TSTP Solution File: SWC324-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC324-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:03:19 EDT 2022
% Result : Unsatisfiable 4.50s 4.75s
% Output : Refutation 5.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC324-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 06:24:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.50/4.75
% 4.50/4.75 SPASS V 3.9
% 4.50/4.75 SPASS beiseite: Proof found.
% 4.50/4.75 % SZS status Theorem
% 4.50/4.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.50/4.75 SPASS derived 10314 clauses, backtracked 4343 clauses, performed 89 splits and kept 9207 clauses.
% 4.50/4.75 SPASS allocated 86837 KBytes.
% 4.50/4.75 SPASS spent 0:00:04.40 on the problem.
% 4.50/4.75 0:00:00.04 for the input.
% 4.50/4.75 0:00:00.00 for the FLOTTER CNF translation.
% 4.50/4.75 0:00:00.09 for inferences.
% 4.50/4.75 0:00:00.11 for the backtracking.
% 4.50/4.75 0:00:03.93 for the reduction.
% 4.50/4.75
% 4.50/4.75
% 4.50/4.75 Here is a proof with depth 3, length 121 :
% 4.50/4.75 % SZS output start Refutation
% 4.50/4.75 1[0:Inp] || -> ssList(sk1)*.
% 4.50/4.75 2[0:Inp] || -> ssList(sk2)*.
% 4.50/4.75 5[0:Inp] || -> equal(sk4,sk2)**.
% 4.50/4.75 6[0:Inp] || -> equal(sk3,sk1)**.
% 4.50/4.75 7[0:Inp] ssList(u) ssList(v) || equal(app(u,v),sk1)**+ equal(app(v,u),sk2)** -> .
% 4.50/4.75 8[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),sk4)** -> equal(app(v,cons(u,nil)),sk3)**.
% 4.50/4.75 9[0:Inp] || equal(nil,sk4) -> equal(sk3,nil)**.
% 4.50/4.75 10[0:Inp] || -> equalelemsP(nil)*.
% 4.50/4.75 11[0:Inp] || -> duplicatefreeP(nil)*.
% 4.50/4.75 12[0:Inp] || -> strictorderedP(nil)*.
% 4.50/4.75 13[0:Inp] || -> totalorderedP(nil)*.
% 4.50/4.75 14[0:Inp] || -> strictorderP(nil)*.
% 4.50/4.75 15[0:Inp] || -> totalorderP(nil)*.
% 4.50/4.75 16[0:Inp] || -> cyclefreeP(nil)*.
% 4.50/4.75 17[0:Inp] || -> ssList(nil)*.
% 4.50/4.75 22[0:Inp] || -> ssList(skaf82(u))*.
% 4.50/4.75 56[0:Inp] || -> ssItem(skaf44(u))*.
% 4.50/4.75 63[0:Inp] || equal(skac2,skac3)** -> .
% 4.50/4.75 73[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 4.50/4.75 74[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 4.50/4.75 75[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 4.50/4.75 76[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 4.50/4.75 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 4.50/4.75 78[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 4.50/4.75 79[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 4.50/4.75 81[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 4.50/4.75 82[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 4.50/4.75 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 4.50/4.75 94[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 4.50/4.75 95[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 4.50/4.75 106[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 4.50/4.75 118[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 4.50/4.75 125[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 4.50/4.75 129[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 4.50/4.75 132[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 4.50/4.75 166[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 4.50/4.75 179[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 4.50/4.75 186[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).
% 4.50/4.75 188[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)* -> .
% 4.50/4.75 197[0:Rew:6.0,9.1,5.0,9.0] || equal(nil,sk2)** -> equal(nil,sk1).
% 4.50/4.75 198[0:Rew:6.0,8.3,129.2,8.2,5.0,8.2] ssList(u) ssItem(v) || equal(cons(v,u),sk2) -> equal(app(u,cons(v,nil)),sk1)**.
% 4.50/4.75 262[0:Res:2.0,118.0] || -> equal(nil,sk2) equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 4.50/4.75 457[0:Res:1.0,82.0] || -> equal(app(sk1,nil),sk1)**.
