TSTP Solution File: SWC229-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC229-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 22:02:38 EDT 2022
% Result : Unsatisfiable 7.18s 7.38s
% Output : Refutation 8.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC229-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 06:36:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.18/7.38
% 7.18/7.38 SPASS V 3.9
% 7.18/7.38 SPASS beiseite: Proof found.
% 7.18/7.38 % SZS status Theorem
% 7.18/7.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.18/7.38 SPASS derived 12483 clauses, backtracked 3699 clauses, performed 114 splits and kept 9081 clauses.
% 7.18/7.38 SPASS allocated 90240 KBytes.
% 7.18/7.38 SPASS spent 0:00:07.02 on the problem.
% 7.18/7.38 0:00:00.04 for the input.
% 7.18/7.38 0:00:00.00 for the FLOTTER CNF translation.
% 7.18/7.38 0:00:00.13 for inferences.
% 7.18/7.38 0:00:00.20 for the backtracking.
% 7.18/7.38 0:00:06.36 for the reduction.
% 7.18/7.38
% 7.18/7.38
% 7.18/7.38 Here is a proof with depth 2, length 158 :
% 7.18/7.38 % SZS output start Refutation
% 7.18/7.38 1[0:Inp] || -> ssList(sk1)*.
% 7.18/7.38 2[0:Inp] || -> ssList(sk2)*.
% 7.18/7.38 5[0:Inp] || -> equal(sk4,sk2)**.
% 7.18/7.38 6[0:Inp] || -> equal(sk3,sk1)**.
% 7.18/7.38 7[0:Inp] || -> segmentP(sk4,sk3)*.
% 7.18/7.38 8[0:Inp] || equal(nil,sk1)** -> .
% 7.18/7.38 10[0:Inp] ssList(u) ssList(v) ssItem(w) || equal(app(app(v,cons(w,nil)),u),sk1)**+ -> memberP(v,sk5(u,v,w))*.
% 7.18/7.38 14[0:Inp] || neq(sk4,nil)* -> singletonP(sk3).
% 7.18/7.38 15[0:Inp] || -> equalelemsP(nil)*.
% 7.18/7.38 16[0:Inp] || -> duplicatefreeP(nil)*.
% 7.18/7.38 17[0:Inp] || -> strictorderedP(nil)*.
% 7.18/7.38 18[0:Inp] || -> totalorderedP(nil)*.
% 7.18/7.38 19[0:Inp] || -> strictorderP(nil)*.
% 7.18/7.38 20[0:Inp] || -> totalorderP(nil)*.
% 7.18/7.38 21[0:Inp] || -> cyclefreeP(nil)*.
% 7.18/7.38 22[0:Inp] || -> ssList(nil)*.
% 7.18/7.38 26[0:Inp] || -> ssItem(skaf83(u))*.
% 7.18/7.38 27[0:Inp] || -> ssList(skaf82(u))*.
% 7.18/7.38 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 7.18/7.38 79[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 7.18/7.38 80[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 7.18/7.38 81[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 7.18/7.38 82[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 7.18/7.38 83[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 7.18/7.38 84[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 7.18/7.38 85[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 7.18/7.38 86[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 7.18/7.38 88[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 7.18/7.38 94[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 7.18/7.38 99[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 7.18/7.38 100[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 7.18/7.38 102[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 7.18/7.38 111[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 7.18/7.38 115[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 7.18/7.38 116[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 7.18/7.38 123[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 7.18/7.38 130[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 7.18/7.38 171[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 7.18/7.38 177[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 7.18/7.38 178[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 7.18/7.38 179[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 7.18/7.38 180[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 7.18/7.38 191[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).
% 7.18/7.38 193[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)* -> .
% 7.18/7.38 201[0:Rew:6.0,7.0] || -> segmentP(sk4,sk1)*.
% 7.18/7.38 203[0:Rew:5.0,201.0] || -> segmentP(sk2,sk1)*.
% 7.18/7.38 204[0:Rew:6.0,14.1,5.0,14.0] || neq(sk2,nil)* -> singletonP(sk1).
