TSTP Solution File: SWC387+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC387+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 22:03:45 EDT 2022
% Result : Theorem 0.71s 0.88s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC387+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 10:56:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/0.88
% 0.71/0.88 SPASS V 3.9
% 0.71/0.88 SPASS beiseite: Proof found.
% 0.71/0.88 % SZS status Theorem
% 0.71/0.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.71/0.88 SPASS derived 1050 clauses, backtracked 470 clauses, performed 20 splits and kept 1163 clauses.
% 0.71/0.88 SPASS allocated 99143 KBytes.
% 0.71/0.88 SPASS spent 0:00:00.54 on the problem.
% 0.71/0.88 0:00:00.04 for the input.
% 0.71/0.88 0:00:00.06 for the FLOTTER CNF translation.
% 0.71/0.88 0:00:00.01 for inferences.
% 0.71/0.88 0:00:00.01 for the backtracking.
% 0.71/0.88 0:00:00.28 for the reduction.
% 0.71/0.88
% 0.71/0.88
% 0.71/0.88 Here is a proof with depth 3, length 125 :
% 0.71/0.88 % SZS output start Refutation
% 0.71/0.88 1[0:Inp] || -> ssItem(skc7)*.
% 0.71/0.88 2[0:Inp] || -> ssList(skc6)*.
% 0.71/0.88 3[0:Inp] || -> ssList(skc5)*.
% 0.71/0.88 6[0:Inp] || -> ssList(nil)*.
% 0.71/0.88 7[0:Inp] || -> cyclefreeP(nil)*.
% 0.71/0.88 8[0:Inp] || -> totalorderP(nil)*.
% 0.71/0.88 9[0:Inp] || -> strictorderP(nil)*.
% 0.71/0.88 10[0:Inp] || -> totalorderedP(nil)*.
% 0.71/0.88 11[0:Inp] || -> strictorderedP(nil)*.
% 0.71/0.88 12[0:Inp] || -> duplicatefreeP(nil)*.
% 0.71/0.88 13[0:Inp] || -> equalelemsP(nil)*.
% 0.71/0.88 14[0:Inp] || -> ssItem(skf45(u))*.
% 0.71/0.88 67[0:Inp] || equal(skc6,nil)** -> equal(skc5,nil).
% 0.71/0.88 68[0:Inp] || neq(skc6,nil) -> memberP(skc6,skc7)*.
% 0.71/0.88 70[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 0.71/0.88 71[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 0.71/0.88 72[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 0.71/0.88 73[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 0.71/0.88 74[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 0.71/0.88 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 0.71/0.88 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 0.71/0.88 78[0:Inp] || equal(skc6,nil)** equal(skc5,nil) -> .
% 0.71/0.88 81[0:Inp] || neq(skc6,nil) -> equal(cons(skc7,nil),skc5)**.
% 0.71/0.88 86[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 0.71/0.88 105[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 0.71/0.88 106[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 0.71/0.88 108[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 0.71/0.88 109[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 0.71/0.88 110[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 0.71/0.88 111[0:Inp] ssItem(u) || memberP(skc6,u) equal(cons(u,nil),skc5)** -> .
% 0.71/0.88 117[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 0.71/0.88 120[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 0.71/0.88 152[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 0.71/0.88 172[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 0.71/0.88 173[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 0.71/0.88 174[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 0.71/0.88 175[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 0.71/0.88 195[0:Rew:67.1,78.1] || equal(skc6,nil)** equal(nil,nil) -> .
% 0.71/0.88 196[0:Obv:195.1] || equal(skc6,nil)** -> .
% 0.71/0.88 218[0:Res:3.0,175.0] || -> totalorderP(skc5) equal(app(app(skf57(skc5),cons(skf55(skc5),skf58(skc5))),cons(skf56(skc5),skf59(skc5))),skc5)**.
% 0.71/0.88 219[0:Res:3.0,174.0] || -> strictorderP(skc5) equal(app(app(skf62(skc5),cons(skf60(skc5),skf63(skc5))),cons(skf61(skc5),skf64(skc5))),skc5)**.
% 0.71/0.88 220[0:Res:3.0,173.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 0.71/0.88 221[0:Res:3.0,172.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 0.71/0.88 250[0:Res:3.0,117.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 0.71/0.88 251[0:Res:3.0,105.1] singletonP(skc5) || -> equal(cons(skf45(skc5),nil),skc5)**.
% 0.71/0.88 254[0:Res:3.0,108.0] ssItem(u) || equal(cons(u,skc5),nil)** -> .
% 0.71/0.88 264[0:Res:3.0,86.0] || -> cyclefreeP(skc5) leq(skf51(skc5),skf50(skc5))*.
% 0.71/0.88 308[0:Res:3.0,152.1] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)) equal(skc5,nil).
% 0.71/0.88 320[0:Res:3.0,120.1] ssItem(u) || equal(cons(u,nil),skc5)** -> singletonP(skc5).
