TSTP Solution File: SWC327-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC327-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 22:03:20 EDT 2022
% Result : Unsatisfiable 19.82s 20.06s
% Output : Refutation 25.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC327-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 : Sun Jun 12 07:25:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 19.82/20.06
% 19.82/20.06 SPASS V 3.9
% 19.82/20.06 SPASS beiseite: Proof found.
% 19.82/20.06 % SZS status Theorem
% 19.82/20.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.82/20.06 SPASS derived 26154 clauses, backtracked 8914 clauses, performed 69 splits and kept 19565 clauses.
% 19.82/20.06 SPASS allocated 102950 KBytes.
% 19.82/20.06 SPASS spent 0:0:19.67 on the problem.
% 19.82/20.06 0:00:00.04 for the input.
% 19.82/20.06 0:00:00.00 for the FLOTTER CNF translation.
% 19.82/20.06 0:00:00.25 for inferences.
% 19.82/20.06 0:00:00.76 for the backtracking.
% 19.82/20.06 0:0:18.28 for the reduction.
% 19.82/20.06
% 19.82/20.06
% 19.82/20.06 Here is a proof with depth 3, length 175 :
% 19.82/20.06 % SZS output start Refutation
% 19.82/20.06 3[0:Inp] || -> ssList(sk3)*.
% 19.82/20.06 5[0:Inp] || -> equal(sk4,sk2)**.
% 19.82/20.06 6[0:Inp] || -> equal(sk1,sk3)**.
% 19.82/20.06 7[0:Inp] || -> ssList(sk5)*.
% 19.82/20.06 8[0:Inp] || -> equal(app(sk3,sk5),sk4)**.
% 19.82/20.06 9[0:Inp] || -> equalelemsP(sk3)*.
% 19.82/20.06 10[0:Inp] ssItem(u) ssList(v) ssList(w) || equal(app(cons(u,nil),v),sk5)** equal(app(w,cons(u,nil)),sk3)** -> .
% 19.82/20.06 11[0:Inp] || equal(nil,sk3)** -> equal(nil,sk4).
% 19.82/20.06 14[0:Inp] ssList(u) || equal(app(sk1,u),sk2)** equalelemsP(sk1) -> ssList(sk7(u)) equal(sk1,nil).
% 19.82/20.06 15[0:Inp] ssList(u) || equal(app(sk1,u),sk2) equalelemsP(sk1) -> equal(app(cons(sk6(u),nil),sk7(u)),u)** equal(sk1,nil).
% 19.82/20.06 16[0:Inp] ssList(u) || equal(app(sk1,u),sk2)** equalelemsP(sk1) -> ssList(sk8(u)) equal(sk1,nil).
% 19.82/20.06 17[0:Inp] ssList(u) || equal(app(sk1,u),sk2) equalelemsP(sk1) -> equal(app(sk8(u),cons(sk6(u),nil)),sk1)** equal(sk1,nil).
% 19.82/20.06 18[0:Inp] ssList(u) || equal(app(sk1,u),sk2)** equalelemsP(sk1) equal(nil,sk2) -> ssList(sk7(u)).
% 19.82/20.06 19[0:Inp] ssList(u) || equal(app(sk1,u),sk2) equalelemsP(sk1) equal(nil,sk2) -> equal(app(cons(sk6(u),nil),sk7(u)),u)**.
% 19.82/20.06 34[0:Inp] || -> ssList(skaf82(u))*.
% 19.82/20.06 68[0:Inp] || -> ssItem(skaf44(u))*.
% 19.82/20.06 75[0:Inp] || equal(skac2,skac3)** -> .