% 7.18/7.38 305[0:Res:2.0,191.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 7.18/7.38 351[0:Res:2.0,100.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 7.18/7.38 406[0:Res:1.0,180.0] || -> totalorderP(sk1) equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 7.18/7.38 407[0:Res:1.0,179.0] || -> strictorderP(sk1) equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 7.18/7.38 408[0:Res:1.0,178.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 7.18/7.38 409[0:Res:1.0,177.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 7.18/7.38 448[0:Res:1.0,123.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)** equal(nil,sk1).
% 7.18/7.38 450[0:Res:1.0,115.1] singletonP(sk1) || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 7.18/7.38 459[0:Res:1.0,94.0] || segmentP(nil,sk1)* -> equal(nil,sk1).
% 7.18/7.38 466[0:Res:1.0,102.0] || -> cyclefreeP(sk1) leq(skaf49(sk1),skaf50(sk1))*.
% 7.18/7.38 573[0:MRR:459.1,8.0] || segmentP(nil,sk1)* -> .
% 7.18/7.38 577[0:MRR:448.1,8.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 7.18/7.38 589[1:Spt:86.1] || -> ssItem(u)*.
% 7.18/7.38 594[1:MRR:85.0,589.0] || memberP(nil,u)* -> .
% 7.18/7.38 595[1:MRR:84.0,589.0] || -> cyclefreeP(cons(u,nil))*.
% 7.18/7.38 596[1:MRR:83.0,589.0] || -> totalorderP(cons(u,nil))*.
% 7.18/7.38 597[1:MRR:82.0,589.0] || -> strictorderP(cons(u,nil))*.
% 7.18/7.38 598[1:MRR:81.0,589.0] || -> totalorderedP(cons(u,nil))*.
% 7.18/7.38 599[1:MRR:80.0,589.0] || -> strictorderedP(cons(u,nil))*.
% 7.18/7.38 600[1:MRR:79.0,589.0] || -> duplicatefreeP(cons(u,nil))*.
% 7.18/7.38 601[1:MRR:78.0,589.0] || -> equalelemsP(cons(u,nil))*.
% 7.18/7.38 621[1:MRR:116.1,116.0,589.0] || -> equal(u,v) neq(u,v)*.
% 7.18/7.38 712[1:MRR:100.1,589.0] ssList(u) || -> ssList(cons(v,u))*.
% 7.18/7.38 715[1:MRR:111.1,589.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 7.18/7.38 717[1:MRR:130.1,589.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 7.18/7.38 796[1:MRR:171.2,589.0] ssList(u) ssList(v) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 7.18/7.38 801[1:MRR:10.2,589.0] ssList(u) ssList(v) || equal(app(app(v,cons(w,nil)),u),sk1)**+ -> memberP(v,sk5(u,v,w))*.
% 7.18/7.38 807[2:Spt:305.5] || -> equal(nil,sk2)**.
% 7.18/7.38 860[2:Rew:807.0,573.0] || segmentP(sk2,sk1)* -> .
% 7.18/7.38 923[2:MRR:860.0,203.0] || -> .
% 7.18/7.38 1002[2:Spt:923.0,305.5,807.0] || equal(nil,sk2)** -> .
% 7.18/7.38 1003[2:Spt:923.0,305.0,305.1,305.2,305.3,305.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 7.18/7.38 1017[3:Spt:409.0] || -> strictorderedP(sk1)*.
% 7.18/7.38 1020[4:Spt:408.0] || -> totalorderedP(sk1)*.
% 7.18/7.38 1031[5:Spt:466.0] || -> cyclefreeP(sk1)*.
% 7.18/7.38 1035[6:Spt:407.0] || -> strictorderP(sk1)*.
% 7.18/7.38 1036[7:Spt:406.0] || -> totalorderP(sk1)*.
% 7.18/7.38 1043[8:Spt:204.0] || neq(sk2,nil)* -> .
% 7.18/7.38 1058[8:Res:621.1,1043.0] || -> equal(nil,sk2)**.
% 7.18/7.38 1059[8:MRR:1058.0,1002.0] || -> .
% 7.18/7.38 1060[8:Spt:1059.0,204.0,1043.0] || -> neq(sk2,nil)*.
% 7.18/7.38 1061[8:Spt:1059.0,204.1] || -> singletonP(sk1)*.
