TSTP Solution File: SWC198+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC198+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 22:02:25 EDT 2022
% Result : Theorem 2.05s 2.24s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC198+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 23:54:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.05/2.24
% 2.05/2.24 SPASS V 3.9
% 2.05/2.24 SPASS beiseite: Proof found.
% 2.05/2.24 % SZS status Theorem
% 2.05/2.24 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.05/2.24 SPASS derived 3934 clauses, backtracked 1220 clauses, performed 37 splits and kept 2883 clauses.
% 2.05/2.24 SPASS allocated 103135 KBytes.
% 2.05/2.24 SPASS spent 0:00:01.87 on the problem.
% 2.05/2.24 0:00:00.04 for the input.
% 2.05/2.24 0:00:00.07 for the FLOTTER CNF translation.
% 2.05/2.24 0:00:00.04 for inferences.
% 2.05/2.24 0:00:00.04 for the backtracking.
% 2.05/2.24 0:00:01.51 for the reduction.
% 2.05/2.24
% 2.05/2.24
% 2.05/2.24 Here is a proof with depth 4, length 149 :
% 2.05/2.24 % SZS output start Refutation
% 2.05/2.24 1[0:Inp] || -> ssList(skc5)*.
% 2.05/2.24 2[0:Inp] || -> ssList(skc4)*.
% 2.05/2.24 5[0:Inp] || -> ssList(nil)*.
% 2.05/2.24 6[0:Inp] || -> cyclefreeP(nil)*.
% 2.05/2.24 7[0:Inp] || -> totalorderP(nil)*.
% 2.05/2.24 8[0:Inp] || -> strictorderP(nil)*.
% 2.05/2.24 9[0:Inp] || -> totalorderedP(nil)*.
% 2.05/2.24 10[0:Inp] || -> strictorderedP(nil)*.
% 2.05/2.24 11[0:Inp] || -> duplicatefreeP(nil)*.
% 2.05/2.24 12[0:Inp] || -> equalelemsP(nil)*.
% 2.05/2.24 13[0:Inp] || -> ssItem(skf45(u))*.
% 2.05/2.24 14[0:Inp] || -> ssItem(skf49(u))*.
% 2.05/2.24 52[0:Inp] || -> ssItem(skf46(u,v))*.
% 2.05/2.24 68[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc5).
% 2.05/2.24 69[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc4).
% 2.05/2.24 70[0:Inp] ssItem(u) || -> memberP(skc4,skf45(u))*.
% 2.05/2.24 71[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.05/2.24 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.05/2.24 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.05/2.24 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.05/2.24 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.05/2.24 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.05/2.24 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.05/2.24 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.05/2.24 80[0:Inp] ssItem(u) || equal(skf45(u),u)** -> .
% 2.05/2.24 81[0:Inp] || -> SkP0(u,v) memberP(u,skf46(u,v))*.
% 2.05/2.24 86[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 2.05/2.24 88[0:Inp] || -> SkP0(u,v) equal(cons(skf46(u,v),nil),v)**.
% 2.05/2.24 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf55(u),skf54(u))*.
% 2.05/2.24 91[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(skf80(u),skf79(u))**.
% 2.05/2.24 108[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf49(u),nil),u)**.
% 2.05/2.24 113[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 2.05/2.24 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 2.05/2.24 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 2.05/2.24 171[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 2.05/2.24 174[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf76(u),cons(skf74(u),skf77(u))),cons(skf75(u),skf78(u))),u)**.
% 2.05/2.24 175[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf71(u),cons(skf69(u),skf72(u))),cons(skf70(u),skf73(u))),u)**.
% 2.05/2.24 176[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf66(u),cons(skf64(u),skf67(u))),cons(skf65(u),skf68(u))),u)**.
% 2.05/2.24 177[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf61(u),cons(skf59(u),skf62(u))),cons(skf60(u),skf63(u))),u)**.
% 2.05/2.24 189[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).
% 2.05/2.24 198[0:Rew:69.1,68.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4).
% 2.05/2.24 220[0:Res:2.0,177.0] || -> totalorderP(skc4) equal(app(app(skf61(skc4),cons(skf59(skc4),skf62(skc4))),cons(skf60(skc4),skf63(skc4))),skc4)**.
% 2.05/2.24 221[0:Res:2.0,176.0] || -> strictorderP(skc4) equal(app(app(skf66(skc4),cons(skf64(skc4),skf67(skc4))),cons(skf65(skc4),skf68(skc4))),skc4)**.