% 19.82/20.06 85[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 19.82/20.06 86[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 19.82/20.06 87[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 19.82/20.06 88[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 19.82/20.06 89[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 19.82/20.06 90[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 19.82/20.06 91[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 19.82/20.06 93[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 19.82/20.06 94[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 19.82/20.06 95[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 19.82/20.06 106[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 19.82/20.06 107[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 19.82/20.06 118[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 19.82/20.06 119[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 19.82/20.06 141[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 19.82/20.06 144[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 19.82/20.06 170[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 19.82/20.06 178[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 19.82/20.06 191[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 19.82/20.06 200[0:Inp] ssList(u) duplicatefreeP(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 19.82/20.06 209[0:Rew:5.0,8.0] || -> equal(app(sk3,sk5),sk2)**.
% 19.82/20.06 210[0:Rew:5.0,11.1] || equal(nil,sk3)** -> equal(nil,sk2).
% 19.82/20.06 211[0:Rew:6.0,16.4,6.0,16.2,6.0,16.1] ssList(u) || equal(app(sk3,u),sk2)** equalelemsP(sk3) -> ssList(sk8(u)) equal(nil,sk3).
% 19.82/20.06 212[0:MRR:211.2,9.0] ssList(u) || equal(app(sk3,u),sk2)** -> ssList(sk8(u)) equal(nil,sk3).
% 19.82/20.06 213[0:Rew:6.0,14.4,6.0,14.2,6.0,14.1] ssList(u) || equal(app(sk3,u),sk2)** equalelemsP(sk3) -> ssList(sk7(u)) equal(nil,sk3).
% 19.82/20.06 214[0:MRR:213.2,9.0] ssList(u) || equal(app(sk3,u),sk2)** -> ssList(sk7(u)) equal(nil,sk3).
% 19.82/20.06 219[0:Rew:214.3,18.3,6.0,18.2,6.0,18.1] ssList(u) || equal(app(sk3,u),sk2)** equalelemsP(sk3) equal(sk3,sk2) -> ssList(sk7(u)).
% 19.82/20.06 220[0:MRR:219.2,9.0] ssList(u) || equal(sk3,sk2) equal(app(sk3,u),sk2)** -> ssList(sk7(u)).
% 19.82/20.06 227[0:Rew:6.0,15.4,6.0,15.2,6.0,15.1] ssList(u) || equal(app(sk3,u),sk2) equalelemsP(sk3) -> equal(app(cons(sk6(u),nil),sk7(u)),u)** equal(nil,sk3).
% 19.82/20.06 228[0:MRR:227.2,9.0] ssList(u) || equal(app(sk3,u),sk2) -> equal(nil,sk3) equal(app(cons(sk6(u),nil),sk7(u)),u)**.
% 19.82/20.06 229[0:Rew:6.0,17.4,6.0,17.3,6.0,17.2,6.0,17.1] ssList(u) || equal(app(sk3,u),sk2) equalelemsP(sk3) -> equal(app(sk8(u),cons(sk6(u),nil)),sk3)** equal(nil,sk3).
% 19.82/20.06 230[0:MRR:229.2,9.0] ssList(u) || equal(app(sk3,u),sk2) -> equal(nil,sk3) equal(app(sk8(u),cons(sk6(u),nil)),sk3)**.
% 19.82/20.06 231[0:Rew:141.2,10.3] ssList(u) ssList(v) ssItem(w) || equal(cons(w,v),sk5)** equal(app(u,cons(w,nil)),sk3)**+ -> .
% 19.82/20.06 232[0:Rew:228.3,19.3,6.0,19.2,6.0,19.1] ssList(u) || equal(app(sk3,u),sk2) equalelemsP(sk3) equal(sk3,sk2) -> equal(app(cons(sk6(u),nil),sk7(u)),u)**.
% 19.82/20.06 233[0:MRR:232.2,9.0] ssList(u) || equal(sk3,sk2) equal(app(sk3,u),sk2) -> equal(app(cons(sk6(u),nil),sk7(u)),u)**.
% 19.82/20.06 247[0:Res:7.0,233.0] || equal(app(sk3,sk5),sk2) equal(sk3,sk2) -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)**.