% 7.18/7.38 1062[8:MRR:450.0,1061.0] || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 7.18/7.38 1063[8:SpR:1062.0,601.0] || -> equalelemsP(sk1)*.
% 7.18/7.38 1064[8:SpR:1062.0,600.0] || -> duplicatefreeP(sk1)*.
% 7.18/7.38 1141[8:SpR:1062.0,715.1] ssList(nil) || -> equal(hd(sk1),skaf44(sk1))**.
% 7.18/7.38 1143[1:SpR:577.0,715.1] ssList(skaf82(sk1)) || -> equal(hd(sk1),skaf83(sk1))**.
% 7.18/7.38 1148[8:SSi:1141.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0] || -> equal(hd(sk1),skaf44(sk1))**.
% 7.18/7.38 1160[8:Rew:1148.0,1143.1] ssList(skaf82(sk1)) || -> equal(skaf44(sk1),skaf83(sk1))**.
% 7.18/7.38 1161[8:SSi:1160.0,27.0,1017.0,1.0,1020.0,1031.0,1035.0,1036.0,1061.0,1063.0,1064.0] || -> equal(skaf44(sk1),skaf83(sk1))**.
% 7.18/7.38 1162[8:Rew:1161.0,1062.0] || -> equal(cons(skaf83(sk1),nil),sk1)**.
% 7.18/7.38 1420[1:EqR:717.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 7.18/7.38 1423[1:SSi:1420.0,712.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,601.0,600.0,599.0,598.0,597.0,596.0,595.1] || -> singletonP(cons(u,nil))*.
% 7.18/7.38 1487[1:SpR:115.2,599.0] ssList(u) singletonP(u) || -> strictorderedP(u)*.
% 7.18/7.38 1488[1:SpR:115.2,598.0] ssList(u) singletonP(u) || -> totalorderedP(u)*.
% 7.18/7.38 1489[1:SpR:115.2,597.0] ssList(u) singletonP(u) || -> strictorderP(u)*.
% 7.18/7.38 1490[1:SpR:115.2,596.0] ssList(u) singletonP(u) || -> totalorderP(u)*.
% 7.18/7.38 1491[1:SpR:115.2,595.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 7.18/7.38 5134[1:SpL:88.1,801.2] ssList(cons(u,nil)) ssList(v) ssList(nil) || equal(app(cons(u,nil),v),sk1) -> memberP(nil,sk5(v,nil,u))*.
% 7.18/7.38 5148[1:Rew:88.1,5134.3,796.2,5134.3] ssList(cons(u,nil)) ssList(v) ssList(nil) || equal(cons(u,v),sk1) -> memberP(nil,sk5(v,nil,u))*.
% 7.18/7.38 5149[1:SSi:5148.2,5148.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,712.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.1,601.0,600.0,599.0,598.0,597.0,596.0,595.0,1423.0] ssList(u) || equal(cons(v,u),sk1) -> memberP(nil,sk5(u,nil,v))*.
% 7.18/7.38 5150[1:MRR:5149.2,594.0] ssList(u) || equal(cons(v,u),sk1)** -> .
% 7.18/7.38 5177[8:SpL:1162.0,5150.1] ssList(nil) || equal(sk1,sk1)* -> .
% 7.18/7.38 5185[8:Obv:5177.1] ssList(nil) || -> .
% 8.38/8.55 5186[8:SSi:5185.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0] || -> .
% 8.38/8.55 5191[7:Spt:5186.0,406.0,1036.0] || totalorderP(sk1)* -> .
% 8.38/8.55 5192[7:Spt:5186.0,406.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 8.38/8.55 5302[7:Res:1490.2,5191.0] ssList(sk1) singletonP(sk1) || -> .
% 8.38/8.55 5303[7:SSi:5302.0,1017.0,1.0,1020.0,1031.0,1035.0] singletonP(sk1) || -> .
% 8.38/8.55 5304[7:MRR:204.1,5303.0] || neq(sk2,nil)* -> .
% 8.38/8.55 5308[7:Res:621.1,5304.0] || -> equal(nil,sk2)**.
% 8.38/8.55 5309[7:MRR:5308.0,1002.0] || -> .
