TSTP Solution File: SWC025+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC025+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 22:01:11 EDT 2022
% Result : Theorem 2.64s 2.85s
% Output : Refutation 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC025+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n023.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sun Jun 12 17:18:06 EDT 2022
% 0.06/0.25 % CPUTime :
% 2.64/2.85
% 2.64/2.85 SPASS V 3.9
% 2.64/2.85 SPASS beiseite: Proof found.
% 2.64/2.85 % SZS status Theorem
% 2.64/2.85 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/2.85 SPASS derived 6972 clauses, backtracked 2373 clauses, performed 59 splits and kept 5560 clauses.
% 2.64/2.85 SPASS allocated 104478 KBytes.
% 2.64/2.85 SPASS spent 0:00:02.38 on the problem.
% 2.64/2.85 0:00:00.02 for the input.
% 2.64/2.85 0:00:00.05 for the FLOTTER CNF translation.
% 2.64/2.85 0:00:00.05 for inferences.
% 2.64/2.85 0:00:00.04 for the backtracking.
% 2.64/2.85 0:00:02.03 for the reduction.
% 2.64/2.85
% 2.64/2.85
% 2.64/2.85 Here is a proof with depth 6, length 112 :
% 2.64/2.85 % SZS output start Refutation
% 2.64/2.85 1[0:Inp] || -> ssList(skc5)*.
% 2.64/2.85 2[0:Inp] || -> ssList(skc4)*.
% 2.64/2.85 4[0:Inp] || -> ssItem(skc7)*.
% 2.64/2.85 5[0:Inp] || -> ssItem(skc6)*.
% 2.64/2.85 52[0:Inp] || equal(skc7,skc6)** -> .
% 2.64/2.85 59[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 2.64/2.85 68[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 2.64/2.85 69[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.64/2.85 70[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.64/2.85 71[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.64/2.85 72[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.64/2.85 73[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.64/2.85 74[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.64/2.85 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.64/2.85 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.64/2.85 78[0:Inp] || SkP0(skc5,skc4)* SkP0(skc4,skc5) -> .
% 2.64/2.85 79[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 2.64/2.85 83[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 2.64/2.85 84[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 2.64/2.85 85[0:Inp] ssItem(u) || memberP(skc4,u) -> memberP(skc5,u)*.
% 2.64/2.85 86[0:Inp] ssItem(u) || memberP(skc5,u)* -> memberP(skc4,u).
% 2.64/2.85 90[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 2.64/2.85 110[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 2.64/2.85 117[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 2.64/2.85 132[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 2.64/2.85 147[0:Inp] ssList(u) ssItem(v) ssItem(w) || equal(w,v) -> memberP(cons(v,u),w)*.
% 2.64/2.85 151[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 2.64/2.85 152[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 2.64/2.85 243[0:Res:2.0,132.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 2.64/2.85 249[0:Res:2.0,117.0] || -> equal(skc4,nil) equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 2.64/2.85 274[0:Res:2.0,83.0] || -> ssItem(hd(skc4))* equal(skc4,nil).
% 2.64/2.85 275[0:Res:2.0,84.0] || -> ssList(tl(skc4))* equal(skc4,nil).
% 2.64/2.85 306[0:Res:2.0,151.1] ssItem(u) || totalorderedP(cons(u,skc4))* -> leq(u,hd(skc4)) equal(skc4,nil).
% 2.64/2.85 307[0:Res:2.0,152.1] ssItem(u) || strictorderedP(cons(u,skc4))* -> lt(u,hd(skc4)) equal(skc4,nil).
% 2.64/2.85 414[0:Res:1.0,132.0] ssList(u) || -> equal(skc5,nil) equal(hd(app(skc5,u)),hd(skc5))**.
% 2.64/2.85 420[0:Res:1.0,117.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.64/2.85 425[0:Res:1.0,110.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 2.64/2.85 437[0:Res:1.0,90.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 2.64/2.85 445[0:Res:1.0,83.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 2.64/2.85 446[0:Res:1.0,84.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 2.64/2.85 477[0:Res:1.0,151.1] ssItem(u) || totalorderedP(cons(u,skc5))* -> leq(u,hd(skc5)) equal(skc5,nil).
