TSTP Solution File: SWC312-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC312-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 22:03:14 EDT 2022
% Result : Unsatisfiable 6.42s 6.61s
% Output : Refutation 8.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC312-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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 03:42:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.42/6.61
% 6.42/6.61 SPASS V 3.9
% 6.42/6.61 SPASS beiseite: Proof found.
% 6.42/6.61 % SZS status Theorem
% 6.42/6.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.42/6.61 SPASS derived 13551 clauses, backtracked 4043 clauses, performed 90 splits and kept 9824 clauses.
% 6.42/6.61 SPASS allocated 90697 KBytes.
% 6.42/6.61 SPASS spent 0:00:06.25 on the problem.
% 6.42/6.61 0:00:00.04 for the input.
% 6.42/6.61 0:00:00.00 for the FLOTTER CNF translation.
% 6.42/6.61 0:00:00.12 for inferences.
% 6.42/6.61 0:00:00.15 for the backtracking.
% 6.42/6.61 0:00:05.71 for the reduction.
% 6.42/6.61
% 6.42/6.61
% 6.42/6.61 Here is a proof with depth 3, length 155 :
% 6.42/6.61 % SZS output start Refutation
% 6.42/6.61 1[0:Inp] || -> ssList(sk1)*.
% 6.42/6.61 5[0:Inp] || -> equal(sk2,sk4)**.
% 6.42/6.61 6[0:Inp] || -> equal(sk3,sk1)**.
% 6.42/6.61 7[0:Inp] || equal(nil,sk4)** -> equal(nil,sk3).
% 6.42/6.61 9[0:Inp] || neq(sk4,nil)* -> ssList(sk6).
% 6.42/6.61 10[0:Inp] || neq(sk4,nil) -> equal(app(cons(sk5,nil),sk6),sk4)**.
% 6.42/6.61 11[0:Inp] || neq(sk4,nil) -> equal(app(sk6,cons(sk5,nil)),sk3)**.
% 6.42/6.61 13[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),sk2)** equal(app(v,cons(u,nil)),sk1)** -> equal(nil,sk2).
% 6.42/6.61 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 6.42/6.61 16[0:Inp] || -> equalelemsP(nil)*.
% 6.42/6.61 17[0:Inp] || -> duplicatefreeP(nil)*.
% 6.42/6.61 18[0:Inp] || -> strictorderedP(nil)*.
% 6.42/6.61 19[0:Inp] || -> totalorderedP(nil)*.
% 6.42/6.61 20[0:Inp] || -> strictorderP(nil)*.
% 6.42/6.61 21[0:Inp] || -> totalorderP(nil)*.
% 6.42/6.61 22[0:Inp] || -> cyclefreeP(nil)*.
% 6.42/6.61 23[0:Inp] || -> ssList(nil)*.
% 6.42/6.61 28[0:Inp] || -> ssList(skaf82(u))*.
% 6.42/6.61 62[0:Inp] || -> ssItem(skaf44(u))*.
% 6.42/6.61 69[0:Inp] || equal(skac2,skac3)** -> .
% 6.42/6.61 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 6.42/6.61 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 6.42/6.61 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 6.42/6.61 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 6.42/6.61 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 6.42/6.61 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 6.42/6.61 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 6.42/6.61 86[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 6.42/6.61 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 6.42/6.61 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 6.42/6.61 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 6.42/6.61 100[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 6.42/6.61 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 6.42/6.61 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 6.42/6.61 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 6.42/6.61 131[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.42/6.61 135[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.42/6.61 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 6.42/6.61 153[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 6.42/6.61 156[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(w,u) -> memberP(app(v,w),u)*.
% 6.42/6.61 172[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.42/6.61 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 6.42/6.61 192[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).
% 6.42/6.61 194[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)* -> .
% 6.42/6.61 204[0:Rew:5.0,14.1] || equal(nil,sk1) -> neq(sk4,nil)*.
% 6.42/6.61 205[0:Rew:6.0,7.1] || equal(nil,sk4)** -> equal(nil,sk1).
