TSTP Solution File: SWC397-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC397-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 22:03:48 EDT 2022
% Result : Unsatisfiable 7.23s 7.43s
% Output : Refutation 8.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC397-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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 08:38:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.23/7.43
% 7.23/7.43 SPASS V 3.9
% 7.23/7.43 SPASS beiseite: Proof found.
% 7.23/7.43 % SZS status Theorem
% 7.23/7.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.23/7.43 SPASS derived 11538 clauses, backtracked 3458 clauses, performed 48 splits and kept 9216 clauses.
% 7.23/7.43 SPASS allocated 89320 KBytes.
% 7.23/7.43 SPASS spent 0:00:07.06 on the problem.
% 7.23/7.43 0:00:00.04 for the input.
% 7.23/7.43 0:00:00.00 for the FLOTTER CNF translation.
% 7.23/7.43 0:00:00.12 for inferences.
% 7.23/7.43 0:00:00.22 for the backtracking.
% 7.23/7.43 0:00:06.49 for the reduction.
% 7.23/7.43
% 7.23/7.43
% 7.23/7.43 Here is a proof with depth 4, length 137 :
% 7.23/7.43 % SZS output start Refutation
% 7.23/7.43 2[0:Inp] || -> ssList(sk2)*.
% 7.23/7.43 5[0:Inp] || -> equal(sk4,sk2)**.
% 7.23/7.43 6[0:Inp] || -> equal(sk3,sk1)**.
% 7.23/7.43 8[0:Inp] || -> memberP(sk1,sk5)*.
% 7.23/7.43 9[0:Inp] || memberP(sk2,sk5)* -> .
% 7.23/7.43 10[0:Inp] || equal(nil,sk4) -> equal(sk3,nil)**.
% 7.23/7.43 11[0:Inp] || neq(sk4,nil)* -> ssItem(sk6).
% 7.23/7.43 12[0:Inp] || neq(sk4,nil)* -> ssList(sk7).
% 7.23/7.43 13[0:Inp] || neq(sk4,nil) -> equal(app(cons(sk6,nil),sk7),sk3)**.
% 7.23/7.43 14[0:Inp] || neq(sk4,nil) -> equal(app(sk7,cons(sk6,nil)),sk4)**.
% 7.23/7.43 15[0:Inp] || -> equalelemsP(nil)*.
% 7.23/7.43 16[0:Inp] || -> duplicatefreeP(nil)*.
% 7.23/7.43 17[0:Inp] || -> strictorderedP(nil)*.
% 7.23/7.43 18[0:Inp] || -> totalorderedP(nil)*.
% 7.23/7.43 19[0:Inp] || -> strictorderP(nil)*.
% 7.23/7.43 20[0:Inp] || -> totalorderP(nil)*.
% 7.23/7.43 21[0:Inp] || -> cyclefreeP(nil)*.
% 7.23/7.43 22[0:Inp] || -> ssList(nil)*.
% 7.23/7.43 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 7.23/7.43 79[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 7.23/7.43 80[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 7.23/7.43 81[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 7.23/7.43 82[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 7.23/7.43 83[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 7.23/7.43 84[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 7.23/7.43 85[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 7.23/7.43 86[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 7.23/7.43 99[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 7.23/7.43 100[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 7.23/7.43 114[0:Inp] ssList(u) ssList(v) || -> equal(u,v) neq(u,v)*.
% 7.23/7.43 116[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 7.23/7.43 130[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 7.23/7.43 134[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 7.23/7.43 152[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 7.23/7.43 154[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 7.23/7.43 155[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(w,u) -> memberP(app(v,w),u)*.
% 7.23/7.43 171[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 7.23/7.43 175[0:Inp] ssItem(u) ssItem(v) ssList(w) || memberP(cons(v,w),u)* -> equal(u,v) memberP(w,u).
% 7.23/7.43 191[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).
% 7.23/7.43 193[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)* -> .
% 7.23/7.43 202[0:Rew:5.0,12.0] || neq(sk2,nil)* -> ssList(sk7).
% 7.23/7.43 203[0:Rew:5.0,11.0] || neq(sk2,nil)* -> ssItem(sk6).
% 7.23/7.43 204[0:Rew:6.0,10.1,5.0,10.0] || equal(nil,sk2)** -> equal(nil,sk1).
% 7.23/7.43 205[0:Rew:5.0,14.1,5.0,14.0] || neq(sk2,nil) -> equal(app(sk7,cons(sk6,nil)),sk2)**.
% 7.23/7.43 206[0:Rew:6.0,13.1,5.0,13.0] || neq(sk2,nil) -> equal(app(cons(sk6,nil),sk7),sk1)**.
% 7.23/7.43 394[0:Res:2.0,86.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 7.23/7.43 409[0:Res:2.0,191.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 7.23/7.43 448[0:Res:2.0,114.1] ssList(u) || -> equal(sk2,u) neq(sk2,u)*.
% 7.23/7.43 450[0:Res:2.0,100.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 7.23/7.43 491[1:Spt:86.1] || -> ssItem(u)*.
% 7.23/7.43 495[1:MRR:85.0,491.0] || memberP(nil,u)* -> .
% 7.23/7.43 496[1:MRR:84.0,491.0] || -> cyclefreeP(cons(u,nil))*.
% 7.23/7.43 497[1:MRR:83.0,491.0] || -> totalorderP(cons(u,nil))*.
% 7.23/7.43 498[1:MRR:82.0,491.0] || -> strictorderP(cons(u,nil))*.
