TSTP Solution File: SWC098-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% 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 : n025.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 : Unsatisfiable 2.29s 2.50s
% Output : Refutation 2.39s
% 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.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 23:14:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.29/2.50
% 2.29/2.50 SPASS V 3.9
% 2.29/2.50 SPASS beiseite: Proof found.
% 2.29/2.50 % SZS status Theorem
% 2.29/2.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.29/2.50 SPASS derived 5762 clauses, backtracked 3024 clauses, performed 79 splits and kept 6370 clauses.
% 2.29/2.50 SPASS allocated 80506 KBytes.
% 2.29/2.50 SPASS spent 0:00:02.15 on the problem.
% 2.29/2.50 0:00:00.04 for the input.
% 2.29/2.50 0:00:00.00 for the FLOTTER CNF translation.
% 2.29/2.50 0:00:00.03 for inferences.
% 2.29/2.50 0:00:00.04 for the backtracking.
% 2.29/2.50 0:00:01.83 for the reduction.
% 2.29/2.50
% 2.29/2.50
% 2.29/2.50 Here is a proof with depth 3, length 207 :
% 2.29/2.50 % SZS output start Refutation
% 2.29/2.50 1[0:Inp] || -> ssList(sk1)*.
% 2.29/2.50 2[0:Inp] || -> ssList(sk2)*.
% 2.29/2.50 5[0:Inp] || -> equal(sk4,sk2)**.
% 2.29/2.50 6[0:Inp] || -> equal(sk3,sk1)**.
% 2.29/2.50 7[0:Inp] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1)** -> ssItem(sk5(u)).
% 2.29/2.50 8[0:Inp] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1) -> memberP(sk2,sk5(u))*.
% 2.29/2.50 9[0:Inp] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1) -> leq(u,sk5(u))*.
% 2.29/2.50 10[0:Inp] ssItem(u) || memberP(sk2,u) equal(sk5(u),u) equal(cons(u,nil),sk1)** -> .
% 2.29/2.50 11[0:Inp] || equal(nil,sk1) equal(nil,sk2)** -> .
% 2.29/2.50 12[0:Inp] || -> ssItem(sk6)* equal(nil,sk4).
% 2.29/2.50 13[0:Inp] || -> ssItem(sk6)* equal(nil,sk3).
% 2.29/2.50 14[0:Inp] || -> equal(cons(sk6,nil),sk3)** equal(nil,sk4).
% 2.29/2.50 17[0:Inp] || -> equal(cons(sk6,nil),sk3)** equal(nil,sk3).
% 2.29/2.50 18[0:Inp] || -> memberP(sk4,sk6)* equal(nil,sk3).
% 2.29/2.50 19[0:Inp] ssItem(u) || memberP(sk4,u) leq(sk6,u)* -> equal(sk6,u) equal(nil,sk3).
% 2.29/2.50 20[0:Inp] || -> equalelemsP(nil)*.
% 2.29/2.50 21[0:Inp] || -> duplicatefreeP(nil)*.
% 2.29/2.50 22[0:Inp] || -> strictorderedP(nil)*.
% 2.29/2.50 23[0:Inp] || -> totalorderedP(nil)*.
% 2.29/2.50 24[0:Inp] || -> strictorderP(nil)*.
% 2.29/2.50 25[0:Inp] || -> totalorderP(nil)*.
% 2.29/2.50 26[0:Inp] || -> cyclefreeP(nil)*.
% 2.29/2.50 27[0:Inp] || -> ssList(nil)*.
% 2.29/2.50 30[0:Inp] || singletonP(nil)* -> .
% 2.29/2.50 31[0:Inp] || -> ssItem(skaf83(u))*.
% 2.29/2.50 83[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.29/2.50 84[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.29/2.50 85[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.29/2.50 86[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.29/2.50 87[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.29/2.50 88[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.29/2.50 89[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.29/2.50 91[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 2.29/2.50 93[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 2.29/2.50 105[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 2.29/2.50 115[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 2.29/2.50 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 2.29/2.50 135[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 2.29/2.50 152[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(app(tl(u),v),tl(app(u,v)))**.
