TSTP Solution File: SWC378-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC378-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 22:03:41 EDT 2022
% Result : Unsatisfiable 33.82s 33.99s
% Output : Refutation 44.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : SWC378-1 : TPTP v8.1.0. Released v2.4.0.
% 0.05/0.09 % Command : run_spass %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Sun Jun 12 23:55:11 EDT 2022
% 0.07/0.27 % CPUTime :
% 33.82/33.99
% 33.82/33.99 SPASS V 3.9
% 33.82/33.99 SPASS beiseite: Proof found.
% 33.82/33.99 % SZS status Theorem
% 33.82/33.99 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.82/33.99 SPASS derived 36460 clauses, backtracked 20550 clauses, performed 133 splits and kept 34729 clauses.
% 33.82/33.99 SPASS allocated 109595 KBytes.
% 33.82/33.99 SPASS spent 0:0:33.67 on the problem.
% 33.82/33.99 0:00:00.03 for the input.
% 33.82/33.99 0:00:00.00 for the FLOTTER CNF translation.
% 33.82/33.99 0:00:00.35 for inferences.
% 33.82/33.99 0:00:01.12 for the backtracking.
% 33.82/33.99 0:0:31.80 for the reduction.
% 33.82/33.99
% 33.82/33.99
% 33.82/33.99 Here is a proof with depth 3, length 174 :
% 33.82/33.99 % SZS output start Refutation
% 33.82/33.99 5[0:Inp] || -> equal(sk4,sk2)**.
% 33.82/33.99 6[0:Inp] || -> equal(sk3,sk1)**.
% 33.82/33.99 7[0:Inp] || -> ssList(sk5)*.
% 33.82/33.99 8[0:Inp] || -> ssList(sk6)*.
% 33.82/33.99 9[0:Inp] || -> equal(app(sk5,sk6),sk4)**.
% 33.82/33.99 10[0:Inp] || -> equal(app(sk6,sk5),sk3)**.
% 33.82/33.99 12[0:Inp] || -> memberP(sk1,sk7) memberP(sk2,sk7)*.
% 33.82/33.99 13[0:Inp] || memberP(sk1,sk7) memberP(sk2,sk7)* -> .
% 33.82/33.99 25[0:Inp] || -> ssItem(skaf83(u))*.
% 33.82/33.99 85[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 33.82/33.99 98[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 33.82/33.99 99[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 33.82/33.99 101[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 33.82/33.99 153[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 33.82/33.99 154[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(w,u) -> memberP(app(v,w),u)*.
% 33.82/33.99 170[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 33.82/33.99 171[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(app(v,w),u)* -> memberP(v,u) memberP(w,u).
% 33.82/33.99 176[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 33.82/33.99 177[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 33.82/33.99 178[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 33.82/33.99 179[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 33.82/33.99 192[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)* -> .
% 33.82/33.99 201[0:Rew:6.0,10.0] || -> equal(app(sk6,sk5),sk1)**.
% 33.82/33.99 202[0:Rew:5.0,9.0] || -> equal(app(sk5,sk6),sk2)**.
% 33.82/33.99 325[0:Res:8.0,179.0] || -> totalorderP(sk6) equal(app(app(skaf56(sk6),cons(skaf54(sk6),skaf57(sk6))),cons(skaf55(sk6),skaf58(sk6))),sk6)**.
% 33.82/33.99 326[0:Res:8.0,178.0] || -> strictorderP(sk6) equal(app(app(skaf61(sk6),cons(skaf59(sk6),skaf62(sk6))),cons(skaf60(sk6),skaf63(sk6))),sk6)**.
% 33.82/33.99 327[0:Res:8.0,177.0] || -> totalorderedP(sk6) equal(app(app(skaf66(sk6),cons(skaf64(sk6),skaf67(sk6))),cons(skaf65(sk6),skaf68(sk6))),sk6)**.
