TSTP Solution File: SWC312-1 by SPASS---3.9

View Problem - 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  
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