% 6.42/6.61 206[0:Rew:6.0,11.1] || neq(sk4,nil) -> equal(app(sk6,cons(sk5,nil)),sk1)**.
% 6.42/6.61 211[0:Rew:5.0,13.4,135.2,13.2,5.0,13.2] ssList(u) ssItem(v) || equal(cons(v,u),sk4) equal(app(u,cons(v,nil)),sk1)** -> equal(nil,sk4).
% 6.42/6.61 482[0:Res:1.0,192.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 6.42/6.61 513[0:Res:1.0,138.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 6.42/6.61 520[0:Res:1.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 6.42/6.61 525[0:Res:1.0,101.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 6.42/6.61 536[0:Res:1.0,172.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 6.42/6.61 569[1:Spt:87.1] || -> ssItem(u)*.
% 6.42/6.61 572[1:MRR:525.0,569.0] || -> ssList(cons(u,sk1))*.
% 6.42/6.61 574[1:MRR:86.0,569.0] || memberP(nil,u)* -> .
% 6.42/6.61 575[1:MRR:85.0,569.0] || -> cyclefreeP(cons(u,nil))*.
% 6.42/6.61 576[1:MRR:84.0,569.0] || -> totalorderP(cons(u,nil))*.
% 6.42/6.61 577[1:MRR:83.0,569.0] || -> strictorderP(cons(u,nil))*.
% 6.42/6.61 578[1:MRR:82.0,569.0] || -> totalorderedP(cons(u,nil))*.
% 6.42/6.61 579[1:MRR:81.0,569.0] || -> strictorderedP(cons(u,nil))*.
% 6.42/6.61 580[1:MRR:80.0,569.0] || -> duplicatefreeP(cons(u,nil))*.
% 6.42/6.61 581[1:MRR:79.0,569.0] || -> equalelemsP(cons(u,nil))*.
% 6.42/6.61 585[1:MRR:520.0,569.0] || -> equal(hd(cons(u,sk1)),u)**.
% 6.42/6.61 599[1:MRR:117.1,117.0,569.0] || -> equal(u,v) neq(u,v)*.
% 6.42/6.61 648[1:MRR:156.0,569.0] ssList(u) ssList(v) || memberP(v,w) -> memberP(app(u,v),w)*.
% 6.42/6.61 651[1:MRR:153.1,153.0,569.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 6.42/6.61 696[1:MRR:101.1,569.0] ssList(u) || -> ssList(cons(v,u))*.
% 6.42/6.61 701[1:MRR:131.1,569.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.42/6.61 702[1:MRR:135.1,569.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.42/6.61 703[1:MRR:536.1,569.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 6.42/6.61 716[1:MRR:211.1,569.0] ssList(u) || equal(cons(v,u),sk4) equal(app(u,cons(v,nil)),sk1)** -> equal(nil,sk4).
% 6.42/6.61 768[1:MRR:185.3,185.2,569.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 6.42/6.61 770[2:Spt:513.0,513.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 6.42/6.61 778[3:Spt:482.5] || -> equal(nil,sk1)**.
% 6.42/6.61 863[3:Rew:778.0,89.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 6.42/6.61 864[3:Rew:778.0,88.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 6.42/6.61 869[3:Rew:778.0,575.0] || -> cyclefreeP(cons(u,sk1))*.
% 6.42/6.61 870[3:Rew:778.0,576.0] || -> totalorderP(cons(u,sk1))*.
% 6.42/6.61 871[3:Rew:778.0,577.0] || -> strictorderP(cons(u,sk1))*.
% 6.42/6.61 872[3:Rew:778.0,578.0] || -> totalorderedP(cons(u,sk1))*.
% 6.42/6.61 873[3:Rew:778.0,579.0] || -> strictorderedP(cons(u,sk1))*.
% 6.42/6.61 874[3:Rew:778.0,580.0] || -> duplicatefreeP(cons(u,sk1))*.
% 6.42/6.61 875[3:Rew:778.0,581.0] || -> equalelemsP(cons(u,sk1))*.