% 2.64/2.85 478[0:Res:1.0,152.1] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)) equal(skc5,nil).
% 2.64/2.85 544[1:Spt:414.0,414.2] ssList(u) || -> equal(hd(app(skc5,u)),hd(skc5))**.
% 2.64/2.85 548[2:Spt:243.0,243.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 2.64/2.85 552[3:Spt:478.3] || -> equal(skc5,nil)**.
% 2.64/2.85 553[3:Rew:552.0,544.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 2.64/2.85 573[3:Rew:552.0,437.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 2.64/2.85 574[3:Rew:552.0,425.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 2.64/2.85 726[3:Rew:79.1,553.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 2.64/2.85 1129[3:SpR:574.1,726.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 2.64/2.85 1132[3:SSi:1129.1,76.1,75.1,72.1,71.1,70.1,74.1,73.1,573.1] ssItem(u) || -> equal(u,hd(nil))*.
% 2.64/2.85 1218[3:SpR:1132.1,1132.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 2.64/2.85 1312[3:EmS:1218.0,4.0] ssItem(u) || -> equal(u,skc7)*.
% 2.64/2.85 1334[3:EmS:1312.0,5.0] || -> equal(skc7,skc6)**.
% 2.64/2.85 1335[3:MRR:1334.0,52.0] || -> .
% 2.64/2.85 1521[3:Spt:1335.0,478.3,552.0] || equal(skc5,nil)** -> .
% 2.64/2.85 1522[3:Spt:1335.0,478.0,478.1,478.2] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)).
% 2.64/2.85 1536[4:Spt:306.3] || -> equal(skc4,nil)**.
% 2.64/2.85 1665[4:Rew:1536.0,548.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 2.64/2.85 1707[4:Rew:79.1,1665.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 2.64/2.85 1865[4:SpR:425.1,1707.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 2.64/2.85 5576[4:SSi:1865.1,90.0,1.2] ssItem(u) || -> equal(u,hd(nil))*.
% 2.64/2.85 5787[4:SpR:5576.1,5576.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 2.64/2.85 6349[4:EmS:5787.0,4.0] ssItem(u) || -> equal(u,skc7)*.
% 2.64/2.85 6370[4:EmS:6349.0,5.0] || -> equal(skc7,skc6)**.
% 2.64/2.85 6371[4:MRR:6370.0,52.0] || -> .
% 2.64/2.85 6665[4:Spt:6371.0,306.3,1536.0] || equal(skc4,nil)** -> .
% 2.64/2.85 6666[4:Spt:6371.0,306.0,306.1,306.2] ssItem(u) || totalorderedP(cons(u,skc4))* -> leq(u,hd(skc4)).
% 2.64/2.85 6756[0:Res:68.1,78.0] || equal(skc5,nil) SkP0(skc4,skc5)* -> .
% 2.64/2.85 6757[0:Res:59.0,78.0] || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 2.64/2.85 6758[4:MRR:6757.1,6665.0] || SkP0(skc4,skc5)* -> .
% 2.64/2.85 6761[4:Res:59.0,6758.0] || -> equal(skc5,nil)**.
% 2.64/2.85 6762[4:MRR:6761.0,1521.0] || -> .
% 2.64/2.85 6763[2:Spt:6762.0,243.1] || -> equal(skc4,nil)**.
% 2.64/2.85 6816[2:Rew:6763.0,86.2] ssItem(u) || memberP(skc5,u)* -> memberP(nil,u).
% 2.64/2.85 6901[2:Rew:6763.0,6756.1] || equal(skc5,nil) SkP0(nil,skc5)* -> .
% 2.64/2.85 6905[2:MRR:6816.2,69.1] ssItem(u) || memberP(skc5,u)* -> .
% 2.64/2.85 7014[3:Spt:477.3] || -> equal(skc5,nil)**.
% 2.64/2.85 7145[3:Rew:7014.0,6901.0] || equal(nil,nil) SkP0(nil,skc5)* -> .
% 2.64/2.85 7174[3:Obv:7145.0] || SkP0(nil,skc5)* -> .
% 2.64/2.85 7175[3:Rew:7014.0,7174.0] || SkP0(nil,nil)* -> .
