TSTP Solution File: SWC392+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC392+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:03:47 EDT 2022
% Result : Theorem 2.63s 2.84s
% Output : Refutation 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC392+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 06:28:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.63/2.84
% 2.63/2.84 SPASS V 3.9
% 2.63/2.84 SPASS beiseite: Proof found.
% 2.63/2.84 % SZS status Theorem
% 2.63/2.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.63/2.84 SPASS derived 4330 clauses, backtracked 1326 clauses, performed 37 splits and kept 3221 clauses.
% 2.63/2.84 SPASS allocated 103875 KBytes.
% 2.63/2.84 SPASS spent 0:00:02.49 on the problem.
% 2.63/2.84 0:00:00.04 for the input.
% 2.63/2.84 0:00:00.05 for the FLOTTER CNF translation.
% 2.63/2.84 0:00:00.05 for inferences.
% 2.63/2.84 0:00:00.05 for the backtracking.
% 2.63/2.84 0:00:02.15 for the reduction.
% 2.63/2.84
% 2.63/2.84
% 2.63/2.84 Here is a proof with depth 5, length 148 :
% 2.63/2.84 % SZS output start Refutation
% 2.63/2.84 1[0:Inp] || -> ssItem(skc7)*.
% 2.63/2.84 2[0:Inp] || -> ssList(skc6)*.
% 2.63/2.84 3[0:Inp] || -> ssList(skc5)*.
% 2.63/2.84 6[0:Inp] || -> ssList(nil)*.
% 2.63/2.84 7[0:Inp] || -> cyclefreeP(nil)*.
% 2.63/2.84 8[0:Inp] || -> totalorderP(nil)*.
% 2.63/2.84 9[0:Inp] || -> strictorderP(nil)*.
% 2.63/2.84 10[0:Inp] || -> totalorderedP(nil)*.
% 2.63/2.84 11[0:Inp] || -> strictorderedP(nil)*.
% 2.63/2.84 12[0:Inp] || -> duplicatefreeP(nil)*.
% 2.63/2.84 13[0:Inp] || -> equalelemsP(nil)*.
% 2.63/2.84 14[0:Inp] || -> memberP(skc5,skc7)*.
% 2.63/2.84 15[0:Inp] || -> ssItem(skf47(u))*.
% 2.63/2.84 53[0:Inp] || -> ssItem(skf44(u,v))*.
% 2.63/2.84 54[0:Inp] || memberP(skc6,skc7)* -> .
% 2.63/2.84 70[0:Inp] || SkP0(skc6,skc5)* -> equal(nil,skc6).
% 2.63/2.84 71[0:Inp] || SkP0(skc6,skc5)* -> equal(nil,skc5).
% 2.63/2.84 72[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.63/2.84 73[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.63/2.84 74[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.63/2.84 75[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.63/2.84 76[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.63/2.84 77[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.63/2.84 78[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.63/2.84 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.63/2.84 81[0:Inp] || -> SkP0(u,v) memberP(u,skf44(u,v))*.
% 2.63/2.84 86[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 2.63/2.84 88[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 2.63/2.84 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf53(u),skf52(u))*.
% 2.63/2.84 91[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(skf78(u),skf77(u))**.
% 2.63/2.84 108[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 2.63/2.84 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 2.63/2.84 113[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 2.63/2.84 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 2.63/2.84 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 2.63/2.84 171[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 2.63/2.84 174[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf74(u),cons(skf72(u),skf75(u))),cons(skf73(u),skf76(u))),u)**.
% 2.63/2.84 175[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf69(u),cons(skf67(u),skf70(u))),cons(skf68(u),skf71(u))),u)**.
% 2.63/2.84 176[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf64(u),cons(skf62(u),skf65(u))),cons(skf63(u),skf66(u))),u)**.
% 2.63/2.84 177[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf59(u),cons(skf57(u),skf60(u))),cons(skf58(u),skf61(u))),u)**.
% 2.63/2.84 189[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).
% 2.63/2.84 198[0:Rew:71.1,70.1] || SkP0(skc6,skc5)* -> equal(skc6,skc5).
% 2.63/2.84 220[0:Res:3.0,177.0] || -> totalorderP(skc5) equal(app(app(skf59(skc5),cons(skf57(skc5),skf60(skc5))),cons(skf58(skc5),skf61(skc5))),skc5)**.
