TSTP Solution File: SWC320-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC320-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 22:03:17 EDT 2022
% Result : Unsatisfiable 6.88s 7.06s
% Output : Refutation 8.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC320-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 11 21:48:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.88/7.06
% 6.88/7.06 SPASS V 3.9
% 6.88/7.06 SPASS beiseite: Proof found.
% 6.88/7.06 % SZS status Theorem
% 6.88/7.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/7.06 SPASS derived 13509 clauses, backtracked 4011 clauses, performed 90 splits and kept 9685 clauses.
% 6.88/7.06 SPASS allocated 90781 KBytes.
% 6.88/7.06 SPASS spent 0:00:06.69 on the problem.
% 6.88/7.06 0:00:00.04 for the input.
% 6.88/7.06 0:00:00.00 for the FLOTTER CNF translation.
% 6.88/7.06 0:00:00.13 for inferences.
% 6.88/7.06 0:00:00.16 for the backtracking.
% 6.88/7.06 0:00:06.06 for the reduction.
% 6.88/7.06
% 6.88/7.06
% 6.88/7.06 Here is a proof with depth 3, length 155 :
% 6.88/7.06 % SZS output start Refutation
% 6.88/7.06 1[0:Inp] || -> ssList(sk1)*.
% 6.88/7.06 5[0:Inp] || -> equal(sk2,sk4)**.
% 6.88/7.06 6[0:Inp] || -> equal(sk3,sk1)**.
% 6.88/7.06 7[0:Inp] || equal(nil,sk4)** -> equal(nil,sk3).
% 6.88/7.06 9[0:Inp] || neq(sk4,nil)* -> ssList(sk6).
% 6.88/7.06 10[0:Inp] || neq(sk4,nil) -> equal(app(cons(sk5,nil),sk6),sk3)**.
% 6.88/7.06 11[0:Inp] || neq(sk4,nil) -> equal(app(sk6,cons(sk5,nil)),sk4)**.
% 6.88/7.06 13[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),sk1)** equal(app(v,cons(u,nil)),sk2)** -> equal(nil,sk2).
% 6.88/7.06 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 6.88/7.06 16[0:Inp] || -> equalelemsP(nil)*.
% 6.88/7.06 17[0:Inp] || -> duplicatefreeP(nil)*.
% 6.88/7.06 18[0:Inp] || -> strictorderedP(nil)*.
% 6.88/7.06 19[0:Inp] || -> totalorderedP(nil)*.
% 6.88/7.06 20[0:Inp] || -> strictorderP(nil)*.
% 6.88/7.06 21[0:Inp] || -> totalorderP(nil)*.
% 6.88/7.06 22[0:Inp] || -> cyclefreeP(nil)*.
% 6.88/7.06 23[0:Inp] || -> ssList(nil)*.
% 6.88/7.06 28[0:Inp] || -> ssList(skaf82(u))*.
% 6.88/7.06 62[0:Inp] || -> ssItem(skaf44(u))*.
% 6.88/7.06 69[0:Inp] || equal(skac2,skac3)** -> .
% 6.88/7.06 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 6.88/7.06 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 6.88/7.06 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 6.88/7.06 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 6.88/7.06 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 6.88/7.06 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 6.88/7.06 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 6.88/7.06 86[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 6.88/7.06 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 6.88/7.06 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 6.88/7.06 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 6.88/7.06 100[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 6.88/7.06 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 6.88/7.06 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 6.88/7.06 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 6.88/7.06 131[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.88/7.06 135[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.88/7.06 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 6.88/7.06 153[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 6.88/7.06 155[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 6.88/7.06 172[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.88/7.06 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 6.88/7.06 192[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).
% 6.88/7.06 194[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)* -> .
% 6.88/7.06 204[0:Rew:5.0,14.1] || equal(nil,sk1) -> neq(sk4,nil)*.
% 6.88/7.06 205[0:Rew:6.0,7.1] || equal(nil,sk4)** -> equal(nil,sk1).
% 6.88/7.06 206[0:Rew:6.0,10.1] || neq(sk4,nil) -> equal(app(cons(sk5,nil),sk6),sk1)**.
