  -> equal(skc11,skc10)**.
% 13.93/14.12  2931[0:Rew:2928.0,117.0] ||  -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc10,nil)),skc13),skc8)**.
% 13.93/14.12  3351[0:EqR:127.2] ssList(cons(u,nil)) ssItem(u) ||  -> singletonP(cons(u,nil))*.
% 13.93/14.12  3356[0:SSi:3351.0,83.0,82.0,81.0,80.0,79.0,78.0,77.0,95.0,16.2,15.1,14.1,13.1,12.1,11.1,10.1,9.1] ssItem(u) ||  -> singletonP(cons(u,nil))*.
% 13.93/14.12  3410[0:SpR:2796.1,3356.1] ssItem(hd(u)) ||  -> SkP0(v,u)* singletonP(u).
% 13.93/14.12  3412[0:MRR:3410.0,2880.1] ||  -> SkP0(u,v)* singletonP(v).
% 13.93/14.12  3415[4:Res:3412.0,2523.0] ||  -> singletonP(skc8)*.
% 13.93/14.12  5679[0:SpR:167.3,2931.0] ssList(skc13) ssList(cons(skc10,nil)) ssList(app(skc12,cons(skc10,nil))) ||  -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8)**.
% 13.93/14.12  5747[0:SSi:5679.2,5679.1,5679.0,96.0,2.0,83.0,4.0,82.0,4.0,81.0,4.0,80.0,4.0,79.2,4.0,78.1,4.0,77.1,4.0,3356.1,4.0,95.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,83.0,4.0,82.0,4.0,81.0,4.0,80.0,4.0,79.2,4.0,78.1,4.0,77.1,4.0,3356.1,4.0,95.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,1.2] ||  -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8)**.
% 13.93/14.12  10664[0:SpR:134.2,5747.0] ssItem(skc10) ssList(skc13) ||  -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 13.93/14.12  10678[0:SSi:10664.1,10664.0,1.0,4.0] ||  -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 14.94/15.11  13936[0:SpL:10678.0,200.8] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) ssItem(skc10) duplicatefreeP(u) || equal(skc10,skc10)* equal(skc8,u)* -> .
% 14.94/15.11  13948[0:Obv:13936.7] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) duplicatefreeP(u) || equal(skc8,u)* -> .
% 14.94/15.11  13949[0:SSi:13948.4,13948.3,13948.2,13948.1,4.0,2.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,1.0] ssList(u) duplicatefreeP(u) || equal(skc8,u)* -> .
% 14.94/15.11  13964[0:EmS:13949.0,13949.1,9.0,15.0] || equal(nil,skc8)** -> .
% 14.94/15.11  14018[0:EmS:13949.0,13949.1,6.0,2728.2] singletonP(skc8) ssList(skc8) || equal(skc8,skc8)* -> .
% 14.94/15.11  14021[0:Obv:14018.2] singletonP(skc8) ssList(skc8) ||  -> .
% 14.94/15.11  15606[0:Obv:14018.2] singletonP(skc8) ssList(skc8) ||  -> .
% 14.94/15.11  15607[4:SSi:15606.1,6.0,2649.0] singletonP(skc8) ||  -> .
% 14.94/15.11  15608[4:MRR:15607.0,3415.0] ||  -> .
% 14.94/15.11  15787[2:Spt:15608.0,252.1] ||  -> equal(nil,skc8)**.
% 14.94/15.11  16235[2:Rew:15787.0,13964.0] || equal(skc8,skc8)* -> .
% 14.94/15.11  16236[2:Obv:16235.0] ||  -> .
% 14.94/15.11  16237[0:SSi:14021.1,6.0] singletonP(skc8) ||  -> .
% 14.94/15.11  17317[1:Spt:16236.0,423.1] ||  -> equal(nil,skc9)**.
% 14.94/15.11  17334[1:Rew:17317.0,13964.0] || equal(skc9,skc8)** -> .
% 14.94/15.11  17374[1:Rew:17317.0,75.1] || SkP0(skc9,skc8)* -> equal(skc9,skc8).
% 14.94/15.11  17375[1:MRR:17374.1,17334.0] || SkP0(skc9,skc8)* -> .
% 14.94/15.11  18375[1:Res:3412.0,17375.0] ||  -> singletonP(skc8)*.
% 14.94/15.11  18385[1:MRR:18375.0,16237.0] ||  -> .
% 14.94/15.11  % SZS output end Refutation
% 14.94/15.11  Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax16 ax26 ax1 ax18 ax23 ax81 ax85 ax82 ax77 ax13
% 14.94/15.11  
%------------------------------------------------------------------------------