% 4.50/4.75 474[0:Res:1.0,186.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 4.50/4.75 505[0:Res:1.0,132.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 4.50/4.75 512[0:Res:1.0,106.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 4.50/4.75 517[0:Res:1.0,95.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 4.50/4.75 528[0:Res:1.0,166.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 4.50/4.75 560[1:Spt:81.1] || -> ssItem(u)*.
% 4.50/4.75 563[1:MRR:517.0,560.0] || -> ssList(cons(u,sk1))*.
% 4.50/4.75 566[1:MRR:79.0,560.0] || -> cyclefreeP(cons(u,nil))*.
% 4.50/4.75 567[1:MRR:78.0,560.0] || -> totalorderP(cons(u,nil))*.
% 4.50/4.75 568[1:MRR:77.0,560.0] || -> strictorderP(cons(u,nil))*.
% 4.50/4.75 569[1:MRR:76.0,560.0] || -> totalorderedP(cons(u,nil))*.
% 4.50/4.75 570[1:MRR:75.0,560.0] || -> strictorderedP(cons(u,nil))*.
% 4.50/4.75 571[1:MRR:74.0,560.0] || -> duplicatefreeP(cons(u,nil))*.
% 4.50/4.75 572[1:MRR:73.0,560.0] || -> equalelemsP(cons(u,nil))*.
% 4.50/4.75 576[1:MRR:512.0,560.0] || -> equal(hd(cons(u,sk1)),u)**.
% 4.50/4.75 686[1:MRR:95.1,560.0] ssList(u) || -> ssList(cons(v,u))*.
% 4.50/4.75 691[1:MRR:125.1,560.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 4.50/4.75 692[1:MRR:129.1,560.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 4.50/4.75 693[1:MRR:528.1,560.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 4.50/4.75 697[1:MRR:198.1,560.0] ssList(u) || equal(cons(v,u),sk2) -> equal(app(u,cons(v,nil)),sk1)**.
% 4.50/4.75 757[1:MRR:179.3,179.2,560.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 4.50/4.75 758[2:Spt:505.0,505.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 4.50/4.75 766[3:Spt:474.5] || -> equal(nil,sk1)**.
% 4.50/4.75 845[3:Rew:766.0,83.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 4.50/4.75 846[3:Rew:766.0,82.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 4.50/4.75 851[3:Rew:766.0,566.0] || -> cyclefreeP(cons(u,sk1))*.
% 4.50/4.75 852[3:Rew:766.0,567.0] || -> totalorderP(cons(u,sk1))*.
% 4.50/4.75 853[3:Rew:766.0,568.0] || -> strictorderP(cons(u,sk1))*.
% 4.50/4.75 854[3:Rew:766.0,569.0] || -> totalorderedP(cons(u,sk1))*.
% 4.50/4.75 855[3:Rew:766.0,570.0] || -> strictorderedP(cons(u,sk1))*.
% 4.50/4.75 856[3:Rew:766.0,571.0] || -> duplicatefreeP(cons(u,sk1))*.
% 4.50/4.75 857[3:Rew:766.0,572.0] || -> equalelemsP(cons(u,sk1))*.
% 4.50/4.75 906[3:Rew:845.1,758.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 4.50/4.75 931[3:Rew:846.1,693.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 4.50/4.75 1267[3:SpR:906.1,576.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 4.50/4.75 1274[3:SSi:1267.0,563.0,851.0,852.0,853.0,854.0,855.0,856.0,857.0] || -> equal(hd(sk1),u)*.
% 4.50/4.75 1336[3:Rew:1274.0,931.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 4.50/4.75 1496[3:Rew:1274.0,757.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 4.50/4.75 1608[3:Con:1496.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 4.50/4.75 1609[3:AED:63.0,1608.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 4.50/4.75 1610[3:Rew:1336.1,1609.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 4.50/4.75 1611[3:Obv:1610.1] ssList(u) || -> .
% 4.50/4.75 1612[3:UnC:1611.0,2.0] || -> .
% 4.50/4.75 1772[3:Spt:1612.0,474.5,766.0] || equal(nil,sk1)** -> .
% 4.50/4.75 1773[3:Spt:1612.0,474.0,474.1,474.2,474.3,474.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 4.50/4.75 1778[3:MRR:197.1,1772.0] || equal(nil,sk2)** -> .
