TSTP Solution File: SWC313-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC313-1 : 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 22:03:14 EDT 2022
% Result : Unsatisfiable 3.46s 3.63s
% Output : Refutation 3.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC313-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 05:51:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.46/3.63
% 3.46/3.63 SPASS V 3.9
% 3.46/3.63 SPASS beiseite: Proof found.
% 3.46/3.63 % SZS status Theorem
% 3.46/3.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.46/3.63 SPASS derived 7418 clauses, backtracked 3678 clauses, performed 84 splits and kept 7281 clauses.
% 3.46/3.63 SPASS allocated 84547 KBytes.
% 3.46/3.63 SPASS spent 0:00:03.27 on the problem.
% 3.46/3.63 0:00:00.04 for the input.
% 3.46/3.63 0:00:00.00 for the FLOTTER CNF translation.
% 3.46/3.63 0:00:00.05 for inferences.
% 3.46/3.63 0:00:00.07 for the backtracking.
% 3.46/3.63 0:00:02.91 for the reduction.
% 3.46/3.63
% 3.46/3.63
% 3.46/3.63 Here is a proof with depth 3, length 133 :
% 3.46/3.63 % SZS output start Refutation
% 3.46/3.63 1[0:Inp] || -> ssList(sk1)*.
% 3.46/3.63 4[0:Inp] || -> ssList(sk4)*.
% 3.46/3.63 5[0:Inp] || -> equal(sk2,sk4)**.
% 3.46/3.63 6[0:Inp] || -> equal(sk3,sk1)**.
% 3.46/3.63 7[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),sk4)** -> equal(app(v,cons(u,nil)),sk3)**.
% 3.46/3.63 8[0:Inp] || equal(nil,sk4)** -> equal(nil,sk3).
% 3.46/3.63 10[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),sk2)** equal(app(v,cons(u,nil)),sk1)** -> equal(nil,sk2).
% 3.46/3.63 11[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 3.46/3.63 12[0:Inp] ssItem(u) ssList(v) || equal(nil,sk1) equal(app(cons(u,nil),v),sk2)** equal(app(v,cons(u,nil)),sk1)** -> .
% 3.46/3.63 25[0:Inp] || -> ssList(skaf82(u))*.
% 3.46/3.63 59[0:Inp] || -> ssItem(skaf44(u))*.
% 3.46/3.63 66[0:Inp] || equal(skac2,skac3)** -> .
% 3.46/3.63 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.46/3.63 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.46/3.63 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.46/3.63 79[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.46/3.63 80[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.46/3.63 81[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.46/3.63 82[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.46/3.63 84[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 3.46/3.63 85[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 3.46/3.63 86[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.46/3.63 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 3.46/3.63 97[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 3.46/3.63 98[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 3.46/3.63 109[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 3.46/3.63 116[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 3.46/3.63 129[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 3.46/3.63 132[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.46/3.63 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 3.46/3.63 169[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 3.46/3.63 182[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.46/3.63 189[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).
% 3.46/3.63 191[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)* -> .
% 3.46/3.63 201[0:Rew:5.0,11.1] || equal(nil,sk1) -> neq(sk4,nil)*.
% 3.46/3.63 202[0:Rew:6.0,8.1] || equal(nil,sk4)** -> equal(nil,sk1).
% 3.46/3.63 203[0:Rew:6.0,7.3,132.2,7.2] ssItem(u) ssList(v) || equal(cons(u,v),sk4) -> equal(app(v,cons(u,nil)),sk1)**.
% 3.46/3.63 208[0:Rew:5.0,10.4,203.3,10.3,132.2,10.2,5.0,10.2] ssItem(u) ssList(v) || equal(cons(u,v),sk4)** equal(sk1,sk1) -> equal(nil,sk4).
% 3.46/3.63 209[0:Obv:208.3] ssList(u) ssItem(v) || equal(cons(v,u),sk4)** -> equal(nil,sk4).
% 3.46/3.63 210[0:Rew:209.3,203.3] ssList(u) ssItem(v) || equal(cons(v,u),sk4) -> equal(app(u,cons(v,sk4)),sk1)**.
% 3.46/3.63 211[0:Rew:210.3,12.4,209.3,12.4,132.2,12.3,5.0,12.3] ssItem(u) ssList(v) || equal(nil,sk1) equal(cons(u,v),sk4)** equal(sk1,sk1) -> .
% 3.46/3.63 212[0:Obv:211.4] ssList(u) ssItem(v) || equal(nil,sk1) equal(cons(v,u),sk4)** -> .
% 3.46/3.63 270[0:Res:4.0,116.0] || -> equal(nil,sk4) equal(cons(hd(sk4),tl(sk4)),sk4)**.
% 3.46/3.63 290[0:Res:4.0,89.0] || -> ssList(tl(sk4))* equal(nil,sk4).
% 3.46/3.63 309[0:Res:4.0,189.1] ssList(u) || equal(hd(u),hd(sk4))* equal(tl(u),tl(sk4)) -> equal(u,sk4) equal(nil,u) equal(nil,sk4).