% 6.42/6.61 927[3:Rew:863.1,770.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 6.42/6.61 950[3:Rew:864.1,703.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 6.42/6.61 1234[3:SpR:927.1,585.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 6.42/6.61 1239[3:SSi:1234.0,572.0,869.0,870.0,871.0,872.0,873.0,874.0,875.0] || -> equal(hd(sk1),u)*.
% 6.42/6.61 1270[3:Rew:1239.0,950.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 6.42/6.61 1363[3:Rew:1239.0,768.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 6.42/6.61 1442[3:Con:1363.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 6.42/6.61 1443[3:AED:69.0,1442.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 6.42/6.61 1444[3:Rew:1270.1,1443.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 6.42/6.61 1445[3:Obv:1444.1] ssList(u) || -> .
% 6.42/6.61 1446[3:UnC:1445.0,28.0] || -> .
% 6.42/6.61 1544[3:Spt:1446.0,482.5,778.0] || equal(nil,sk1)** -> .
% 6.42/6.61 1545[3:Spt:1446.0,482.0,482.1,482.2,482.3,482.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 6.42/6.61 1550[3:MRR:205.1,1544.0] || equal(nil,sk4)** -> .
% 6.42/6.61 1572[3:MRR:716.3,1550.0] ssList(u) || equal(cons(v,u),sk4) equal(app(u,cons(v,nil)),sk1)** -> .
% 6.42/6.61 1575[4:Spt:9.0] || neq(sk4,nil)* -> .
% 6.42/6.61 1576[4:Res:599.1,1575.0] || -> equal(nil,sk4)**.
% 6.42/6.61 1577[4:MRR:1576.0,1550.0] || -> .
% 6.42/6.61 1578[4:Spt:1577.0,9.0,1575.0] || -> neq(sk4,nil)*.
% 6.42/6.61 1579[4:Spt:1577.0,9.1] || -> ssList(sk6)*.
% 6.42/6.61 1580[4:MRR:206.0,1578.0] || -> equal(app(sk6,cons(sk5,nil)),sk1)**.
% 6.42/6.61 1581[4:MRR:10.0,1578.0] || -> equal(app(cons(sk5,nil),sk6),sk4)**.
% 6.42/6.61 1829[1:EqR:701.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 6.42/6.61 1830[1:SSi:1829.0,696.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,581.0,580.0,579.0,578.0,577.0,576.0,575.1] || -> singletonP(cons(u,nil))*.
% 6.42/6.61 1940[4:SpR:702.1,1581.0] ssList(sk6) || -> equal(cons(sk5,sk6),sk4)**.
% 6.42/6.61 1951[4:SSi:1940.0,1579.0] || -> equal(cons(sk5,sk6),sk4)**.
% 6.42/6.61 2898[4:SpL:1580.0,1572.2] ssList(sk6) || equal(cons(sk5,sk6),sk4)** equal(sk1,sk1) -> .
% 6.42/6.61 2958[4:Obv:2898.2] ssList(sk6) || equal(cons(sk5,sk6),sk4)** -> .
% 6.42/6.61 2959[4:Rew:1951.0,2958.1] ssList(sk6) || equal(sk4,sk4)* -> .
% 6.42/6.61 2960[4:Obv:2959.1] ssList(sk6) || -> .
% 6.42/6.61 2961[4:SSi:2960.0,1579.0] || -> .
% 6.42/6.61 2980[2:Spt:2961.0,513.1] || -> equal(nil,sk1)**.
% 6.42/6.61 2996[2:Rew:2980.0,16.0] || -> equalelemsP(sk1)*.
% 6.42/6.61 2997[2:Rew:2980.0,17.0] || -> duplicatefreeP(sk1)*.
% 6.42/6.61 2998[2:Rew:2980.0,18.0] || -> strictorderedP(sk1)*.
% 6.42/6.61 2999[2:Rew:2980.0,19.0] || -> totalorderedP(sk1)*.
% 6.42/6.61 3000[2:Rew:2980.0,20.0] || -> strictorderP(sk1)*.
% 6.42/6.61 3001[2:Rew:2980.0,21.0] || -> totalorderP(sk1)*.