% 0.71/0.88 423[0:Res:2.0,106.0] ssList(u) || -> neq(skc6,u)* equal(skc6,u).
% 0.71/0.88 564[1:Spt:308.3] || -> equal(skc5,nil)**.
% 0.71/0.88 585[1:Rew:564.0,254.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 0.71/0.88 680[1:Rew:564.0,81.1] || neq(skc6,nil) -> equal(cons(skc7,nil),nil)**.
% 0.71/0.88 880[1:SpL:680.1,585.1] ssItem(skc7) || neq(skc6,nil)* equal(nil,nil) -> .
% 0.71/0.88 881[1:Obv:880.2] ssItem(skc7) || neq(skc6,nil)* -> .
% 0.71/0.88 882[1:SSi:881.0,1.0] || neq(skc6,nil)* -> .
% 0.71/0.88 1036[1:Res:423.1,882.0] ssList(nil) || -> equal(skc6,nil)**.
% 0.71/0.88 1037[1:SSi:1036.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil)**.
% 0.71/0.88 1038[1:MRR:1037.0,196.0] || -> .
% 0.71/0.88 1039[1:Spt:1038.0,308.3,564.0] || equal(skc5,nil)** -> .
% 0.71/0.88 1040[1:Spt:1038.0,308.0,308.1,308.2] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)).
% 0.71/0.88 1046[1:MRR:250.0,1039.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 0.71/0.88 1061[2:Spt:221.0] || -> strictorderedP(skc5)*.
% 0.71/0.88 1064[3:Spt:220.0] || -> totalorderedP(skc5)*.
% 0.71/0.88 1070[4:Spt:264.0] || -> cyclefreeP(skc5)*.
% 0.71/0.88 1074[5:Spt:219.0] || -> strictorderP(skc5)*.
% 0.71/0.88 1075[6:Spt:218.0] || -> totalorderP(skc5)*.
% 0.71/0.88 1076[0:SpR:81.1,76.1] ssItem(skc7) || neq(skc6,nil)* -> equalelemsP(skc5).
% 0.71/0.88 1077[0:SpR:81.1,75.1] ssItem(skc7) || neq(skc6,nil)* -> duplicatefreeP(skc5).
% 0.71/0.88 1085[0:SSi:1076.0,1.0] || neq(skc6,nil)* -> equalelemsP(skc5).
% 0.71/0.88 1086[0:SSi:1077.0,1.0] || neq(skc6,nil)* -> duplicatefreeP(skc5).
% 0.71/0.88 1095[0:Res:423.1,1085.0] ssList(nil) || -> equal(skc6,nil) equalelemsP(skc5)*.
% 0.71/0.88 1096[0:SSi:1095.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil) equalelemsP(skc5)*.
% 0.71/0.88 1097[0:MRR:1096.0,196.0] || -> equalelemsP(skc5)*.
% 0.71/0.88 1099[0:Res:423.1,1086.0] ssList(nil) || -> equal(skc6,nil) duplicatefreeP(skc5)*.
% 0.71/0.88 1100[0:SSi:1099.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil) duplicatefreeP(skc5)*.
% 0.71/0.88 1101[0:MRR:1100.0,196.0] || -> duplicatefreeP(skc5)*.
% 0.71/0.88 1154[0:SpL:81.1,320.1] ssItem(skc7) || neq(skc6,nil)* equal(skc5,skc5) -> singletonP(skc5).
% 0.71/0.88 1155[0:Obv:1154.2] ssItem(skc7) || neq(skc6,nil)* -> singletonP(skc5).
% 0.71/0.88 1156[0:SSi:1155.0,1.0] || neq(skc6,nil)* -> singletonP(skc5).
% 0.71/0.88 1159[0:Res:423.1,1156.0] ssList(nil) || -> equal(skc6,nil) singletonP(skc5)*.
% 0.71/0.88 1160[0:SSi:1159.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil) singletonP(skc5)*.
% 0.71/0.88 1161[0:MRR:1160.0,196.0] || -> singletonP(skc5)*.
% 0.71/0.88 1162[0:MRR:251.0,1161.0] || -> equal(cons(skf45(skc5),nil),skc5)**.
% 0.71/0.88 1165[0:SpR:1162.0,72.1] ssItem(skf45(skc5)) || -> strictorderP(skc5)*.
% 0.71/0.88 1166[0:SpR:1162.0,71.1] ssItem(skf45(skc5)) || -> totalorderP(skc5)*.
% 0.71/0.88 1167[0:SpR:1162.0,70.1] ssItem(skf45(skc5)) || -> cyclefreeP(skc5)*.
% 0.71/0.88 1168[0:SpR:1162.0,74.1] ssItem(skf45(skc5)) || -> strictorderedP(skc5)*.
% 0.71/0.88 1169[0:SpR:1162.0,73.1] ssItem(skf45(skc5)) || -> totalorderedP(skc5)*.
% 0.71/0.88 1224[0:SpR:1162.0,110.2] ssItem(skf45(skc5)) ssList(nil) || -> equal(tl(skc5),nil)**.