% 19.82/20.06 248[0:Res:7.0,230.0] || equal(app(sk3,sk5),sk2) -> equal(app(sk8(sk5),cons(sk6(sk5),nil)),sk3)** equal(nil,sk3).
% 19.82/20.06 249[0:Res:7.0,228.0] || equal(app(sk3,sk5),sk2) -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)** equal(nil,sk3).
% 19.82/20.06 271[0:Res:7.0,170.0] ssList(u) ssList(v) || -> equal(app(app(u,v),sk5),app(u,app(v,sk5)))**.
% 19.82/20.06 273[0:Res:7.0,220.0] || equal(app(sk3,sk5),sk2)** equal(sk3,sk2) -> ssList(sk7(sk5)).
% 19.82/20.06 277[0:Res:7.0,214.0] || equal(app(sk3,sk5),sk2)** -> ssList(sk7(sk5)) equal(nil,sk3).
% 19.82/20.06 278[0:Res:7.0,212.0] || equal(app(sk3,sk5),sk2)** -> ssList(sk8(sk5)) equal(nil,sk3).
% 19.82/20.06 327[0:Res:7.0,95.0] || -> equal(app(nil,sk5),sk5)**.
% 19.82/20.06 373[0:Res:7.0,144.1] ssList(u) || -> equal(nil,sk5) equal(hd(app(sk5,u)),hd(sk5))**.
% 19.82/20.06 380[0:Res:7.0,118.1] ssItem(u) || -> equal(hd(cons(u,sk5)),u)**.
% 19.82/20.06 385[0:Res:7.0,107.1] ssItem(u) || -> ssList(cons(u,sk5))*.
% 19.82/20.06 509[0:Res:3.0,94.0] || -> equal(app(sk3,nil),sk3)**.
% 19.82/20.06 608[0:Rew:209.0,277.0] || equal(sk2,sk2) -> ssList(sk7(sk5))* equal(nil,sk3).
% 19.82/20.06 609[0:Obv:608.0] || -> ssList(sk7(sk5))* equal(nil,sk3).
% 19.82/20.06 610[0:Rew:209.0,278.0] || equal(sk2,sk2) -> ssList(sk8(sk5))* equal(nil,sk3).
% 19.82/20.06 611[0:Obv:610.0] || -> ssList(sk8(sk5))* equal(nil,sk3).
% 19.82/20.06 618[0:Rew:209.0,273.0] || equal(sk2,sk2) equal(sk3,sk2) -> ssList(sk7(sk5))*.
% 19.82/20.06 619[0:Obv:618.0] || equal(sk3,sk2) -> ssList(sk7(sk5))*.
% 19.82/20.06 624[0:Rew:209.0,248.0] || equal(sk2,sk2) -> equal(app(sk8(sk5),cons(sk6(sk5),nil)),sk3)** equal(nil,sk3).
% 19.82/20.06 625[0:Obv:624.0] || -> equal(nil,sk3) equal(app(sk8(sk5),cons(sk6(sk5),nil)),sk3)**.
% 19.82/20.06 626[0:Rew:209.0,249.0] || equal(sk2,sk2) -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)** equal(nil,sk3).
% 19.82/20.06 627[0:Obv:626.0] || -> equal(nil,sk3) equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)**.
% 19.82/20.06 630[0:Rew:209.0,247.0] || equal(sk2,sk2) equal(sk3,sk2) -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)**.
% 19.82/20.06 631[0:Obv:630.0] || equal(sk3,sk2) -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)**.
% 19.82/20.06 634[1:Spt:93.1] || -> ssItem(u)*.
% 19.82/20.06 638[1:MRR:385.0,634.0] || -> ssList(cons(u,sk5))*.
% 19.82/20.06 640[1:MRR:91.0,634.0] || -> cyclefreeP(cons(u,nil))*.
% 19.82/20.06 641[1:MRR:90.0,634.0] || -> totalorderP(cons(u,nil))*.
% 19.82/20.06 642[1:MRR:89.0,634.0] || -> strictorderP(cons(u,nil))*.