% 33.82/33.99 328[0:Res:8.0,176.0] || -> strictorderedP(sk6) equal(app(app(skaf71(sk6),cons(skaf69(sk6),skaf72(sk6))),cons(skaf70(sk6),skaf73(sk6))),sk6)**.
% 33.82/33.99 385[0:Res:8.0,101.0] || -> cyclefreeP(sk6) leq(skaf49(sk6),skaf50(sk6))*.
% 33.82/33.99 446[0:Res:8.0,99.1] ssItem(u) || -> ssList(cons(u,sk6))*.
% 33.82/33.99 482[1:Spt:85.1] || -> ssItem(u)*.
% 33.82/33.99 579[1:MRR:154.0,482.0] ssList(u) ssList(v) || memberP(v,w) -> memberP(app(u,v),w)*.
% 33.82/33.99 580[1:MRR:153.0,482.0] ssList(u) ssList(v) || memberP(u,w) -> memberP(app(u,v),w)*.
% 33.82/33.99 602[1:MRR:171.0,482.0] ssList(u) ssList(v) || memberP(app(u,v),w)* -> memberP(u,w) memberP(v,w).
% 33.82/33.99 1147[2:Spt:327.0] || -> totalorderedP(sk6)*.
% 33.82/33.99 1151[3:Spt:328.0] || -> strictorderedP(sk6)*.
% 33.82/33.99 1154[4:Spt:385.0] || -> cyclefreeP(sk6)*.
% 33.82/33.99 1156[5:Spt:325.0] || -> totalorderP(sk6)*.
% 33.82/33.99 1157[6:Spt:326.0] || -> strictorderP(sk6)*.
% 33.82/33.99 1162[7:Spt:12.0] || -> memberP(sk1,sk7)*.
% 33.82/33.99 1163[7:MRR:13.0,1162.0] || memberP(sk2,sk7)* -> .
% 33.82/33.99 1853[1:SpR:201.0,579.3] ssList(sk6) ssList(sk5) || memberP(sk5,u)* -> memberP(sk1,u).
% 33.82/33.99 1855[1:SpR:202.0,579.3] ssList(sk5) ssList(sk6) || memberP(sk6,u)* -> memberP(sk2,u).
% 33.82/33.99 1865[1:SpR:201.0,580.3] ssList(sk6) ssList(sk5) || memberP(sk6,u)* -> memberP(sk1,u).
% 33.82/33.99 1867[1:SpR:202.0,580.3] ssList(sk5) ssList(sk6) || memberP(sk5,u)* -> memberP(sk2,u).
% 33.82/33.99 4105[1:SpL:202.0,602.2] ssList(sk5) ssList(sk6) || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 33.82/33.99 4108[1:SpL:201.0,602.2] ssList(sk6) ssList(sk5) || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 33.82/33.99 6371[6:SSi:1853.1,1853.0,7.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 33.82/33.99 6372[6:SSi:1855.1,1855.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 33.82/33.99 6373[6:SSi:1865.1,1865.0,7.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 33.82/33.99 6374[6:SSi:1867.1,1867.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 33.82/33.99 6388[6:SSi:4105.1,4105.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 33.82/33.99 6389[6:SSi:4108.1,4108.0,7.0,8.0,1157.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 33.82/33.99 7994[6:Res:6389.1,6372.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 33.82/33.99 7995[6:MRR:7994.1,6374.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 33.82/33.99 7996[7:Res:7995.1,1163.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 7997[7:MRR:7996.0,1162.0] || -> .
% 33.82/33.99 7998[7:Spt:7997.0,12.0,1162.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 7999[7:Spt:7997.0,12.1] || -> memberP(sk2,sk7)*.
% 33.82/33.99 10091[6:Res:6388.2,6373.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 33.82/33.99 10093[6:MRR:10091.1,6371.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 33.82/33.99 10096[7:Res:7999.0,10093.0] || -> memberP(sk1,sk7)*.