% 2.29/2.50 196[0:Inp] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(nil,v) equal(nil,u).
% 2.29/2.50 207[0:Rew:6.0,13.1] || -> ssItem(sk6)* equal(nil,sk1).
% 2.29/2.50 208[0:Rew:207.1,12.1,5.0,12.1] || -> ssItem(sk6)* equal(sk2,sk1).
% 2.29/2.50 209[0:Rew:6.0,18.1,5.0,18.0] || -> equal(nil,sk1) memberP(sk2,sk6)*.
% 2.29/2.50 211[0:Rew:6.0,17.1,6.0,17.0] || -> equal(nil,sk1) equal(cons(sk6,nil),sk1)**.
% 2.29/2.50 212[0:Rew:211.1,14.1,5.0,14.1,6.0,14.0] || -> equal(sk2,sk1) equal(cons(sk6,nil),sk1)**.
% 2.29/2.50 213[0:Rew:6.0,19.4,5.0,19.1] ssItem(u) || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u) equal(nil,sk1).
% 2.29/2.50 300[0:Res:2.0,91.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 2.29/2.50 471[0:Res:1.0,91.0] || -> ssItem(u)* duplicatefreeP(sk1)*.
% 2.29/2.50 486[0:Res:1.0,196.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 2.29/2.50 503[0:Res:1.0,152.1] ssList(u) || -> equal(nil,sk1) equal(app(tl(sk1),u),tl(app(sk1,u)))**.
% 2.29/2.50 521[0:Res:1.0,115.1] ssItem(u) || -> equal(tl(cons(u,sk1)),sk1)**.
% 2.29/2.50 524[0:Res:1.0,118.1] ssItem(u) || equal(cons(u,sk1),sk1)** -> .
% 2.29/2.50 527[0:Res:1.0,105.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 2.29/2.50 565[1:Spt:91.1] || -> ssItem(u)*.
% 2.29/2.50 579[1:MRR:524.0,565.0] || equal(cons(u,sk1),sk1)** -> .
% 2.29/2.50 636[1:MRR:213.0,565.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u) equal(nil,sk1).
% 2.29/2.50 638[1:MRR:9.0,565.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> leq(u,sk5(u))*.
% 2.29/2.50 639[1:MRR:8.0,565.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> memberP(sk2,sk5(u))*.
% 2.29/2.50 654[1:MRR:10.0,565.0] || memberP(sk2,u) equal(sk5(u),u) equal(cons(u,nil),sk1)** -> .
% 2.29/2.50 774[2:Spt:486.5] || -> equal(nil,sk1)**.
% 2.29/2.50 779[2:Rew:774.0,11.0] || equal(sk1,sk1) equal(nil,sk2)** -> .
% 2.29/2.50 783[2:Rew:774.0,212.1] || -> equal(sk2,sk1) equal(cons(sk6,sk1),sk1)**.
% 2.29/2.50 920[2:Obv:779.0] || equal(nil,sk2)** -> .
% 2.29/2.50 921[2:Rew:774.0,920.0] || equal(sk2,sk1)** -> .
% 2.29/2.50 928[2:MRR:783.0,783.1,921.0,579.0] || -> .
% 2.29/2.50 992[2:Spt:928.0,486.5,774.0] || equal(nil,sk1)** -> .
% 2.29/2.50 993[2:Spt:928.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.29/2.50 995[2:MRR:209.0,992.0] || -> memberP(sk2,sk6)*.
% 2.29/2.50 999[2:MRR:211.0,992.0] || -> equal(cons(sk6,nil),sk1)**.
% 2.29/2.50 1008[2:MRR:636.3,992.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u).
% 2.29/2.50 1892[2:Res:638.2,1008.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 1894[2:Rew:999.0,1892.1] || memberP(sk2,sk6) equal(sk1,sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 1895[2:Obv:1894.1] || memberP(sk2,sk6) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 1896[2:MRR:1895.0,995.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 1924[2:SpL:999.0,654.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) equal(sk1,sk1) -> .
% 2.29/2.50 1927[2:Obv:1924.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) -> .