% 2.63/2.84 221[0:Res:3.0,176.0] || -> strictorderP(skc5) equal(app(app(skf64(skc5),cons(skf62(skc5),skf65(skc5))),cons(skf63(skc5),skf66(skc5))),skc5)**.
% 2.63/2.84 222[0:Res:3.0,175.0] || -> totalorderedP(skc5) equal(app(app(skf69(skc5),cons(skf67(skc5),skf70(skc5))),cons(skf68(skc5),skf71(skc5))),skc5)**.
% 2.63/2.84 223[0:Res:3.0,174.0] || -> strictorderedP(skc5) equal(app(app(skf74(skc5),cons(skf72(skc5),skf75(skc5))),cons(skf73(skc5),skf76(skc5))),skc5)**.
% 2.63/2.84 252[0:Res:3.0,119.0] || -> equal(nil,skc5) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.63/2.84 253[0:Res:3.0,108.1] singletonP(skc5) || -> equal(cons(skf47(skc5),nil),skc5)**.
% 2.63/2.84 266[0:Res:3.0,89.0] || -> cyclefreeP(skc5) leq(skf53(skc5),skf52(skc5))*.
% 2.63/2.84 268[0:Res:3.0,91.0] || -> duplicatefreeP(skc5) equal(skf78(skc5),skf77(skc5))**.
% 2.63/2.84 277[0:Res:3.0,86.0] || -> ssItem(hd(skc5))* equal(nil,skc5).
% 2.63/2.84 287[0:Res:3.0,189.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 2.63/2.84 322[0:Res:3.0,122.1] ssItem(u) || equal(cons(u,nil),skc5)** -> singletonP(skc5).
% 2.63/2.84 458[0:Res:2.0,189.1] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u) equal(nil,skc6).
% 2.63/2.84 558[1:Spt:458.5] || -> equal(nil,skc6)**.
% 2.63/2.84 631[1:Rew:558.0,13.0] || -> equalelemsP(skc6)*.
% 2.63/2.84 632[1:Rew:558.0,12.0] || -> duplicatefreeP(skc6)*.
% 2.63/2.84 633[1:Rew:558.0,11.0] || -> strictorderedP(skc6)*.
% 2.63/2.84 634[1:Rew:558.0,10.0] || -> totalorderedP(skc6)*.
% 2.63/2.84 635[1:Rew:558.0,9.0] || -> strictorderP(skc6)*.
% 2.63/2.84 636[1:Rew:558.0,8.0] || -> totalorderP(skc6)*.
% 2.63/2.84 637[1:Rew:558.0,7.0] || -> cyclefreeP(skc6)*.
% 2.63/2.84 653[1:Rew:558.0,72.1] ssItem(u) || memberP(skc6,u)* -> .
% 2.63/2.84 759[2:Spt:198.1] || -> equal(skc6,skc5)**.
% 2.63/2.84 833[2:Rew:759.0,54.0] || memberP(skc5,skc7)* -> .
% 2.63/2.84 919[2:MRR:833.0,14.0] || -> .
% 2.63/2.84 1012[2:Spt:919.0,198.1,759.0] || equal(skc6,skc5)** -> .
% 2.63/2.84 1013[2:Spt:919.0,198.0] || SkP0(skc6,skc5)* -> .
% 2.63/2.84 1062[1:Res:81.1,653.1] ssItem(skf44(skc6,u)) || -> SkP0(skc6,u)*.
% 2.63/2.84 1063[1:SSi:1062.0,53.0,637.0,636.0,635.0,634.0,633.0,632.0,631.0,2.0] || -> SkP0(skc6,u)*.
% 2.63/2.84 1064[2:UnC:1063.0,1013.0] || -> .
% 2.63/2.84 1065[1:Spt:1064.0,458.5,558.0] || equal(nil,skc6)** -> .
% 2.63/2.84 1066[1:Spt:1064.0,458.0,458.1,458.2,458.3,458.4] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u).
% 2.63/2.84 1081[2:Spt:287.5] || -> equal(nil,skc5)**.
% 2.63/2.84 1116[2:Rew:1081.0,72.1] ssItem(u) || memberP(skc5,u)* -> .
% 2.63/2.84 1272[2:Res:14.0,1116.1] ssItem(skc7) || -> .
% 2.63/2.84 1274[2:SSi:1272.0,1.0] || -> .
% 2.63/2.84 1276[2:Spt:1274.0,287.5,1081.0] || equal(nil,skc5)** -> .