% 33.82/33.99 10097[7:MRR:10096.0,7998.0] || -> .
% 33.82/33.99 10098[6:Spt:10097.0,326.0,1157.0] || strictorderP(sk6)* -> .
% 33.82/33.99 10099[6:Spt:10097.0,326.1] || -> equal(app(app(skaf61(sk6),cons(skaf59(sk6),skaf62(sk6))),cons(skaf60(sk6),skaf63(sk6))),sk6)**.
% 33.82/33.99 10124[5:SSi:1853.1,1853.0,7.0,8.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 33.82/33.99 10125[5:SSi:1855.1,1855.0,8.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 33.82/33.99 10126[5:SSi:1865.1,1865.0,7.0,8.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 33.82/33.99 10127[5:SSi:1867.1,1867.0,8.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 33.82/33.99 10145[5:SSi:4105.1,4105.0,8.0,1156.0,1154.0,1151.0,1147.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 33.82/33.99 10146[5:SSi:4108.1,4108.0,7.0,8.0,1156.0,1154.0,1151.0,1147.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 33.82/33.99 10233[7:Spt:12.0] || -> memberP(sk1,sk7)*.
% 33.82/33.99 10234[7:MRR:13.0,10233.0] || memberP(sk2,sk7)* -> .
% 33.82/33.99 11922[5:Res:10146.1,10125.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 33.82/33.99 11923[5:MRR:11922.1,10127.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 33.82/33.99 11928[7:Res:11923.1,10234.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 11929[7:MRR:11928.0,10233.0] || -> .
% 33.82/33.99 11930[7:Spt:11929.0,12.0,10233.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 11931[7:Spt:11929.0,12.1] || -> memberP(sk2,sk7)*.
% 33.82/33.99 13307[5:Res:10145.2,10126.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 33.82/33.99 13309[5:MRR:13307.1,10124.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 33.82/33.99 13310[7:Res:11931.0,13309.0] || -> memberP(sk1,sk7)*.
% 33.82/33.99 13313[7:MRR:13310.0,11930.0] || -> .
% 33.82/33.99 13314[5:Spt:13313.0,325.0,1156.0] || totalorderP(sk6)* -> .
% 33.82/33.99 13315[5:Spt:13313.0,325.1] || -> equal(app(app(skaf56(sk6),cons(skaf54(sk6),skaf57(sk6))),cons(skaf55(sk6),skaf58(sk6))),sk6)**.
% 33.82/33.99 13340[4:SSi:1853.1,1853.0,7.0,8.0,1154.0,1151.0,1147.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 33.82/33.99 13341[4:SSi:1855.1,1855.0,8.0,1154.0,1151.0,1147.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 33.82/33.99 13342[4:SSi:1865.1,1865.0,7.0,8.0,1154.0,1151.0,1147.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 33.82/33.99 13343[4:SSi:1867.1,1867.0,8.0,1154.0,1151.0,1147.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 33.82/33.99 13363[4:SSi:4105.1,4105.0,8.0,1154.0,1151.0,1147.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 33.82/33.99 13364[4:SSi:4108.1,4108.0,7.0,8.0,1154.0,1151.0,1147.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 33.82/33.99 13476[6:Spt:12.0] || -> memberP(sk1,sk7)*.
% 33.82/33.99 13477[6:MRR:13.0,13476.0] || memberP(sk2,sk7)* -> .
% 33.82/33.99 15042[4:Res:13364.1,13341.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 33.82/33.99 15043[4:MRR:15042.1,13343.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 33.82/33.99 15044[6:Res:15043.1,13477.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 15045[6:MRR:15044.0,13476.0] || -> .
% 33.82/33.99 15046[6:Spt:15045.0,12.0,13476.0] || memberP(sk1,sk7)* -> .
% 33.82/33.99 15047[6:Spt:15045.0,12.1] || -> memberP(sk2,sk7)*.