% 0.71/0.88 1227[6:SSi:1224.1,1224.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0,14.0,3.0,1061.0,1064.0,1070.0,1074.0,1075.0,1097.0,1101.0,1161.0] || -> equal(tl(skc5),nil)**.
% 0.71/0.88 1229[6:Rew:1227.0,1046.0] || -> equal(cons(hd(skc5),nil),skc5)**.
% 0.71/0.88 1266[0:SpR:81.1,109.2] ssItem(skc7) ssList(nil) || neq(skc6,nil)* -> equal(hd(skc5),skc7).
% 0.71/0.88 1270[0:SSi:1266.1,1266.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0,1.0] || neq(skc6,nil)* -> equal(hd(skc5),skc7).
% 0.71/0.88 1332[0:Res:423.1,1270.0] ssList(nil) || -> equal(skc6,nil) equal(hd(skc5),skc7)**.
% 0.71/0.88 1333[0:SSi:1332.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil) equal(hd(skc5),skc7)**.
% 0.71/0.88 1334[0:MRR:1333.0,196.0] || -> equal(hd(skc5),skc7)**.
% 0.71/0.88 1338[6:Rew:1334.0,1229.0] || -> equal(cons(skc7,nil),skc5)**.
% 0.71/0.88 1430[6:SpL:1338.0,111.2] ssItem(skc7) || memberP(skc6,skc7)* equal(skc5,skc5) -> .
% 0.71/0.88 1431[6:Obv:1430.2] ssItem(skc7) || memberP(skc6,skc7)* -> .
% 0.71/0.88 1432[6:SSi:1431.0,1.0] || memberP(skc6,skc7)* -> .
% 0.71/0.88 1433[6:MRR:68.1,1432.0] || neq(skc6,nil)* -> .
% 0.71/0.88 1436[6:Res:423.1,1433.0] ssList(nil) || -> equal(skc6,nil)**.
% 0.71/0.88 1439[6:SSi:1436.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc6,nil)**.
% 0.71/0.88 1440[6:MRR:1439.0,196.0] || -> .
% 0.71/0.88 1444[6:Spt:1440.0,218.0,1075.0] || totalorderP(skc5)* -> .
% 0.71/0.88 1445[6:Spt:1440.0,218.1] || -> equal(app(app(skf57(skc5),cons(skf55(skc5),skf58(skc5))),cons(skf56(skc5),skf59(skc5))),skc5)**.
% 0.71/0.88 1446[5:SSi:1166.0,14.0,3.0,1061.0,1064.0,1070.0,1074.0,1097.0,1101.0,1161.0] || -> totalorderP(skc5)*.
% 0.71/0.88 1447[6:MRR:1446.0,1444.0] || -> .
% 0.71/0.88 1480[5:Spt:1447.0,219.0,1074.0] || strictorderP(skc5)* -> .
% 0.71/0.89 1481[5:Spt:1447.0,219.1] || -> equal(app(app(skf62(skc5),cons(skf60(skc5),skf63(skc5))),cons(skf61(skc5),skf64(skc5))),skc5)**.
% 0.71/0.89 1483[4:SSi:1165.0,14.0,3.0,1061.0,1064.0,1070.0,1097.0,1101.0,1161.0] || -> strictorderP(skc5)*.
% 0.71/0.89 1484[5:MRR:1483.0,1480.0] || -> .
% 0.71/0.89 1510[4:Spt:1484.0,264.0,1070.0] || cyclefreeP(skc5)* -> .
% 0.71/0.89 1511[4:Spt:1484.0,264.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 0.71/0.89 1513[3:SSi:1167.0,14.0,3.0,1061.0,1064.0,1097.0,1101.0,1161.0] || -> cyclefreeP(skc5)*.
% 0.71/0.89 1514[4:MRR:1513.0,1510.0] || -> .
% 0.71/0.89 1552[3:Spt:1514.0,220.0,1064.0] || totalorderedP(skc5)* -> .
% 0.71/0.89 1553[3:Spt:1514.0,220.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 0.71/0.89 1555[2:SSi:1169.0,14.0,3.0,1061.0,1097.0,1101.0,1161.0] || -> totalorderedP(skc5)*.
% 0.71/0.89 1556[3:MRR:1555.0,1552.0] || -> .
% 0.71/0.89 1603[2:Spt:1556.0,221.0,1061.0] || strictorderedP(skc5)* -> .
% 0.71/0.89 1604[2:Spt:1556.0,221.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 0.71/0.89 1606[0:SSi:1168.0,14.0,3.0,1097.0,1101.0,1161.0] || -> strictorderedP(skc5)*.
% 0.71/0.89 1607[2:MRR:1606.0,1603.0] || -> .
% 0.71/0.89 % SZS output end Refutation
% 0.71/0.89 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax8 ax15 ax21 ax23 ax25 ax78 ax70 ax12 ax11 ax10 ax9
% 0.71/0.89
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