% 2.29/2.50 1928[2:MRR:1927.0,995.0] || equal(sk5(sk6),sk6)** -> .
% 2.29/2.50 1929[2:MRR:1896.1,1928.0] || memberP(sk2,sk5(sk6))* -> .
% 2.29/2.50 1931[2:Res:639.2,1929.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1)** -> .
% 2.29/2.50 1933[2:Rew:999.0,1931.1] || memberP(sk2,sk6)* equal(sk1,sk1) -> .
% 2.29/2.50 1934[2:Obv:1933.1] || memberP(sk2,sk6)* -> .
% 2.29/2.50 1935[2:MRR:1934.0,995.0] || -> .
% 2.29/2.50 1936[1:Spt:1935.0,91.0,91.2] ssList(u) || -> duplicatefreeP(u)*.
% 2.29/2.50 1962[2:Spt:503.0,503.2] ssList(u) || -> equal(app(tl(sk1),u),tl(app(sk1,u)))**.
% 2.29/2.50 1972[3:Spt:471.0] || -> ssItem(u)*.
% 2.29/2.50 1993[3:MRR:524.0,1972.0] || equal(cons(u,sk1),sk1)** -> .
% 2.29/2.50 2041[3:MRR:8.0,1972.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> memberP(sk2,sk5(u))*.
% 2.29/2.50 2042[3:MRR:9.0,1972.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> leq(u,sk5(u))*.
% 2.29/2.50 2044[3:MRR:213.0,1972.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u) equal(nil,sk1).
% 2.29/2.50 2049[3:MRR:10.0,1972.0] || memberP(sk2,u) equal(sk5(u),u) equal(cons(u,nil),sk1)** -> .
% 2.29/2.50 2175[4:Spt:486.5] || -> equal(nil,sk1)**.
% 2.29/2.50 2233[4:Rew:2175.0,11.0] || equal(sk1,sk1) equal(nil,sk2)** -> .
% 2.29/2.50 2254[4:Rew:2175.0,212.1] || -> equal(sk2,sk1) equal(cons(sk6,sk1),sk1)**.
% 2.29/2.50 2348[4:Obv:2233.0] || equal(nil,sk2)** -> .
% 2.29/2.50 2349[4:Rew:2175.0,2348.0] || equal(sk2,sk1)** -> .
% 2.29/2.50 2358[4:MRR:2254.0,2254.1,2349.0,1993.0] || -> .
% 2.29/2.50 2400[4:Spt:2358.0,486.5,2175.0] || equal(nil,sk1)** -> .
% 2.29/2.50 2401[4:Spt:2358.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.29/2.50 2403[4:MRR:209.0,2400.0] || -> memberP(sk2,sk6)*.
% 2.29/2.50 2407[4:MRR:211.0,2400.0] || -> equal(cons(sk6,nil),sk1)**.
% 2.29/2.50 2419[4:MRR:2044.3,2400.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u).
% 2.29/2.50 3309[4:Res:2042.2,2419.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 3311[4:Rew:2407.0,3309.1] || memberP(sk2,sk6) equal(sk1,sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 3312[4:Obv:3311.1] || memberP(sk2,sk6) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 3313[4:MRR:3312.0,2403.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.29/2.50 3341[4:SpL:2407.0,2049.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) equal(sk1,sk1) -> .
% 2.29/2.50 3344[4:Obv:3341.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) -> .
% 2.29/2.50 3345[4:MRR:3344.0,2403.0] || equal(sk5(sk6),sk6)** -> .
% 2.29/2.50 3346[4:MRR:3313.1,3345.0] || memberP(sk2,sk5(sk6))* -> .
% 2.29/2.50 3348[4:Res:2041.2,3346.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1)** -> .
% 2.29/2.50 3350[4:Rew:2407.0,3348.1] || memberP(sk2,sk6)* equal(sk1,sk1) -> .
% 2.29/2.50 3351[4:Obv:3350.1] || memberP(sk2,sk6)* -> .
% 2.29/2.50 3352[4:MRR:3351.0,2403.0] || -> .