% 19.82/20.06 643[1:MRR:88.0,634.0] || -> totalorderedP(cons(u,nil))*.
% 19.82/20.06 644[1:MRR:87.0,634.0] || -> strictorderedP(cons(u,nil))*.
% 19.82/20.06 645[1:MRR:86.0,634.0] || -> duplicatefreeP(cons(u,nil))*.
% 19.82/20.06 646[1:MRR:85.0,634.0] || -> equalelemsP(cons(u,nil))*.
% 19.82/20.06 654[1:MRR:380.0,634.0] || -> equal(hd(cons(u,sk5)),u)**.
% 19.82/20.06 761[1:MRR:119.1,634.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 19.82/20.06 765[1:MRR:141.1,634.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 19.82/20.06 831[1:MRR:231.2,634.0] ssList(u) ssList(v) || equal(cons(w,v),sk5)** equal(app(u,cons(w,nil)),sk3)**+ -> .
% 19.82/20.06 833[1:MRR:191.3,191.2,634.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 19.82/20.06 836[2:Spt:373.0,373.2] ssList(u) || -> equal(hd(app(sk5,u)),hd(sk5))**.
% 19.82/20.06 842[3:Spt:212.3] || -> equal(nil,sk3)**.
% 19.82/20.06 847[3:Rew:842.0,210.0] || equal(sk3,sk3) -> equal(nil,sk2)**.
% 19.82/20.06 923[3:Rew:842.0,327.0] || -> equal(app(sk3,sk5),sk5)**.
% 19.82/20.06 928[3:Rew:842.0,95.1] ssList(u) || -> equal(app(sk3,u),u)**.
% 19.82/20.06 929[3:Rew:842.0,94.1] ssList(u) || -> equal(app(u,sk3),u)**.
% 19.82/20.06 934[3:Rew:842.0,640.0] || -> cyclefreeP(cons(u,sk3))*.
% 19.82/20.06 935[3:Rew:842.0,641.0] || -> totalorderP(cons(u,sk3))*.
% 19.82/20.06 936[3:Rew:842.0,642.0] || -> strictorderP(cons(u,sk3))*.
% 19.82/20.06 937[3:Rew:842.0,643.0] || -> totalorderedP(cons(u,sk3))*.
% 19.82/20.06 938[3:Rew:842.0,644.0] || -> strictorderedP(cons(u,sk3))*.
% 25.84/26.06 939[3:Rew:842.0,645.0] || -> duplicatefreeP(cons(u,sk3))*.
% 25.84/26.06 940[3:Rew:842.0,646.0] || -> equalelemsP(cons(u,sk3))*.
% 25.84/26.06 949[3:Rew:842.0,765.1] ssList(u) || -> equal(app(cons(v,sk3),u),cons(v,u))**.
% 25.84/26.06 968[3:Rew:209.0,923.0] || -> equal(sk5,sk2)**.
% 25.84/26.06 969[3:Rew:968.0,836.1] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 25.84/26.06 1051[3:Rew:968.0,271.2] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,app(v,sk2)))**.
% 25.84/26.06 1054[3:Rew:968.0,638.0] || -> ssList(cons(u,sk2))*.
% 25.84/26.06 1055[3:Rew:968.0,654.0] || -> equal(hd(cons(u,sk2)),u)**.
% 25.84/26.06 1116[3:Obv:847.0] || -> equal(nil,sk2)**.
% 25.84/26.06 1117[3:Rew:842.0,1116.0] || -> equal(sk3,sk2)**.
% 25.84/26.06 1164[3:Rew:1117.0,934.0] || -> cyclefreeP(cons(u,sk2))*.
% 25.84/26.06 1165[3:Rew:1117.0,935.0] || -> totalorderP(cons(u,sk2))*.
% 25.84/26.06 1166[3:Rew:1117.0,936.0] || -> strictorderP(cons(u,sk2))*.