% 2.05/2.24 222[0:Res:2.0,175.0] || -> totalorderedP(skc4) equal(app(app(skf71(skc4),cons(skf69(skc4),skf72(skc4))),cons(skf70(skc4),skf73(skc4))),skc4)**.
% 2.05/2.24 223[0:Res:2.0,174.0] || -> strictorderedP(skc4) equal(app(app(skf76(skc4),cons(skf74(skc4),skf77(skc4))),cons(skf75(skc4),skf78(skc4))),skc4)**.
% 2.05/2.24 252[0:Res:2.0,119.0] || -> equal(nil,skc4) equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 2.05/2.24 253[0:Res:2.0,108.1] singletonP(skc4) || -> equal(cons(skf49(skc4),nil),skc4)**.
% 2.05/2.24 266[0:Res:2.0,89.0] || -> cyclefreeP(skc4) leq(skf55(skc4),skf54(skc4))*.
% 2.05/2.24 268[0:Res:2.0,91.0] || -> duplicatefreeP(skc4) equal(skf80(skc4),skf79(skc4))**.
% 2.05/2.24 277[0:Res:2.0,86.0] || -> ssItem(hd(skc4))* equal(nil,skc4).
% 2.05/2.24 287[0:Res:2.0,189.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(nil,skc4).
% 2.05/2.24 322[0:Res:2.0,122.1] ssItem(u) || equal(cons(u,nil),skc4)** -> singletonP(skc4).
% 2.05/2.24 448[0:Res:1.0,86.0] || -> ssItem(hd(skc5))* equal(nil,skc5).
% 2.05/2.24 458[0:Res:1.0,189.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 2.05/2.24 558[1:Spt:458.5] || -> equal(nil,skc5)**.
% 2.05/2.24 631[1:Rew:558.0,12.0] || -> equalelemsP(skc5)*.
% 2.05/2.24 632[1:Rew:558.0,11.0] || -> duplicatefreeP(skc5)*.
% 2.05/2.24 633[1:Rew:558.0,10.0] || -> strictorderedP(skc5)*.
% 2.05/2.24 634[1:Rew:558.0,9.0] || -> totalorderedP(skc5)*.
% 2.05/2.24 635[1:Rew:558.0,8.0] || -> strictorderP(skc5)*.
% 2.05/2.24 636[1:Rew:558.0,7.0] || -> totalorderP(skc5)*.
% 2.05/2.24 637[1:Rew:558.0,6.0] || -> cyclefreeP(skc5)*.
% 2.05/2.24 653[1:Rew:558.0,71.1] ssItem(u) || memberP(skc5,u)* -> .
% 2.05/2.24 759[2:Spt:198.1] || -> equal(skc5,skc4)**.
% 2.05/2.24 877[2:Rew:759.0,653.1] ssItem(u) || memberP(skc4,u)* -> .
% 2.05/2.24 1013[2:Res:70.1,877.1] ssItem(u) ssItem(skf45(u)) || -> .
% 2.05/2.24 1014[2:SSi:1013.1,13.0] ssItem(u) || -> .
% 2.05/2.24 1015[2:UnC:1014.0,52.0] || -> .
% 2.05/2.24 1016[2:Spt:1015.0,198.1,759.0] || equal(skc5,skc4)** -> .
% 2.05/2.24 1017[2:Spt:1015.0,198.0] || SkP0(skc5,skc4)* -> .
% 2.05/2.24 1066[1:Res:81.1,653.1] ssItem(skf46(skc5,u)) || -> SkP0(skc5,u)*.
% 2.05/2.24 1067[1:SSi:1066.0,52.0,637.0,636.0,635.0,634.0,633.0,632.0,631.0,1.0] || -> SkP0(skc5,u)*.
% 2.05/2.24 1068[2:UnC:1067.0,1017.0] || -> .
% 2.05/2.24 1069[1:Spt:1068.0,458.5,558.0] || equal(nil,skc5)** -> .
% 2.05/2.24 1070[1:Spt:1068.0,458.0,458.1,458.2,458.3,458.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 2.05/2.24 1072[1:MRR:448.1,1069.0] || -> ssItem(hd(skc5))*.
% 2.05/2.24 1085[2:Spt:287.5] || -> equal(nil,skc4)**.
% 2.05/2.24 1120[2:Rew:1085.0,71.1] ssItem(u) || memberP(skc4,u)* -> .
% 2.05/2.24 1275[2:Res:70.1,1120.1] ssItem(u) ssItem(skf45(u)) || -> .
% 2.05/2.24 1277[2:SSi:1275.1,13.0] ssItem(u) || -> .