% 2.29/2.50 3353[3:Spt:3352.0,471.1] || -> duplicatefreeP(sk1)*.
% 2.29/2.50 3356[4:Spt:300.0] || -> ssItem(u)*.
% 2.29/2.50 3370[4:MRR:524.0,3356.0] || equal(cons(u,sk1),sk1)** -> .
% 2.29/2.50 3427[4:MRR:213.0,3356.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u) equal(nil,sk1).
% 2.29/2.50 3429[4:MRR:9.0,3356.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> leq(u,sk5(u))*.
% 2.29/2.50 3430[4:MRR:8.0,3356.0] || memberP(sk2,u) equal(cons(u,nil),sk1) -> memberP(sk2,sk5(u))*.
% 2.39/2.57 3445[4:MRR:10.0,3356.0] || memberP(sk2,u) equal(sk5(u),u) equal(cons(u,nil),sk1)** -> .
% 2.39/2.57 3557[5:Spt:486.5] || -> equal(nil,sk1)**.
% 2.39/2.57 3615[5:Rew:3557.0,11.0] || equal(sk1,sk1) equal(nil,sk2)** -> .
% 2.39/2.57 3636[5:Rew:3557.0,212.1] || -> equal(sk2,sk1) equal(cons(sk6,sk1),sk1)**.
% 2.39/2.57 3730[5:Obv:3615.0] || equal(nil,sk2)** -> .
% 2.39/2.57 3731[5:Rew:3557.0,3730.0] || equal(sk2,sk1)** -> .
% 2.39/2.57 3740[5:MRR:3636.0,3636.1,3731.0,3370.0] || -> .
% 2.39/2.57 3782[5:Spt:3740.0,486.5,3557.0] || equal(nil,sk1)** -> .
% 2.39/2.57 3783[5:Spt:3740.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.39/2.57 3785[5:MRR:209.0,3782.0] || -> memberP(sk2,sk6)*.
% 2.39/2.57 3789[5:MRR:211.0,3782.0] || -> equal(cons(sk6,nil),sk1)**.
% 2.39/2.57 3801[5:MRR:3427.3,3782.0] || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u).
% 2.39/2.57 4683[5:Res:3429.2,3801.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 4685[5:Rew:3789.0,4683.1] || memberP(sk2,sk6) equal(sk1,sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 4686[5:Obv:4685.1] || memberP(sk2,sk6) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 4687[5:MRR:4686.0,3785.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 4716[5:SpL:3789.0,3445.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) equal(sk1,sk1) -> .
% 2.39/2.57 4719[5:Obv:4716.2] || memberP(sk2,sk6)* equal(sk5(sk6),sk6) -> .
% 2.39/2.57 4720[5:MRR:4719.0,3785.0] || equal(sk5(sk6),sk6)** -> .
% 2.39/2.57 4721[5:MRR:4687.1,4720.0] || memberP(sk2,sk5(sk6))* -> .
% 2.39/2.57 4723[5:Res:3430.2,4721.0] || memberP(sk2,sk6) equal(cons(sk6,nil),sk1)** -> .
% 2.39/2.57 4725[5:Rew:3789.0,4723.1] || memberP(sk2,sk6)* equal(sk1,sk1) -> .
% 2.39/2.57 4726[5:Obv:4725.1] || memberP(sk2,sk6)* -> .
% 2.39/2.57 4727[5:MRR:4726.0,3785.0] || -> .
% 2.39/2.57 4728[4:Spt:4727.0,300.1] || -> duplicatefreeP(sk2)*.
% 2.39/2.57 4729[5:Spt:486.5] || -> equal(nil,sk1)**.
% 2.39/2.57 4759[5:Rew:4729.0,93.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 2.39/2.57 4788[5:Rew:4729.0,11.0] || equal(sk1,sk1) equal(nil,sk2)** -> .
% 2.39/2.57 4810[5:Rew:4729.0,83.1] ssItem(u) || -> equalelemsP(cons(u,sk1))*.
% 2.39/2.57 4811[5:Rew:4729.0,84.1] ssItem(u) || -> duplicatefreeP(cons(u,sk1))*.