% 4.50/4.75 1787[3:MRR:262.0,1778.0] || -> equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 4.50/4.75 2044[1:EqR:691.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 4.50/4.75 2045[1:SSi:2044.0,686.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,17.0,572.0,571.0,570.0,569.0,568.0,567.0,566.1] || -> singletonP(cons(u,nil))*.
% 4.50/4.75 3151[0:SpL:457.0,7.2] ssList(sk1) ssList(nil) || equal(sk1,sk1) equal(app(nil,sk1),sk2)** -> .
% 4.50/4.75 3158[1:SpL:697.2,7.2] ssList(u) ssList(u) ssList(cons(v,nil)) || equal(cons(v,u),sk2) equal(sk1,sk1) equal(app(cons(v,nil),u),sk2)** -> .
% 4.50/4.75 3163[0:Obv:3151.2] ssList(sk1) ssList(nil) || equal(app(nil,sk1),sk2)** -> .
% 4.50/4.75 3164[0:Rew:83.1,3163.2] ssList(sk1) ssList(nil) || equal(sk2,sk1)** -> .
% 4.50/4.75 3173[1:Obv:3158.4] ssList(u) ssList(cons(v,nil)) || equal(cons(v,u),sk2) equal(app(cons(v,nil),u),sk2)** -> .
% 4.50/4.75 3174[1:Rew:692.1,3173.3] ssList(u) ssList(cons(v,nil)) || equal(cons(v,u),sk2)** equal(cons(v,u),sk2)** -> .
% 4.50/4.75 3175[1:Obv:3174.2] ssList(u) ssList(cons(v,nil)) || equal(cons(v,u),sk2)** -> .
% 4.50/4.75 3176[1:SSi:3175.1,686.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,17.0,572.0,571.0,570.0,569.0,568.0,567.0,566.0,2045.1] ssList(u) || equal(cons(v,u),sk2)** -> .
% 4.50/4.75 3187[3:SpL:1787.0,3176.1] ssList(skaf82(sk2)) || equal(sk2,sk2)* -> .
% 4.50/4.75 3410[0:SSi:3164.1,3164.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,17.0,1.0] || equal(sk2,sk1)** -> .
% 4.50/4.75 3465[3:Obv:3187.1] ssList(skaf82(sk2)) || -> .
% 4.50/4.75 3466[3:SSi:3465.0,22.0,2.0] || -> .
% 4.50/4.75 3499[2:Spt:3466.0,505.1] || -> equal(nil,sk1)**.
% 4.50/4.75 3697[2:Rew:3499.0,262.0] || -> equal(sk2,sk1) equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 4.50/4.75 3698[2:MRR:3697.0,3410.0] || -> equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 4.50/4.75 3824[2:SpL:3698.0,3176.1] ssList(skaf82(sk2)) || equal(sk2,sk2)* -> .
% 4.50/4.75 3989[2:Obv:3824.1] ssList(skaf82(sk2)) || -> .
% 4.50/4.75 3990[2:SSi:3989.0,22.0,2.0] || -> .
% 4.50/4.75 4013[1:Spt:3990.0,81.0,81.2] ssList(u) || -> duplicatefreeP(u)*.
% 4.50/4.75 4021[1:MRR:188.1,4013.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 4.50/4.75 14115[0:SpR:166.3,94.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 5.22/5.40 14166[0:Obv:14115.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 5.22/5.40 14167[0:SSi:14166.2,95.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 5.22/5.40 15651[1:EqR:4021.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 5.22/5.40 15683[1:SSi:15651.0,94.2,94.2,95.2,95.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 5.22/5.40 15684[1:MRR:14167.3,15683.1] ssList(u) ssItem(v) ssList(w) || -> .
% 5.22/5.40 15687[1:Con:15684.2] ssList(u) ssItem(v) || -> .
% 5.22/5.40 15689[1:MRR:517.1,15687.0] ssItem(u) || -> .
% 5.22/5.40 15691[1:UnC:15689.0,56.0] || -> .
% 5.22/5.40 % SZS output end Refutation
% 5.22/5.40 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause85 clause86 clause97 clause109 clause116 clause120 clause123 clause157 clause170 clause177 clause179
% 5.22/5.40
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