% 2.05/2.24 1278[2:UnC:1277.0,1072.0] || -> .
% 2.05/2.24 1280[2:Spt:1278.0,287.5,1085.0] || equal(nil,skc4)** -> .
% 2.05/2.24 1281[2:Spt:1278.0,287.0,287.1,287.2,287.3,287.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 2.05/2.24 1283[2:MRR:277.1,1280.0] || -> ssItem(hd(skc4))*.
% 2.05/2.24 1287[2:MRR:69.1,1280.0] || SkP0(skc5,skc4)* -> .
% 2.05/2.24 1288[2:MRR:252.0,1280.0] || -> equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 2.05/2.24 1304[3:Spt:222.0] || -> totalorderedP(skc4)*.
% 2.05/2.24 1308[4:Spt:223.0] || -> strictorderedP(skc4)*.
% 2.05/2.24 1313[5:Spt:266.0] || -> cyclefreeP(skc4)*.
% 2.05/2.24 1317[6:Spt:220.0] || -> totalorderP(skc4)*.
% 2.05/2.24 1318[7:Spt:221.0] || -> strictorderP(skc4)*.
% 2.05/2.24 1327[8:Spt:268.0] || -> duplicatefreeP(skc4)*.
% 2.05/2.24 1407[0:SpR:88.1,78.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 2.05/2.24 1408[0:SpR:88.1,77.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* duplicatefreeP(v).
% 2.05/2.24 1409[0:SpR:88.1,76.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* strictorderedP(v).
% 2.05/2.24 1410[0:SpR:88.1,75.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* totalorderedP(v).
% 2.05/2.24 1411[0:SpR:88.1,74.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* strictorderP(v).
% 2.05/2.24 1412[0:SpR:88.1,73.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* totalorderP(v).
% 2.05/2.24 1413[0:SpR:88.1,72.1] ssItem(skf46(u,v)) || -> SkP0(u,v)* cyclefreeP(v).
% 2.05/2.24 1416[0:SSi:1407.0,52.0] || -> SkP0(u,v)* equalelemsP(v).
% 2.05/2.24 1417[0:SSi:1408.0,52.0] || -> SkP0(u,v)* duplicatefreeP(v).
% 2.05/2.24 1418[0:SSi:1409.0,52.0] || -> SkP0(u,v)* strictorderedP(v).
% 2.05/2.24 1419[0:SSi:1410.0,52.0] || -> SkP0(u,v)* totalorderedP(v).
% 2.05/2.24 1420[0:SSi:1411.0,52.0] || -> SkP0(u,v)* strictorderP(v).
% 2.05/2.24 1421[0:SSi:1412.0,52.0] || -> SkP0(u,v)* totalorderP(v).
% 2.05/2.24 1422[0:SSi:1413.0,52.0] || -> SkP0(u,v)* cyclefreeP(v).
% 2.05/2.24 1424[2:Res:1416.0,1287.0] || -> equalelemsP(skc4)*.
% 2.05/2.24 1426[2:Res:1417.0,1287.0] || -> duplicatefreeP(skc4)*.
% 2.05/2.24 1427[2:Res:1418.0,1287.0] || -> strictorderedP(skc4)*.
% 2.05/2.24 1428[2:Res:1419.0,1287.0] || -> totalorderedP(skc4)*.
% 2.05/2.24 1429[2:Res:1420.0,1287.0] || -> strictorderP(skc4)*.
% 2.05/2.24 1430[2:Res:1421.0,1287.0] || -> totalorderP(skc4)*.
% 2.05/2.24 1431[2:Res:1422.0,1287.0] || -> cyclefreeP(skc4)*.
% 2.05/2.24 1437[0:SpL:88.1,322.1] ssItem(skf46(u,v)) || equal(v,skc4) -> SkP0(u,v)* singletonP(skc4).
% 2.05/2.24 1438[0:SSi:1437.0,52.0] || equal(u,skc4) -> SkP0(v,u)* singletonP(skc4).
% 2.05/2.24 1439[9:Spt:1438.0,1438.1] || equal(u,skc4) -> SkP0(v,u)*.
% 2.05/2.24 1440[9:Res:1439.1,1287.0] || equal(skc4,skc4)* -> .
% 2.05/2.24 1441[9:Obv:1440.0] || -> .
% 2.05/2.24 1442[9:Spt:1441.0,1438.2] || -> singletonP(skc4)*.
% 2.05/2.24 1443[9:MRR:253.0,1442.0] || -> equal(cons(skf49(skc4),nil),skc4)**.