% 33.82/33.99 16355[4:Res:13363.2,13342.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 33.82/33.99 16357[4:MRR:16355.1,13340.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 44.46/44.65 16358[6:Res:15047.0,16357.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 16361[6:MRR:16358.0,15046.0] || -> .
% 44.46/44.65 16362[4:Spt:16361.0,385.0,1154.0] || cyclefreeP(sk6)* -> .
% 44.46/44.65 16363[4:Spt:16361.0,385.1] || -> leq(skaf49(sk6),skaf50(sk6))*.
% 44.46/44.65 16387[3:SSi:1853.1,1853.0,7.0,1151.0,8.0,1147.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 44.46/44.65 16388[3:SSi:1855.1,1855.0,1151.0,8.0,1147.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 44.46/44.65 16389[3:SSi:1865.1,1865.0,7.0,1151.0,8.0,1147.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 44.46/44.65 16390[3:SSi:1867.1,1867.0,1151.0,8.0,1147.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 44.46/44.65 16410[3:SSi:4105.1,4105.0,1151.0,8.0,1147.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 44.46/44.65 16411[3:SSi:4108.1,4108.0,7.0,1151.0,8.0,1147.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 44.46/44.65 16488[5:Spt:12.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 16489[5:MRR:13.0,16488.0] || memberP(sk2,sk7)* -> .
% 44.46/44.65 17950[3:Res:16411.1,16388.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 44.46/44.65 17951[3:MRR:17950.1,16390.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 44.46/44.65 17956[5:Res:17951.1,16489.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 17957[5:MRR:17956.0,16488.0] || -> .
% 44.46/44.65 17958[5:Spt:17957.0,12.0,16488.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 17959[5:Spt:17957.0,12.1] || -> memberP(sk2,sk7)*.
% 44.46/44.65 19276[3:Res:16410.2,16389.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 44.46/44.65 19278[3:MRR:19276.1,16387.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 44.46/44.65 19279[5:Res:17959.0,19278.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 19282[5:MRR:19279.0,17958.0] || -> .
% 44.46/44.65 19283[3:Spt:19282.0,328.0,1151.0] || strictorderedP(sk6)* -> .
% 44.46/44.65 19284[3:Spt:19282.0,328.1] || -> equal(app(app(skaf71(sk6),cons(skaf69(sk6),skaf72(sk6))),cons(skaf70(sk6),skaf73(sk6))),sk6)**.
% 44.46/44.65 19307[2:SSi:1853.1,1853.0,7.0,8.0,1147.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 44.46/44.65 19308[2:SSi:1855.1,1855.0,8.0,1147.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 44.46/44.65 19309[2:SSi:1865.1,1865.0,7.0,8.0,1147.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 44.46/44.65 19310[2:SSi:1867.1,1867.0,8.0,1147.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 44.46/44.65 19329[2:SSi:4105.1,4105.0,8.0,1147.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 44.46/44.65 19330[2:SSi:4108.1,4108.0,7.0,8.0,1147.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 44.46/44.65 19457[4:Spt:12.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 19458[4:MRR:13.0,19457.0] || memberP(sk2,sk7)* -> .
% 44.46/44.65 20923[2:Res:19330.1,19308.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 44.46/44.65 20924[2:MRR:20923.1,19310.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 44.46/44.65 20925[4:Res:20924.1,19458.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 20926[4:MRR:20925.0,19457.0] || -> .
% 44.46/44.65 20927[4:Spt:20926.0,12.0,19457.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 20928[4:Spt:20926.0,12.1] || -> memberP(sk2,sk7)*.
% 44.46/44.65 22082[2:Res:19329.2,19309.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 44.46/44.65 22084[2:MRR:22082.1,19307.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 44.46/44.65 22085[4:Res:20928.0,22084.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 22088[4:MRR:22085.0,20927.0] || -> .