% 8.38/8.55 5310[6:Spt:5309.0,407.0,1035.0] || strictorderP(sk1)* -> .
% 8.38/8.55 5311[6:Spt:5309.0,407.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 8.38/8.55 5386[6:Res:1489.2,5310.0] ssList(sk1) singletonP(sk1) || -> .
% 8.38/8.55 5387[6:SSi:5386.0,1017.0,1.0,1020.0,1031.0] singletonP(sk1) || -> .
% 8.38/8.55 5388[6:MRR:204.1,5387.0] || neq(sk2,nil)* -> .
% 8.38/8.55 5393[6:Res:621.1,5388.0] || -> equal(nil,sk2)**.
% 8.38/8.55 5394[6:MRR:5393.0,1002.0] || -> .
% 8.38/8.55 5395[5:Spt:5394.0,466.0,1031.0] || cyclefreeP(sk1)* -> .
% 8.38/8.55 5396[5:Spt:5394.0,466.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 8.38/8.55 5477[5:Res:1491.2,5395.0] ssList(sk1) singletonP(sk1) || -> .
% 8.38/8.55 5478[5:SSi:5477.0,1017.0,1.0,1020.0] singletonP(sk1) || -> .
% 8.38/8.55 5479[5:MRR:204.1,5478.0] || neq(sk2,nil)* -> .
% 8.38/8.55 5484[5:Res:621.1,5479.0] || -> equal(nil,sk2)**.
% 8.38/8.55 5485[5:MRR:5484.0,1002.0] || -> .
% 8.38/8.55 5486[4:Spt:5485.0,408.0,1020.0] || totalorderedP(sk1)* -> .
% 8.38/8.55 5487[4:Spt:5485.0,408.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 8.38/8.55 5605[4:Res:1488.2,5486.0] ssList(sk1) singletonP(sk1) || -> .
% 8.38/8.55 5606[4:SSi:5605.0,1017.0,1.0] singletonP(sk1) || -> .
% 8.38/8.55 5607[4:MRR:204.1,5606.0] || neq(sk2,nil)* -> .
% 8.38/8.55 5617[4:Res:621.1,5607.0] || -> equal(nil,sk2)**.
% 8.38/8.55 5618[4:MRR:5617.0,1002.0] || -> .
% 8.38/8.55 5619[3:Spt:5618.0,409.0,1017.0] || strictorderedP(sk1)* -> .
% 8.38/8.55 5620[3:Spt:5618.0,409.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 8.38/8.55 5702[3:Res:1487.2,5619.0] ssList(sk1) singletonP(sk1) || -> .
% 8.38/8.55 5703[3:SSi:5702.0,1.0] singletonP(sk1) || -> .
% 8.38/8.55 5704[3:MRR:204.1,5703.0] || neq(sk2,nil)* -> .
% 8.38/8.55 5709[3:Res:621.1,5704.0] || -> equal(nil,sk2)**.
% 8.38/8.55 5710[3:MRR:5709.0,1002.0] || -> .
% 8.38/8.55 5711[1:Spt:5710.0,86.0,86.2] ssList(u) || -> duplicatefreeP(u)*.
% 8.38/8.55 5722[1:MRR:193.1,5711.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 8.38/8.55 17951[0:SpR:171.3,99.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 8.38/8.55 18007[0:Obv:17951.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.38/8.55 18008[0:SSi:18007.2,100.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.38/8.55 19507[1:EqR:5722.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 8.38/8.55 19546[1:SSi:19507.0,99.2,99.2,100.2,100.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 8.38/8.55 19548[1:MRR:18008.3,19546.1] ssList(u) ssItem(v) ssList(w) || -> .
% 8.38/8.55 19551[1:Con:19548.2] ssList(u) ssItem(v) || -> .
% 8.38/8.55 19553[1:MRR:351.1,19551.0] ssItem(u) || -> .
% 8.38/8.55 19557[1:UnC:19553.0,26.0] || -> .
% 8.38/8.55 % SZS output end Refutation
% 8.38/8.55 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_10 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause80 clause85 clause86 clause88 clause97 clause101 clause102 clause109 clause116 clause157 clause163 clause164 clause165 clause166 clause177 clause179
% 8.38/8.55
%------------------------------------------------------------------------------