% 6.88/7.06 211[0:Rew:5.0,13.4,5.0,13.3,135.2,13.2] ssList(u) ssItem(v) || equal(cons(v,u),sk1) equal(app(u,cons(v,nil)),sk4)** -> equal(nil,sk4).
% 6.88/7.06 482[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).
% 6.88/7.06 513[0:Res:1.0,138.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 6.88/7.06 520[0:Res:1.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 6.88/7.06 525[0:Res:1.0,101.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 6.88/7.06 536[0:Res:1.0,172.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 6.88/7.06 569[1:Spt:87.1] || -> ssItem(u)*.
% 6.88/7.06 572[1:MRR:525.0,569.0] || -> ssList(cons(u,sk1))*.
% 6.88/7.06 574[1:MRR:86.0,569.0] || memberP(nil,u)* -> .
% 6.88/7.06 575[1:MRR:85.0,569.0] || -> cyclefreeP(cons(u,nil))*.
% 6.88/7.06 576[1:MRR:84.0,569.0] || -> totalorderP(cons(u,nil))*.
% 6.88/7.06 577[1:MRR:83.0,569.0] || -> strictorderP(cons(u,nil))*.
% 6.88/7.06 578[1:MRR:82.0,569.0] || -> totalorderedP(cons(u,nil))*.
% 6.88/7.06 579[1:MRR:81.0,569.0] || -> strictorderedP(cons(u,nil))*.
% 6.88/7.06 580[1:MRR:80.0,569.0] || -> duplicatefreeP(cons(u,nil))*.
% 6.88/7.06 581[1:MRR:79.0,569.0] || -> equalelemsP(cons(u,nil))*.
% 6.88/7.06 585[1:MRR:520.0,569.0] || -> equal(hd(cons(u,sk1)),u)**.
% 6.88/7.06 599[1:MRR:117.1,117.0,569.0] || -> equal(u,v) neq(u,v)*.
% 6.88/7.06 649[1:MRR:155.0,569.0] ssList(u) ssList(v) || memberP(u,w) -> memberP(app(u,v),w)*.
% 6.88/7.06 651[1:MRR:153.1,153.0,569.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 6.88/7.06 696[1:MRR:101.1,569.0] ssList(u) || -> ssList(cons(v,u))*.
% 6.88/7.06 701[1:MRR:131.1,569.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.88/7.06 702[1:MRR:135.1,569.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.88/7.06 703[1:MRR:536.1,569.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 6.88/7.06 716[1:MRR:211.1,569.0] ssList(u) || equal(cons(v,u),sk1) equal(app(u,cons(v,nil)),sk4)** -> equal(nil,sk4).
% 6.88/7.06 768[1:MRR:185.3,185.2,569.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 6.88/7.06 770[2:Spt:513.0,513.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 6.88/7.06 778[3:Spt:482.5] || -> equal(nil,sk1)**.
% 6.88/7.06 863[3:Rew:778.0,89.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 6.88/7.06 864[3:Rew:778.0,88.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 6.88/7.06 869[3:Rew:778.0,575.0] || -> cyclefreeP(cons(u,sk1))*.
% 6.88/7.06 870[3:Rew:778.0,576.0] || -> totalorderP(cons(u,sk1))*.
% 6.88/7.06 871[3:Rew:778.0,577.0] || -> strictorderP(cons(u,sk1))*.
% 6.88/7.06 872[3:Rew:778.0,578.0] || -> totalorderedP(cons(u,sk1))*.
% 6.88/7.06 873[3:Rew:778.0,579.0] || -> strictorderedP(cons(u,sk1))*.
% 6.88/7.06 874[3:Rew:778.0,580.0] || -> duplicatefreeP(cons(u,sk1))*.
% 6.88/7.06 875[3:Rew:778.0,581.0] || -> equalelemsP(cons(u,sk1))*.