% 2.39/2.57 4812[5:Rew:4729.0,85.1] ssItem(u) || -> strictorderedP(cons(u,sk1))*.
% 2.39/2.57 4813[5:Rew:4729.0,86.1] ssItem(u) || -> totalorderedP(cons(u,sk1))*.
% 2.39/2.57 4814[5:Rew:4729.0,87.1] ssItem(u) || -> strictorderP(cons(u,sk1))*.
% 2.39/2.57 4815[5:Rew:4729.0,88.1] ssItem(u) || -> totalorderP(cons(u,sk1))*.
% 2.39/2.57 4816[5:Rew:4729.0,89.1] ssItem(u) || -> cyclefreeP(cons(u,sk1))*.
% 2.39/2.57 4826[5:Rew:4729.0,212.1] || -> equal(sk2,sk1) equal(cons(sk6,sk1),sk1)**.
% 2.39/2.57 4888[5:Rew:4759.1,1962.1] ssList(u) || -> equal(app(tl(sk1),u),tl(u))**.
% 2.39/2.57 4903[5:Obv:4788.0] || equal(nil,sk2)** -> .
% 2.39/2.57 4904[5:Rew:4729.0,4903.0] || equal(sk2,sk1)** -> .
% 2.39/2.57 4905[5:MRR:208.1,4904.0] || -> ssItem(sk6)*.
% 2.39/2.57 4915[5:MRR:4826.0,4904.0] || -> equal(cons(sk6,sk1),sk1)**.
% 2.39/2.57 5022[5:SpR:4915.0,521.1] ssItem(sk6) || -> equal(tl(sk1),sk1)**.
% 2.39/2.57 5023[5:SSi:5022.0,4905.0] || -> equal(tl(sk1),sk1)**.
% 2.39/2.57 5024[5:Rew:5023.0,4888.1] ssList(u) || -> equal(app(sk1,u),tl(u))**.
% 2.39/2.57 5025[5:Rew:4759.1,5024.1] ssList(u) || -> equal(tl(u),u)**.
% 2.39/2.57 5043[5:SpR:5025.1,521.1] ssList(cons(u,sk1)) ssItem(u) || -> equal(cons(u,sk1),sk1)**.
% 2.39/2.57 5051[5:SSi:5043.0,4810.1,527.1,4811.1,4812.1,4813.1,4814.1,4815.1,4816.1] ssItem(u) || -> equal(cons(u,sk1),sk1)**.
% 2.39/2.57 5052[5:MRR:5051.1,524.1] ssItem(u) || -> .
% 2.39/2.57 5053[5:UnC:5052.0,31.0] || -> .
% 2.39/2.57 5054[5:Spt:5053.0,486.5,4729.0] || equal(nil,sk1)** -> .
% 2.39/2.57 5055[5:Spt:5053.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.39/2.57 5056[5:MRR:207.1,5054.0] || -> ssItem(sk6)*.
% 2.39/2.57 5058[5:MRR:209.0,5054.0] || -> memberP(sk2,sk6)*.
% 2.39/2.57 5063[5:MRR:211.0,5054.0] || -> equal(cons(sk6,nil),sk1)**.
% 2.39/2.57 5075[5:MRR:213.4,5054.0] ssItem(u) || leq(sk6,u)* memberP(sk2,u) -> equal(sk6,u).
% 2.39/2.57 6023[0:EqR:135.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 2.39/2.57 6027[0:SSi:6023.0,105.1,27.1,26.1,25.1,24.1,23.1,22.1,21.0,20.0,83.0,84.0,85.0,86.0,87.0,88.0,89.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 2.39/2.57 6356[5:SpL:5063.0,7.2] ssItem(sk6) || memberP(sk2,sk6)* equal(sk1,sk1) -> ssItem(sk5(sk6)).
% 2.39/2.57 6359[5:Obv:6356.2] ssItem(sk6) || memberP(sk2,sk6)* -> ssItem(sk5(sk6)).
% 2.39/2.57 6360[5:SSi:6359.0,5056.0] || memberP(sk2,sk6)* -> ssItem(sk5(sk6)).