% 8.13/8.30 3002[2:Rew:2980.0,22.0] || -> cyclefreeP(sk1)*.
% 8.13/8.30 3008[2:Rew:2980.0,581.0] || -> equalelemsP(cons(u,sk1))*.
% 8.13/8.30 3009[2:Rew:2980.0,580.0] || -> duplicatefreeP(cons(u,sk1))*.
% 8.13/8.30 3010[2:Rew:2980.0,579.0] || -> strictorderedP(cons(u,sk1))*.
% 8.13/8.30 3011[2:Rew:2980.0,578.0] || -> totalorderedP(cons(u,sk1))*.
% 8.13/8.30 3012[2:Rew:2980.0,577.0] || -> strictorderP(cons(u,sk1))*.
% 8.13/8.30 3013[2:Rew:2980.0,576.0] || -> totalorderP(cons(u,sk1))*.
% 8.13/8.30 3014[2:Rew:2980.0,575.0] || -> cyclefreeP(cons(u,sk1))*.
% 8.13/8.30 3016[2:Rew:2980.0,1830.0] || -> singletonP(cons(u,sk1))*.
% 8.13/8.30 3017[2:Rew:2980.0,574.0] || memberP(sk1,u)* -> .
% 8.13/8.30 3121[2:Rew:2980.0,9.0] || neq(sk4,sk1)* -> ssList(sk6).
% 8.13/8.30 3142[2:Rew:2980.0,204.1,2980.0,204.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 8.13/8.30 3143[2:Obv:3142.0] || -> neq(sk4,sk1)*.
% 8.13/8.30 3144[2:MRR:3121.0,3143.0] || -> ssList(sk6)*.
% 8.13/8.30 3188[2:Rew:2980.0,206.1,2980.0,206.0] || neq(sk4,sk1) -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 8.13/8.30 3189[2:MRR:3188.0,3143.0] || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 8.13/8.30 3320[2:SpR:3189.0,648.3] ssList(sk6) ssList(cons(sk5,sk1)) || memberP(cons(sk5,sk1),u)* -> memberP(sk1,u).
% 8.13/8.30 3324[2:SSi:3320.1,3320.0,572.0,3008.0,3009.0,3010.0,3011.0,3012.0,3013.0,3014.0,3016.0,3144.0] || memberP(cons(sk5,sk1),u)* -> memberP(sk1,u).
% 8.13/8.30 3325[2:MRR:3324.1,3017.0] || memberP(cons(sk5,sk1),u)* -> .
% 8.13/8.30 3327[2:Res:651.2,3325.0] ssList(sk1) || equal(u,sk5)* -> .
% 8.13/8.30 3330[2:AED:69.0,3327.1] ssList(sk1) || -> .
% 8.13/8.30 3331[2:SSi:3330.0,1.0,2996.0,2997.0,2998.0,2999.0,3000.0,3001.0,3002.0] || -> .
% 8.13/8.30 3332[1:Spt:3331.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 8.13/8.30 3342[1:MRR:194.1,3332.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 8.13/8.30 18382[0:SpR:172.3,100.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 8.13/8.30 18413[0:Obv:18382.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.13/8.30 18414[0:SSi:18413.2,101.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.13/8.30 20122[1:EqR:3342.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 8.13/8.30 20156[1:SSi:20122.0,100.2,100.2,101.2,101.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 8.13/8.30 20157[1:MRR:18414.3,20156.1] ssList(u) ssItem(v) ssList(w) || -> .
% 8.13/8.30 20163[1:Con:20157.2] ssList(u) ssItem(v) || -> .
% 8.13/8.30 20164[1:MRR:525.1,20163.0] ssItem(u) || -> .
% 8.13/8.30 20168[1:UnC:20164.0,62.0] || -> .
% 8.13/8.30 % SZS output end Refutation
% 8.13/8.30 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_9 co1_10 co1_11 co1_13 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause74 clause85 clause86 clause97 clause102 clause116 clause120 clause123 clause138 clause141 clause157 clause170 clause177 clause179
% 8.13/8.30
%------------------------------------------------------------------------------