% 3.46/3.63 353[0:Res:4.0,98.1] ssItem(u) || -> ssList(cons(u,sk4))*.
% 3.46/3.63 515[0:Res:1.0,135.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 3.46/3.63 522[0:Res:1.0,109.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 3.46/3.63 527[0:Res:1.0,98.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 3.46/3.63 538[0:Res:1.0,169.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 3.46/3.63 571[1:Spt:84.1] || -> ssItem(u)*.
% 3.46/3.63 574[1:MRR:527.0,571.0] || -> ssList(cons(u,sk1))*.
% 3.46/3.63 577[1:MRR:82.0,571.0] || -> cyclefreeP(cons(u,nil))*.
% 3.46/3.63 578[1:MRR:81.0,571.0] || -> totalorderP(cons(u,nil))*.
% 3.46/3.63 579[1:MRR:80.0,571.0] || -> strictorderP(cons(u,nil))*.
% 3.46/3.63 580[1:MRR:79.0,571.0] || -> totalorderedP(cons(u,nil))*.
% 3.46/3.63 581[1:MRR:78.0,571.0] || -> strictorderedP(cons(u,nil))*.
% 3.46/3.63 582[1:MRR:77.0,571.0] || -> duplicatefreeP(cons(u,nil))*.
% 3.46/3.63 583[1:MRR:76.0,571.0] || -> equalelemsP(cons(u,nil))*.
% 3.46/3.63 587[1:MRR:522.0,571.0] || -> equal(hd(cons(u,sk1)),u)**.
% 3.46/3.63 613[1:MRR:129.1,129.0,571.0] || neq(u,v)* equal(u,v) -> .
% 3.46/3.63 706[1:MRR:209.1,571.0] ssList(u) || equal(cons(v,u),sk4)** -> equal(nil,sk4).
% 3.46/3.63 707[1:MRR:212.1,571.0] ssList(u) || equal(nil,sk1) equal(cons(v,u),sk4)** -> .
% 3.46/3.63 708[1:MRR:538.1,571.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 3.46/3.63 772[1:MRR:182.3,182.2,571.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.46/3.63 773[1:Rew:706.2,707.1] ssList(u) || equal(sk4,sk1) equal(cons(v,u),sk4)** -> .
% 3.46/3.63 774[2:Spt:515.0,515.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 3.46/3.63 782[3:Spt:309.5] || -> equal(nil,sk4)**.
% 3.46/3.63 787[3:Rew:782.0,202.0] || equal(sk4,sk4) -> equal(nil,sk1)**.
% 3.46/3.63 863[3:Rew:782.0,86.1] ssList(u) || -> equal(app(sk4,u),u)**.
% 3.46/3.63 864[3:Rew:782.0,85.1] ssList(u) || -> equal(app(u,sk4),u)**.
% 3.46/3.63 869[3:Rew:782.0,577.0] || -> cyclefreeP(cons(u,sk4))*.
% 3.46/3.63 870[3:Rew:782.0,578.0] || -> totalorderP(cons(u,sk4))*.
% 3.46/3.63 871[3:Rew:782.0,579.0] || -> strictorderP(cons(u,sk4))*.
% 3.46/3.63 872[3:Rew:782.0,580.0] || -> totalorderedP(cons(u,sk4))*.
% 3.46/3.63 873[3:Rew:782.0,581.0] || -> strictorderedP(cons(u,sk4))*.
% 3.46/3.63 874[3:Rew:782.0,582.0] || -> duplicatefreeP(cons(u,sk4))*.
% 3.46/3.63 875[3:Rew:782.0,583.0] || -> equalelemsP(cons(u,sk4))*.
% 3.46/3.63 911[3:Obv:787.0] || -> equal(nil,sk1)**.
% 3.46/3.63 912[3:Rew:782.0,911.0] || -> equal(sk4,sk1)**.
% 3.46/3.63 956[3:Rew:912.0,869.0] || -> cyclefreeP(cons(u,sk1))*.
% 3.46/3.63 957[3:Rew:912.0,870.0] || -> totalorderP(cons(u,sk1))*.
% 3.46/3.63 958[3:Rew:912.0,871.0] || -> strictorderP(cons(u,sk1))*.
% 3.46/3.63 959[3:Rew:912.0,872.0] || -> totalorderedP(cons(u,sk1))*.
% 3.46/3.63 960[3:Rew:912.0,873.0] || -> strictorderedP(cons(u,sk1))*.
% 3.46/3.63 961[3:Rew:912.0,874.0] || -> duplicatefreeP(cons(u,sk1))*.
% 3.46/3.63 962[3:Rew:912.0,875.0] || -> equalelemsP(cons(u,sk1))*.