% 6.88/7.06 927[3:Rew:863.1,770.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 6.88/7.06 950[3:Rew:864.1,703.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 6.88/7.06 1226[3:SpR:927.1,585.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 6.88/7.06 1231[3:SSi:1226.0,572.0,869.0,870.0,871.0,872.0,873.0,874.0,875.0] || -> equal(hd(sk1),u)*.
% 6.88/7.06 1262[3:Rew:1231.0,950.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 6.88/7.06 1355[3:Rew:1231.0,768.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 6.88/7.06 1434[3:Con:1355.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 6.88/7.06 1435[3:AED:69.0,1434.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 6.88/7.06 1436[3:Rew:1262.1,1435.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 6.88/7.06 1437[3:Obv:1436.1] ssList(u) || -> .
% 6.88/7.06 1438[3:UnC:1437.0,28.0] || -> .
% 6.88/7.06 1536[3:Spt:1438.0,482.5,778.0] || equal(nil,sk1)** -> .
% 6.88/7.06 1537[3:Spt:1438.0,482.0,482.1,482.2,482.3,482.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 6.88/7.06 1542[3:MRR:205.1,1536.0] || equal(nil,sk4)** -> .
% 6.88/7.06 1564[3:MRR:716.3,1542.0] ssList(u) || equal(cons(v,u),sk1) equal(app(u,cons(v,nil)),sk4)** -> .
% 6.88/7.06 1567[4:Spt:9.0] || neq(sk4,nil)* -> .
% 6.88/7.06 1568[4:Res:599.1,1567.0] || -> equal(nil,sk4)**.
% 6.88/7.06 1569[4:MRR:1568.0,1542.0] || -> .
% 6.88/7.06 1570[4:Spt:1569.0,9.0,1567.0] || -> neq(sk4,nil)*.
% 6.88/7.06 1571[4:Spt:1569.0,9.1] || -> ssList(sk6)*.
% 6.88/7.06 1572[4:MRR:11.0,1570.0] || -> equal(app(sk6,cons(sk5,nil)),sk4)**.
% 6.88/7.06 1573[4:MRR:206.0,1570.0] || -> equal(app(cons(sk5,nil),sk6),sk1)**.
% 6.88/7.06 1821[1:EqR:701.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 6.88/7.06 1822[1:SSi:1821.0,696.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,581.0,580.0,579.0,578.0,577.0,576.0,575.1] || -> singletonP(cons(u,nil))*.
% 6.88/7.06 1932[4:SpR:702.1,1573.0] ssList(sk6) || -> equal(cons(sk5,sk6),sk1)**.
% 6.88/7.06 1943[4:SSi:1932.0,1571.0] || -> equal(cons(sk5,sk6),sk1)**.
% 6.88/7.06 2886[4:SpL:1572.0,1564.2] ssList(sk6) || equal(cons(sk5,sk6),sk1)** equal(sk4,sk4) -> .
% 6.88/7.06 2944[4:Obv:2886.2] ssList(sk6) || equal(cons(sk5,sk6),sk1)** -> .
% 6.88/7.06 2945[4:Rew:1943.0,2944.1] ssList(sk6) || equal(sk1,sk1)* -> .
% 6.88/7.06 2946[4:Obv:2945.1] ssList(sk6) || -> .
% 6.88/7.06 2947[4:SSi:2946.0,1571.0] || -> .
% 6.88/7.06 2967[2:Spt:2947.0,513.1] || -> equal(nil,sk1)**.
% 6.88/7.06 2983[2:Rew:2967.0,16.0] || -> equalelemsP(sk1)*.
% 6.88/7.06 2984[2:Rew:2967.0,17.0] || -> duplicatefreeP(sk1)*.
% 6.88/7.06 2985[2:Rew:2967.0,18.0] || -> strictorderedP(sk1)*.
% 6.88/7.06 2986[2:Rew:2967.0,19.0] || -> totalorderedP(sk1)*.
% 6.88/7.06 2987[2:Rew:2967.0,20.0] || -> strictorderP(sk1)*.
% 6.88/7.06 2988[2:Rew:2967.0,21.0] || -> totalorderP(sk1)*.