% 2.63/2.84 1277[2:Spt:1274.0,287.0,287.1,287.2,287.3,287.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 2.63/2.84 1279[2:MRR:277.1,1276.0] || -> ssItem(hd(skc5))*.
% 2.63/2.84 1283[2:MRR:71.1,1276.0] || SkP0(skc6,skc5)* -> .
% 2.63/2.84 1284[2:MRR:252.0,1276.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.63/2.84 1300[3:Spt:222.0] || -> totalorderedP(skc5)*.
% 2.63/2.84 1304[4:Spt:223.0] || -> strictorderedP(skc5)*.
% 2.63/2.84 1309[5:Spt:266.0] || -> cyclefreeP(skc5)*.
% 2.63/2.84 1313[6:Spt:220.0] || -> totalorderP(skc5)*.
% 2.63/2.84 1314[7:Spt:221.0] || -> strictorderP(skc5)*.
% 2.63/2.84 1322[8:Spt:268.0] || -> duplicatefreeP(skc5)*.
% 2.63/2.84 1402[0:SpR:88.1,79.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 2.63/2.84 1403[0:SpR:88.1,78.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* duplicatefreeP(v).
% 2.63/2.84 1404[0:SpR:88.1,77.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderedP(v).
% 2.63/2.84 1405[0:SpR:88.1,76.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderedP(v).
% 2.63/2.84 1406[0:SpR:88.1,75.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderP(v).
% 2.63/2.84 1407[0:SpR:88.1,74.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderP(v).
% 2.63/2.84 1408[0:SpR:88.1,73.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* cyclefreeP(v).
% 2.63/2.84 1411[0:SSi:1402.0,53.0] || -> SkP0(u,v)* equalelemsP(v).
% 2.63/2.84 1412[0:SSi:1403.0,53.0] || -> SkP0(u,v)* duplicatefreeP(v).
% 2.63/2.84 1413[0:SSi:1404.0,53.0] || -> SkP0(u,v)* strictorderedP(v).
% 2.63/2.84 1414[0:SSi:1405.0,53.0] || -> SkP0(u,v)* totalorderedP(v).
% 2.63/2.84 1415[0:SSi:1406.0,53.0] || -> SkP0(u,v)* strictorderP(v).
% 2.63/2.84 1416[0:SSi:1407.0,53.0] || -> SkP0(u,v)* totalorderP(v).
% 2.63/2.84 1417[0:SSi:1408.0,53.0] || -> SkP0(u,v)* cyclefreeP(v).
% 2.63/2.84 1419[2:Res:1411.0,1283.0] || -> equalelemsP(skc5)*.
% 2.63/2.84 1421[2:Res:1412.0,1283.0] || -> duplicatefreeP(skc5)*.
% 2.63/2.84 1422[2:Res:1413.0,1283.0] || -> strictorderedP(skc5)*.
% 2.63/2.84 1423[2:Res:1414.0,1283.0] || -> totalorderedP(skc5)*.
% 2.63/2.84 1424[2:Res:1415.0,1283.0] || -> strictorderP(skc5)*.
% 2.63/2.84 1425[2:Res:1416.0,1283.0] || -> totalorderP(skc5)*.
% 2.63/2.84 1426[2:Res:1417.0,1283.0] || -> cyclefreeP(skc5)*.
% 2.63/2.84 1432[0:SpL:88.1,322.1] ssItem(skf44(u,v)) || equal(v,skc5) -> SkP0(u,v)* singletonP(skc5).
% 2.63/2.84 1433[0:SSi:1432.0,53.0] || equal(u,skc5) -> SkP0(v,u)* singletonP(skc5).
% 2.63/2.84 1434[9:Spt:1433.0,1433.1] || equal(u,skc5) -> SkP0(v,u)*.
% 2.63/2.84 1435[9:Res:1434.1,1283.0] || equal(skc5,skc5)* -> .
% 2.63/2.84 1436[9:Obv:1435.0] || -> .
% 2.63/2.84 1437[9:Spt:1436.0,1433.2] || -> singletonP(skc5)*.
% 2.63/2.84 1438[9:MRR:253.0,1437.0] || -> equal(cons(skf47(skc5),nil),skc5)**.
% 2.63/2.84 1516[9:SpR:1438.0,113.2] ssItem(skf47(skc5)) ssList(nil) || -> equal(tl(skc5),nil)**.
% 2.63/2.84 1520[9:SSi:1516.1,1516.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,15.0,3.0,1300.0,1304.0,1309.0,1313.0,1314.0,1322.0,1419.0,1437.0] || -> equal(tl(skc5),nil)**.