% 44.46/44.65 22089[2:Spt:22088.0,327.0,1147.0] || totalorderedP(sk6)* -> .
% 44.46/44.65 22090[2:Spt:22088.0,327.1] || -> equal(app(app(skaf66(sk6),cons(skaf64(sk6),skaf67(sk6))),cons(skaf65(sk6),skaf68(sk6))),sk6)**.
% 44.46/44.65 22115[1:SSi:1853.1,1853.0,7.0,8.0] || memberP(sk5,u)* -> memberP(sk1,u).
% 44.46/44.65 22116[1:SSi:1855.1,1855.0,8.0,7.0] || memberP(sk6,u)* -> memberP(sk2,u).
% 44.46/44.65 22117[1:SSi:1865.1,1865.0,7.0,8.0] || memberP(sk6,u)* -> memberP(sk1,u).
% 44.46/44.65 22118[1:SSi:1867.1,1867.0,8.0,7.0] || memberP(sk5,u)* -> memberP(sk2,u).
% 44.46/44.65 22136[1:SSi:4105.1,4105.0,8.0,7.0] || memberP(sk2,u) -> memberP(sk5,u) memberP(sk6,u)*.
% 44.46/44.65 22137[1:SSi:4108.1,4108.0,7.0,8.0] || memberP(sk1,u) -> memberP(sk6,u)* memberP(sk5,u).
% 44.46/44.65 22274[3:Spt:12.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 22275[3:MRR:13.0,22274.0] || memberP(sk2,sk7)* -> .
% 44.46/44.65 23629[1:Res:22137.1,22116.0] || memberP(sk1,u) -> memberP(sk5,u)* memberP(sk2,u).
% 44.46/44.65 23630[1:MRR:23629.1,22118.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 44.46/44.65 23631[3:Res:23630.1,22275.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 23632[3:MRR:23631.0,22274.0] || -> .
% 44.46/44.65 23633[3:Spt:23632.0,12.0,22274.0] || memberP(sk1,sk7)* -> .
% 44.46/44.65 23634[3:Spt:23632.0,12.1] || -> memberP(sk2,sk7)*.
% 44.46/44.65 24841[1:Res:22136.2,22117.0] || memberP(sk2,u) -> memberP(sk5,u)* memberP(sk1,u).
% 44.46/44.65 24843[1:MRR:24841.1,22115.0] || memberP(sk2,u)* -> memberP(sk1,u).
% 44.46/44.65 24844[3:Res:23634.0,24843.0] || -> memberP(sk1,sk7)*.
% 44.46/44.65 24847[3:MRR:24844.0,23633.0] || -> .
% 44.46/44.65 24848[1:Spt:24847.0,85.0,85.2] ssList(u) || -> duplicatefreeP(u)*.
% 44.46/44.65 24873[1:MRR:192.1,24848.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 44.46/44.65 51790[0:SpR:170.3,98.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 44.46/44.65 51823[0:Obv:51790.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 44.46/44.65 51824[0:SSi:51823.2,99.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 44.46/44.65 52632[1:EqR:24873.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 44.46/44.65 52658[1:SSi:52632.0,98.2,98.2,99.2,99.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 44.46/44.65 52659[1:MRR:51824.3,52658.1] ssList(u) ssItem(v) ssList(w) || -> .
% 44.46/44.65 52662[1:Con:52659.2] ssList(u) ssItem(v) || -> .
% 44.46/44.65 52663[1:MRR:446.1,52662.0] ssItem(u) || -> .
% 44.46/44.65 52664[1:UnC:52663.0,25.0] || -> .
% 44.46/44.65 % SZS output end Refutation
% 44.46/44.65 Formulae used in the proof : co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_12 co1_13 clause12 clause72 clause85 clause86 clause88 clause140 clause141 clause157 clause158 clause163 clause164 clause165 clause166 clause179
% 44.46/44.65
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