% 25.84/26.06 1167[3:Rew:1117.0,937.0] || -> totalorderedP(cons(u,sk2))*.
% 25.84/26.06 1168[3:Rew:1117.0,938.0] || -> strictorderedP(cons(u,sk2))*.
% 25.84/26.06 1169[3:Rew:1117.0,939.0] || -> duplicatefreeP(cons(u,sk2))*.
% 25.84/26.06 1170[3:Rew:1117.0,940.0] || -> equalelemsP(cons(u,sk2))*.
% 25.84/26.06 1248[3:Rew:1117.0,928.1] ssList(u) || -> equal(app(sk2,u),u)**.
% 25.84/26.06 1250[3:Rew:1117.0,929.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 25.84/26.06 1282[3:Rew:1248.1,969.1] ssList(u) || -> equal(hd(u),hd(sk2))*.
% 25.84/26.06 1309[3:Rew:1117.0,949.1] ssList(u) || -> equal(app(cons(v,sk2),u),cons(v,u))**.
% 25.84/26.06 1410[3:Rew:1250.1,1051.2] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,v))**.
% 25.84/26.06 1469[3:SpR:1282.1,1055.0] ssList(cons(u,sk2)) || -> equal(hd(sk2),u)*.
% 25.84/26.06 1474[3:SSi:1469.0,1054.0,1164.0,1165.0,1166.0,1167.0,1168.0,1169.0,1170.0] || -> equal(hd(sk2),u)*.
% 25.84/26.06 1534[3:Rew:1474.0,833.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk2))** -> equal(w,x)*.
% 25.84/26.06 1553[3:Rew:1474.0,1309.1] ssList(u) || -> equal(app(hd(sk2),u),cons(v,u))*.
% 25.84/26.06 1581[3:Rew:1474.0,1410.2] ssList(u) ssList(v) || -> equal(app(u,v),hd(sk2))**.
% 25.84/26.06 1593[3:Rew:1474.0,170.3] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),hd(sk2))**.
% 25.84/26.06 1670[3:Con:1534.1] ssList(u) || equal(cons(v,u),hd(sk2))** -> equal(v,w)*.
% 25.84/26.06 1671[3:AED:75.0,1670.2] ssList(u) || equal(cons(v,u),hd(sk2))** -> .
% 25.84/26.06 1677[3:Rew:1581.2,1593.3] ssList(u) ssList(v) ssList(w) || -> equal(app(hd(sk2),w),hd(sk2))**.
% 25.84/26.06 1678[3:Con:1677.0] ssList(u) || -> equal(app(hd(sk2),u),hd(sk2))**.
% 25.84/26.06 1679[3:Rew:1678.1,1553.1] ssList(u) || -> equal(cons(v,u),hd(sk2))**.
% 25.84/26.06 1680[3:MRR:1679.1,1671.1] ssList(u) || -> .
% 25.84/26.06 1681[3:UnC:1680.0,34.0] || -> .
% 25.84/26.06 1726[3:Spt:1681.0,212.3,842.0] || equal(nil,sk3)** -> .
% 25.84/26.06 1727[3:Spt:1681.0,212.0,212.1,212.2] ssList(u) || equal(app(sk3,u),sk2)** -> ssList(sk8(u)).
% 25.84/26.06 1728[3:MRR:611.1,1726.0] || -> ssList(sk8(sk5))*.
% 25.84/26.06 1729[3:MRR:609.1,1726.0] || -> ssList(sk7(sk5))*.
% 25.84/26.06 1738[3:MRR:627.0,1726.0] || -> equal(app(cons(sk6(sk5),nil),sk7(sk5)),sk5)**.
% 25.84/26.06 1739[3:MRR:625.0,1726.0] || -> equal(app(sk8(sk5),cons(sk6(sk5),nil)),sk3)**.