% 2.79/2.94 1523[9:Rew:1520.0,1284.0] || -> equal(cons(hd(skc5),nil),skc5)**.
% 2.79/2.94 1563[0:SpR:88.1,112.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 2.79/2.94 1567[0:SSi:1563.1,1563.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,53.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 2.79/2.94 1568[0:Rew:1567.1,81.1] || -> SkP0(u,v) memberP(u,hd(v))*.
% 2.79/2.94 5807[9:SpL:1523.0,171.3] ssList(nil) ssItem(hd(skc5)) ssItem(u) || memberP(skc5,u) -> memberP(nil,u)* equal(u,hd(skc5)).
% 2.79/2.94 5813[9:SSi:5807.1,5807.0,1279.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0] ssItem(u) || memberP(skc5,u) -> memberP(nil,u)* equal(u,hd(skc5)).
% 2.79/2.94 5814[9:MRR:5813.2,72.1] ssItem(u) || memberP(skc5,u)* -> equal(u,hd(skc5)).
% 2.79/2.94 5835[9:Res:14.0,5814.1] ssItem(skc7) || -> equal(hd(skc5),skc7)**.
% 2.79/2.94 5838[9:SSi:5835.0,1.0] || -> equal(hd(skc5),skc7)**.
% 2.79/2.94 6003[9:SpR:5838.0,1568.1] || -> SkP0(u,skc5)* memberP(u,skc7).
% 2.79/2.94 6498[9:Res:6003.0,1283.0] || -> memberP(skc6,skc7)*.
% 2.79/2.94 6499[9:MRR:6498.0,54.0] || -> .
% 2.79/2.94 6500[8:Spt:6499.0,268.0,1322.0] || duplicatefreeP(skc5)* -> .
% 2.79/2.94 6501[8:Spt:6499.0,268.1] || -> equal(skf78(skc5),skf77(skc5))**.
% 2.79/2.94 6502[8:MRR:6500.0,1421.0] || -> .
% 2.79/2.94 6597[7:Spt:6502.0,221.0,1314.0] || strictorderP(skc5)* -> .
% 2.79/2.94 6598[7:Spt:6502.0,221.1] || -> equal(app(app(skf64(skc5),cons(skf62(skc5),skf65(skc5))),cons(skf63(skc5),skf66(skc5))),skc5)**.
% 2.79/2.94 6599[7:MRR:6597.0,1424.0] || -> .
% 2.79/2.94 6717[6:Spt:6599.0,220.0,1313.0] || totalorderP(skc5)* -> .
% 2.79/2.94 6718[6:Spt:6599.0,220.1] || -> equal(app(app(skf59(skc5),cons(skf57(skc5),skf60(skc5))),cons(skf58(skc5),skf61(skc5))),skc5)**.
% 2.79/2.94 6719[6:MRR:6717.0,1425.0] || -> .
% 2.79/2.94 6768[5:Spt:6719.0,266.0,1309.0] || cyclefreeP(skc5)* -> .
% 2.79/2.94 6769[5:Spt:6719.0,266.1] || -> leq(skf53(skc5),skf52(skc5))*.
% 2.79/2.94 6770[5:MRR:6768.0,1426.0] || -> .
% 2.79/2.94 6864[4:Spt:6770.0,223.0,1304.0] || strictorderedP(skc5)* -> .
% 2.79/2.94 6865[4:Spt:6770.0,223.1] || -> equal(app(app(skf74(skc5),cons(skf72(skc5),skf75(skc5))),cons(skf73(skc5),skf76(skc5))),skc5)**.
% 2.79/2.94 6866[4:MRR:6864.0,1422.0] || -> .
% 2.79/2.94 6962[3:Spt:6866.0,222.0,1300.0] || totalorderedP(skc5)* -> .
% 2.79/2.94 6963[3:Spt:6866.0,222.1] || -> equal(app(app(skf69(skc5),cons(skf67(skc5),skf70(skc5))),cons(skf68(skc5),skf71(skc5))),skc5)**.
% 2.79/2.94 6964[3:MRR:6962.0,1423.0] || -> .
% 2.79/2.94 % SZS output end Refutation
% 2.79/2.94 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 ax23 ax25 ax78 ax37 ax12 ax11 ax10 ax9 ax77
% 2.79/2.94
%------------------------------------------------------------------------------