% 2.64/2.85 7260[3:Res:68.1,7175.0] || equal(nil,nil)* -> .
% 2.64/2.85 7262[3:Obv:7260.0] || -> .
% 2.64/2.85 7263[3:Spt:7262.0,477.3,7014.0] || equal(skc5,nil)** -> .
% 2.64/2.85 7264[3:Spt:7262.0,477.0,477.1,477.2] ssItem(u) || totalorderedP(cons(u,skc5))* -> leq(u,hd(skc5)).
% 2.64/2.85 7265[3:MRR:446.1,7263.0] || -> ssList(tl(skc5))*.
% 2.64/2.85 7266[3:MRR:445.1,7263.0] || -> ssItem(hd(skc5))*.
% 2.64/2.85 7270[3:MRR:420.0,7263.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.64/2.85 8482[3:SpR:7270.0,147.4] ssList(tl(skc5)) ssItem(hd(skc5)) ssItem(u) || equal(u,hd(skc5)) -> memberP(skc5,u)*.
% 2.64/2.85 8498[3:SSi:8482.1,8482.0,7266.0,7265.0] ssItem(u) || equal(u,hd(skc5)) -> memberP(skc5,u)*.
% 2.64/2.85 8499[3:MRR:8498.2,6905.1] ssItem(u) || equal(u,hd(skc5))* -> .
% 2.64/2.85 8602[3:EqR:8499.1] ssItem(hd(skc5)) || -> .
% 2.64/2.85 8603[3:SSi:8602.0,7266.0] || -> .
% 2.64/2.85 8604[1:Spt:8603.0,414.1] || -> equal(skc5,nil)**.
% 2.64/2.85 8732[1:Rew:8604.0,6756.1,8604.0,6756.0] || equal(nil,nil) SkP0(skc4,nil)* -> .
% 2.64/2.85 8733[1:Obv:8732.0] || SkP0(skc4,nil)* -> .
% 2.64/2.85 8739[1:Rew:8604.0,85.2] ssItem(u) || memberP(skc4,u)* -> memberP(nil,u).
% 2.64/2.85 8740[1:MRR:8739.2,69.1] ssItem(u) || memberP(skc4,u)* -> .
% 2.64/2.85 8931[2:Spt:307.3] || -> equal(skc4,nil)**.
% 2.64/2.85 9004[2:Rew:8931.0,8733.0] || SkP0(nil,nil)* -> .
% 2.64/2.85 9229[2:Res:68.1,9004.0] || equal(nil,nil)* -> .
% 2.64/2.85 9231[2:Obv:9229.0] || -> .
% 2.64/2.85 9232[2:Spt:9231.0,307.3,8931.0] || equal(skc4,nil)** -> .
% 2.64/2.85 9233[2:Spt:9231.0,307.0,307.1,307.2] ssItem(u) || strictorderedP(cons(u,skc4))* -> lt(u,hd(skc4)).
% 2.64/2.85 9234[2:MRR:275.1,9232.0] || -> ssList(tl(skc4))*.
% 2.64/2.85 9235[2:MRR:274.1,9232.0] || -> ssItem(hd(skc4))*.
% 2.64/2.85 9239[2:MRR:249.0,9232.0] || -> equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 2.64/2.85 9411[2:SpR:9239.0,147.4] ssList(tl(skc4)) ssItem(hd(skc4)) ssItem(u) || equal(u,hd(skc4)) -> memberP(skc4,u)*.
% 2.64/2.85 9428[2:SSi:9411.1,9411.0,9235.0,9234.0] ssItem(u) || equal(u,hd(skc4)) -> memberP(skc4,u)*.
% 2.64/2.85 9429[2:MRR:9428.2,8740.1] ssItem(u) || equal(u,hd(skc4))* -> .
% 2.64/2.85 9783[2:EqR:9429.1] ssItem(hd(skc4)) || -> .
% 2.64/2.85 9784[2:SSi:9783.0,9235.0] || -> .
% 2.64/2.85 % SZS output end Refutation
% 2.64/2.85 Formulae used in the proof : co1 ax2 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax23 ax78 ax85 ax37 ax67 ax70
% 2.64/2.85
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