% 2.39/2.57 6361[5:MRR:6360.0,5058.0] || -> ssItem(sk5(sk6))*.
% 2.39/2.57 6658[5:Res:9.3,5075.1] ssItem(sk6) ssItem(sk5(sk6)) || memberP(sk2,sk6) equal(cons(sk6,nil),sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6659[5:Rew:5063.0,6658.3] ssItem(sk6) ssItem(sk5(sk6)) || memberP(sk2,sk6) equal(sk1,sk1) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6660[5:Obv:6659.3] ssItem(sk6) ssItem(sk5(sk6)) || memberP(sk2,sk6) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6661[5:SSi:6660.1,6660.0,6361.0,5056.0] || memberP(sk2,sk6) memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6662[5:MRR:6661.0,5058.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6663[5:Res:8.3,6662.0] ssItem(sk6) || memberP(sk2,sk6) equal(cons(sk6,nil),sk1)** -> equal(sk5(sk6),sk6).
% 2.39/2.57 6664[5:Rew:5063.0,6663.2] ssItem(sk6) || memberP(sk2,sk6)* equal(sk1,sk1) -> equal(sk5(sk6),sk6).
% 2.39/2.57 6665[5:Obv:6664.2] ssItem(sk6) || memberP(sk2,sk6)* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6666[5:SSi:6665.0,5056.0] || memberP(sk2,sk6)* -> equal(sk5(sk6),sk6).
% 2.39/2.57 6667[5:MRR:6666.0,5058.0] || -> equal(sk5(sk6),sk6)**.
% 2.39/2.57 6891[5:SpL:5063.0,10.3] ssItem(sk6) || memberP(sk2,sk6)* equal(sk5(sk6),sk6) equal(sk1,sk1) -> .
% 2.39/2.57 6895[5:Obv:6891.3] ssItem(sk6) || memberP(sk2,sk6)* equal(sk5(sk6),sk6) -> .
% 2.39/2.57 6896[5:Rew:6667.0,6895.2] ssItem(sk6) || memberP(sk2,sk6)* equal(sk6,sk6) -> .
% 2.39/2.57 6897[5:Obv:6896.2] ssItem(sk6) || memberP(sk2,sk6)* -> .
% 2.39/2.57 6898[5:SSi:6897.0,5056.0] || memberP(sk2,sk6)* -> .
% 2.39/2.57 6899[5:MRR:6898.0,5058.0] || -> .
% 2.39/2.57 6904[2:Spt:6899.0,503.1] || -> equal(nil,sk1)**.
% 2.39/2.57 6926[2:Rew:6904.0,30.0] || singletonP(sk1)* -> .
% 2.39/2.57 6947[2:Rew:6904.0,6027.1] ssItem(u) || -> singletonP(cons(u,sk1))*.
% 2.39/2.57 7056[2:Rew:6904.0,212.1] || -> equal(sk2,sk1) equal(cons(sk6,sk1),sk1)**.
% 2.39/2.57 7057[2:Rew:6904.0,11.1,6904.0,11.0] || equal(sk1,sk1) equal(sk2,sk1)** -> .
% 2.39/2.57 7058[2:Obv:7057.0] || equal(sk2,sk1)** -> .
% 2.39/2.57 7059[2:MRR:208.1,7058.0] || -> ssItem(sk6)*.
% 2.39/2.57 7066[2:MRR:7056.0,7058.0] || -> equal(cons(sk6,sk1),sk1)**.
% 2.39/2.57 7462[2:SpR:7066.0,6947.1] ssItem(sk6) || -> singletonP(sk1)*.
% 2.39/2.57 7463[2:SSi:7462.0,7059.0] || -> singletonP(sk1)*.
% 2.39/2.57 7464[2:MRR:7463.0,6926.0] || -> .
% 2.39/2.57 % SZS output end Refutation
% 2.39/2.57 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_12 co1_13 co1_14 co1_17 co1_18 co1_19 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause11 clause12 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause74 clause86 clause96 clause99 clause116 clause133 clause177
% 2.39/2.57
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