% 3.46/3.63 1059[3:Rew:912.0,863.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 3.46/3.63 1060[3:Rew:1059.1,774.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 3.46/3.63 1073[3:Rew:912.0,864.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 3.46/3.63 1084[3:Rew:1073.1,708.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 3.46/3.63 1217[3:SpR:1060.1,587.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 3.46/3.63 1222[3:SSi:1217.0,574.0,956.0,957.0,958.0,959.0,960.0,961.0,962.0] || -> equal(hd(sk1),u)*.
% 3.46/3.63 1251[3:Rew:1222.0,1084.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 3.46/3.63 1343[3:Rew:1222.0,772.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 3.46/3.63 1422[3:Con:1343.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 3.46/3.63 1423[3:AED:66.0,1422.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 3.46/3.63 1424[3:Rew:1251.1,1423.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 3.46/3.63 1425[3:Obv:1424.1] ssList(u) || -> .
% 3.46/3.63 1426[3:UnC:1425.0,25.0] || -> .
% 3.46/3.63 1519[3:Spt:1426.0,309.5,782.0] || equal(nil,sk4)** -> .
% 3.46/3.63 1520[3:Spt:1426.0,309.0,309.1,309.2,309.3,309.4] ssList(u) || equal(hd(u),hd(sk4))* equal(tl(u),tl(sk4)) -> equal(u,sk4) equal(nil,u).
% 3.46/3.63 1521[3:MRR:290.1,1519.0] || -> ssList(tl(sk4))*.
% 3.46/3.63 1527[3:MRR:270.0,1519.0] || -> equal(cons(hd(sk4),tl(sk4)),sk4)**.
% 3.46/3.63 1534[3:MRR:706.2,1519.0] ssList(u) || equal(cons(v,u),sk4)** -> .
% 3.46/3.63 2360[3:SpL:1527.0,1534.1] ssList(tl(sk4)) || equal(sk4,sk4)* -> .
% 3.46/3.63 2365[3:Obv:2360.1] ssList(tl(sk4)) || -> .
% 3.46/3.63 2366[3:SSi:2365.0,1521.0] || -> .
% 3.46/3.63 2367[2:Spt:2366.0,515.1] || -> equal(nil,sk1)**.
% 3.46/3.63 2443[2:Rew:2367.0,290.1] || -> ssList(tl(sk4))* equal(sk4,sk1).
% 3.46/3.63 2463[2:Rew:2367.0,201.1,2367.0,201.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 3.46/3.63 2464[2:Obv:2463.0] || -> neq(sk4,sk1)*.
% 3.46/3.63 2501[2:Rew:2367.0,270.0] || -> equal(sk4,sk1) equal(cons(hd(sk4),tl(sk4)),sk4)**.
% 3.46/3.63 2516[2:Rew:2367.0,706.2] ssList(u) || equal(cons(v,u),sk4)** -> equal(sk4,sk1).
% 3.46/3.63 2521[2:Rew:2516.2,773.1] ssList(u) || equal(sk1,sk1) equal(cons(v,u),sk4)** -> .
% 3.46/3.63 2522[2:Obv:2521.1] ssList(u) || equal(cons(v,u),sk4)** -> .
% 3.82/4.03 2558[2:Res:2464.0,613.0] || equal(sk4,sk1)** -> .
% 3.82/4.03 2559[2:MRR:2443.1,2558.0] || -> ssList(tl(sk4))*.
% 3.82/4.03 2564[2:MRR:2501.0,2558.0] || -> equal(cons(hd(sk4),tl(sk4)),sk4)**.
% 3.82/4.03 2608[2:SpL:2564.0,2522.1] ssList(tl(sk4)) || equal(sk4,sk4)* -> .
% 3.82/4.03 2611[2:Obv:2608.1] ssList(tl(sk4)) || -> .
% 3.82/4.03 2612[2:SSi:2611.0,2559.0] || -> .
% 3.82/4.03 2613[1:Spt:2612.0,84.0,84.2] ssList(u) || -> duplicatefreeP(u)*.
% 3.82/4.03 2622[1:MRR:191.1,2613.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 3.82/4.03 9369[0:SpR:169.3,97.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 3.82/4.03 9417[0:Obv:9369.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 3.82/4.03 9418[0:SSi:9417.2,98.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 3.82/4.03 11479[1:EqR:2622.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 3.82/4.03 11510[1:SSi:11479.0,97.2,97.2,98.2,98.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 3.82/4.03 11511[1:MRR:9418.3,11510.1] ssList(u) ssItem(v) ssList(w) || -> .
% 3.82/4.03 11514[1:Con:11511.2] ssList(u) ssItem(v) || -> .
% 3.82/4.03 11516[1:MRR:353.1,11514.0] ssItem(u) || -> .
% 3.82/4.03 11518[1:UnC:11516.0,59.0] || -> .
% 3.82/4.03 % SZS output end Refutation
% 3.82/4.03 Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_10 co1_11 co1_12 clause13 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause77 clause85 clause86 clause97 clause104 clause117 clause120 clause123 clause157 clause170 clause177 clause179
% 3.82/4.03
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