% 2.12/2.32 1519[9:SpR:1443.0,113.2] ssItem(skf49(skc4)) ssList(nil) || -> equal(tl(skc4),nil)**.
% 2.12/2.32 1523[9:SSi:1519.1,1519.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0,14.0,2.0,1304.0,1308.0,1313.0,1317.0,1318.0,1327.0,1424.0,1442.0] || -> equal(tl(skc4),nil)**.
% 2.12/2.32 1526[9:Rew:1523.0,1288.0] || -> equal(cons(hd(skc4),nil),skc4)**.
% 2.12/2.32 5808[9:SpL:1526.0,171.3] ssList(nil) ssItem(hd(skc4)) ssItem(u) || memberP(skc4,u) -> memberP(nil,u)* equal(u,hd(skc4)).
% 2.12/2.32 5814[9:SSi:5808.1,5808.0,1283.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0] ssItem(u) || memberP(skc4,u) -> memberP(nil,u)* equal(u,hd(skc4)).
% 2.12/2.32 5815[9:MRR:5814.2,71.1] ssItem(u) || memberP(skc4,u)* -> equal(u,hd(skc4)).
% 2.12/2.32 5834[9:Res:70.1,5815.1] ssItem(u) ssItem(skf45(u)) || -> equal(skf45(u),hd(skc4))**.
% 2.12/2.32 5837[9:SSi:5834.1,13.0] ssItem(u) || -> equal(skf45(u),hd(skc4))**.
% 2.12/2.32 5839[9:Rew:5837.1,80.1] ssItem(u) || equal(hd(skc4),u)* -> .
% 2.12/2.32 5869[9:EqR:5839.1] ssItem(hd(skc4)) || -> .
% 2.12/2.32 5870[9:SSi:5869.0,1283.0] || -> .
% 2.12/2.32 5871[8:Spt:5870.0,268.0,1327.0] || duplicatefreeP(skc4)* -> .
% 2.12/2.32 5872[8:Spt:5870.0,268.1] || -> equal(skf80(skc4),skf79(skc4))**.
% 2.12/2.32 5873[8:MRR:5871.0,1426.0] || -> .
% 2.12/2.32 5954[7:Spt:5873.0,221.0,1318.0] || strictorderP(skc4)* -> .
% 2.12/2.32 5955[7:Spt:5873.0,221.1] || -> equal(app(app(skf66(skc4),cons(skf64(skc4),skf67(skc4))),cons(skf65(skc4),skf68(skc4))),skc4)**.
% 2.12/2.32 5956[7:MRR:5954.0,1429.0] || -> .
% 2.12/2.32 6052[6:Spt:5956.0,220.0,1317.0] || totalorderP(skc4)* -> .
% 2.12/2.32 6053[6:Spt:5956.0,220.1] || -> equal(app(app(skf61(skc4),cons(skf59(skc4),skf62(skc4))),cons(skf60(skc4),skf63(skc4))),skc4)**.
% 2.12/2.32 6054[6:MRR:6052.0,1430.0] || -> .
% 2.12/2.32 6090[5:Spt:6054.0,266.0,1313.0] || cyclefreeP(skc4)* -> .
% 2.12/2.32 6091[5:Spt:6054.0,266.1] || -> leq(skf55(skc4),skf54(skc4))*.
% 2.12/2.32 6092[5:MRR:6090.0,1431.0] || -> .
% 2.12/2.32 6165[4:Spt:6092.0,223.0,1308.0] || strictorderedP(skc4)* -> .
% 2.12/2.32 6166[4:Spt:6092.0,223.1] || -> equal(app(app(skf76(skc4),cons(skf74(skc4),skf77(skc4))),cons(skf75(skc4),skf78(skc4))),skc4)**.
% 2.12/2.32 6167[4:MRR:6165.0,1427.0] || -> .
% 2.12/2.32 6242[3:Spt:6167.0,222.0,1304.0] || totalorderedP(skc4)* -> .
% 2.12/2.32 6243[3:Spt:6167.0,222.1] || -> equal(app(app(skf71(skc4),cons(skf69(skc4),skf72(skc4))),cons(skf70(skc4),skf73(skc4))),skc4)**.
% 2.12/2.32 6244[3:MRR:6242.0,1428.0] || -> .
% 2.12/2.32 % SZS output end Refutation
% 2.12/2.32 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax75 ax8 ax13 ax25 ax78 ax37 ax12 ax11 ax10 ax9 ax77
% 2.12/2.32
%------------------------------------------------------------------------------