% 8.62/8.83 2989[2:Rew:2967.0,22.0] || -> cyclefreeP(sk1)*.
% 8.62/8.83 2995[2:Rew:2967.0,581.0] || -> equalelemsP(cons(u,sk1))*.
% 8.62/8.83 2996[2:Rew:2967.0,580.0] || -> duplicatefreeP(cons(u,sk1))*.
% 8.62/8.83 2997[2:Rew:2967.0,579.0] || -> strictorderedP(cons(u,sk1))*.
% 8.62/8.83 2998[2:Rew:2967.0,578.0] || -> totalorderedP(cons(u,sk1))*.
% 8.62/8.83 2999[2:Rew:2967.0,577.0] || -> strictorderP(cons(u,sk1))*.
% 8.62/8.83 3000[2:Rew:2967.0,576.0] || -> totalorderP(cons(u,sk1))*.
% 8.62/8.83 3001[2:Rew:2967.0,575.0] || -> cyclefreeP(cons(u,sk1))*.
% 8.62/8.83 3003[2:Rew:2967.0,1822.0] || -> singletonP(cons(u,sk1))*.
% 8.62/8.83 3004[2:Rew:2967.0,574.0] || memberP(sk1,u)* -> .
% 8.62/8.83 3104[2:Rew:2967.0,9.0] || neq(sk4,sk1)* -> ssList(sk6).
% 8.62/8.83 3125[2:Rew:2967.0,204.1,2967.0,204.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 8.62/8.83 3126[2:Obv:3125.0] || -> neq(sk4,sk1)*.
% 8.62/8.83 3127[2:MRR:3104.0,3126.0] || -> ssList(sk6)*.
% 8.62/8.83 3173[2:Rew:2967.0,206.1,2967.0,206.0] || neq(sk4,sk1) -> equal(app(cons(sk5,sk1),sk6),sk1)**.
% 8.62/8.83 3174[2:MRR:3173.0,3126.0] || -> equal(app(cons(sk5,sk1),sk6),sk1)**.
% 8.62/8.83 3305[2:SpR:3174.0,649.3] ssList(cons(sk5,sk1)) ssList(sk6) || memberP(cons(sk5,sk1),u)* -> memberP(sk1,u).
% 8.62/8.83 3310[2:SSi:3305.1,3305.0,3127.0,572.0,2995.0,2996.0,2997.0,2998.0,2999.0,3000.0,3001.0,3003.0] || memberP(cons(sk5,sk1),u)* -> memberP(sk1,u).
% 8.62/8.83 3311[2:MRR:3310.1,3004.0] || memberP(cons(sk5,sk1),u)* -> .
% 8.62/8.83 3313[2:Res:651.2,3311.0] ssList(sk1) || equal(u,sk5)* -> .
% 8.62/8.83 3316[2:AED:69.0,3313.1] ssList(sk1) || -> .
% 8.62/8.83 3317[2:SSi:3316.0,1.0,2983.0,2984.0,2985.0,2986.0,2987.0,2988.0,2989.0] || -> .
% 8.62/8.83 3318[1:Spt:3317.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 8.62/8.83 3328[1:MRR:194.1,3318.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 8.62/8.83 18500[0:SpR:172.3,100.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 8.62/8.83 18531[0:Obv:18500.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.62/8.83 18532[0:SSi:18531.2,101.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.62/8.83 20275[1:EqR:3328.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 8.62/8.83 20309[1:SSi:20275.0,100.2,100.2,101.2,101.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 8.62/8.83 20310[1:MRR:18532.3,20309.1] ssList(u) ssItem(v) ssList(w) || -> .
% 8.62/8.83 20316[1:Con:20310.2] ssList(u) ssItem(v) || -> .
% 8.62/8.83 20317[1:MRR:525.1,20316.0] ssItem(u) || -> .
% 8.62/8.83 20321[1:UnC:20317.0,62.0] || -> .
% 8.62/8.83 % SZS output end Refutation
% 8.62/8.83 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 clause140 clause157 clause170 clause177 clause179
% 8.62/8.83
%------------------------------------------------------------------------------