% 25.84/26.06 3115[3:SpR:765.1,1738.0] ssList(sk7(sk5)) || -> equal(cons(sk6(sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 3122[3:SSi:3115.0,1729.0] || -> equal(cons(sk6(sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 6510[3:SpL:1739.0,831.3] ssList(sk8(sk5)) ssList(u) || equal(cons(sk6(sk5),u),sk5)** equal(sk3,sk3) -> .
% 25.84/26.06 6513[3:Obv:6510.3] ssList(sk8(sk5)) ssList(u) || equal(cons(sk6(sk5),u),sk5)** -> .
% 25.84/26.06 6514[3:SSi:6513.0,1728.0] ssList(u) || equal(cons(sk6(sk5),u),sk5)** -> .
% 25.84/26.06 14920[3:SpL:3122.0,6514.1] ssList(sk7(sk5)) || equal(sk5,sk5)* -> .
% 25.84/26.06 14928[3:Obv:14920.1] ssList(sk7(sk5)) || -> .
% 25.84/26.06 14929[3:SSi:14928.0,1729.0] || -> .
% 25.84/26.06 15071[2:Spt:14929.0,373.1] || -> equal(nil,sk5)**.
% 25.84/26.06 15127[2:Rew:15071.0,509.0] || -> equal(app(sk3,sk5),sk3)**.
% 25.84/26.06 15134[2:Rew:15071.0,761.1] ssList(u) || equal(cons(v,u),sk5)** -> .
% 25.84/26.06 15138[2:Rew:15071.0,765.1] ssList(u) || -> equal(app(cons(v,sk5),u),cons(v,u))**.
% 25.84/26.06 15411[2:Rew:209.0,15127.0] || -> equal(sk3,sk2)**.
% 25.84/26.06 15572[2:Rew:15411.0,619.0] || equal(sk2,sk2) -> ssList(sk7(sk5))*.
% 25.84/26.06 15573[2:Obv:15572.0] || -> ssList(sk7(sk5))*.
% 25.84/26.06 15688[2:Rew:15071.0,631.1,15411.0,631.0] || equal(sk2,sk2) -> equal(app(cons(sk6(sk5),sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 15689[2:Obv:15688.0] || -> equal(app(cons(sk6(sk5),sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 18344[2:SpR:15138.1,15689.0] ssList(sk7(sk5)) || -> equal(cons(sk6(sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 18348[2:SSi:18344.0,15573.0] || -> equal(cons(sk6(sk5),sk7(sk5)),sk5)**.
% 25.84/26.06 18360[2:SpL:18348.0,15134.1] ssList(sk7(sk5)) || equal(sk5,sk5)* -> .
% 25.84/26.06 18364[2:Obv:18360.1] ssList(sk7(sk5)) || -> .
% 25.84/26.06 18365[2:SSi:18364.0,15573.0] || -> .
% 25.84/26.06 18372[1:Spt:18365.0,93.0,93.2] ssList(u) || -> duplicatefreeP(u)*.
% 25.84/26.06 18417[1:MRR:200.1,18372.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 25.84/26.06 37414[0:SpR:178.3,106.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 25.84/26.06 37445[0:Obv:37414.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 25.84/26.06 37446[0:SSi:37445.2,107.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 25.84/26.06 38617[1:EqR:18417.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 25.84/26.06 38648[1:SSi:38617.0,106.2,106.2,107.2,107.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 25.84/26.06 38649[1:MRR:37446.3,38648.1] ssList(u) ssItem(v) ssList(w) || -> .
% 25.84/26.06 38652[1:Con:38649.2] ssList(u) ssItem(v) || -> .
% 25.84/26.06 38654[1:MRR:385.1,38652.0] ssItem(u) || -> .
% 25.84/26.06 38666[1:UnC:38654.0,68.0] || -> .
% 25.84/26.06 % SZS output end Refutation
% 25.84/26.06 Formulae used in the proof : co1_3 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_14 co1_15 co1_16 co1_17 co1_18 co1_19 clause13 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause85 clause86 clause97 clause98 clause120 clause123 clause149 clause157 clause170 clause179
% 25.84/26.06
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