% 7.23/7.43 499[1:MRR:81.0,491.0] || -> totalorderedP(cons(u,nil))*.
% 7.23/7.43 500[1:MRR:80.0,491.0] || -> strictorderedP(cons(u,nil))*.
% 7.23/7.43 501[1:MRR:79.0,491.0] || -> duplicatefreeP(cons(u,nil))*.
% 7.23/7.43 502[1:MRR:78.0,491.0] || -> equalelemsP(cons(u,nil))*.
% 7.23/7.43 530[1:MRR:116.1,116.0,491.0] || -> equal(u,v) neq(u,v)*.
% 7.23/7.43 588[1:MRR:155.0,491.0] ssList(u) ssList(v) || memberP(v,w) -> memberP(app(u,v),w)*.
% 7.23/7.43 589[1:MRR:154.0,491.0] ssList(u) ssList(v) || memberP(u,w) -> memberP(app(u,v),w)*.
% 7.23/7.43 591[1:MRR:152.1,152.0,491.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 7.23/7.43 610[1:MRR:175.1,175.0,491.0] ssList(u) || memberP(cons(v,u),w)* -> equal(w,v) memberP(u,w).
% 7.23/7.43 626[1:MRR:100.1,491.0] ssList(u) || -> ssList(cons(v,u))*.
% 7.23/7.43 631[1:MRR:130.1,491.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 7.23/7.43 632[1:MRR:134.1,491.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 7.23/7.43 689[2:Spt:409.5] || -> equal(nil,sk2)**.
% 7.23/7.43 697[2:Rew:689.0,204.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 7.23/7.43 747[2:Rew:689.0,495.0] || memberP(sk2,u)* -> .
% 7.23/7.43 787[2:Obv:697.0] || -> equal(nil,sk1)**.
% 7.23/7.43 788[2:Rew:689.0,787.0] || -> equal(sk2,sk1)**.
% 7.23/7.43 878[2:Rew:788.0,747.0] || memberP(sk1,u)* -> .
% 7.23/7.43 884[2:UnC:878.0,8.0] || -> .
% 7.23/7.43 1001[2:Spt:884.0,409.5,689.0] || equal(nil,sk2)** -> .
% 7.23/7.43 1002[2:Spt:884.0,409.0,409.1,409.2,409.3,409.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 7.23/7.43 1023[3:Spt:202.0] || neq(sk2,nil)* -> .
% 7.23/7.43 1038[3:Res:530.1,1023.0] || -> equal(nil,sk2)**.
% 7.23/7.43 1039[3:MRR:1038.0,1001.0] || -> .
% 7.23/7.43 1040[3:Spt:1039.0,202.0,1023.0] || -> neq(sk2,nil)*.
% 7.23/7.43 1041[3:Spt:1039.0,202.1] || -> ssList(sk7)*.
% 7.23/7.43 1042[3:MRR:205.0,1040.0] || -> equal(app(sk7,cons(sk6,nil)),sk2)**.
% 7.23/7.43 1043[3:MRR:206.0,1040.0] || -> equal(app(cons(sk6,nil),sk7),sk1)**.
% 7.23/7.43 1194[1:EqR:631.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 7.23/7.43 1195[1:SSi:1194.0,626.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,502.0,501.0,500.0,499.0,498.0,497.0,496.1] || -> singletonP(cons(u,nil))*.
% 7.23/7.43 1264[3:SpR:632.1,1043.0] ssList(sk7) || -> equal(cons(sk6,sk7),sk1)**.
% 7.23/7.43 1270[3:SSi:1264.0,1041.0] || -> equal(cons(sk6,sk7),sk1)**.
% 7.23/7.43 1896[3:SpR:1042.0,588.3] ssList(sk7) ssList(cons(sk6,nil)) || memberP(cons(sk6,nil),u)* -> memberP(sk2,u).
% 7.23/7.43 1899[3:SSi:1896.1,1896.0,626.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,502.0,501.0,500.0,499.0,498.0,497.0,496.0,1195.0,1041.1] || memberP(cons(sk6,nil),u)* -> memberP(sk2,u).
% 7.23/7.43 1921[3:SpR:1042.0,589.3] ssList(sk7) ssList(cons(sk6,nil)) || memberP(sk7,u)* -> memberP(sk2,u).
% 7.23/7.43 1923[3:SSi:1921.1,1921.0,626.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,502.0,501.0,500.0,499.0,498.0,497.0,496.0,1195.0,1041.1] || memberP(sk7,u)* -> memberP(sk2,u).
% 7.23/7.43 1942[3:SpL:1270.0,610.1] ssList(sk7) || memberP(sk1,u) -> equal(u,sk6) memberP(sk7,u)*.
% 7.23/7.43 1945[3:SSi:1942.0,1041.0] || memberP(sk1,u) -> equal(u,sk6) memberP(sk7,u)*.
% 7.23/7.43 1964[3:Res:591.2,1899.0] ssList(nil) || equal(u,sk6) -> memberP(sk2,u)*.
% 7.23/7.43 1966[3:SSi:1964.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0] || equal(u,sk6) -> memberP(sk2,u)*.
% 7.23/7.43 6852[3:Res:1945.2,1923.0] || memberP(sk1,u) -> equal(u,sk6) memberP(sk2,u)*.
% 7.23/7.43 6855[3:MRR:6852.1,1966.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 7.23/7.43 6861[3:Res:6855.1,9.0] || memberP(sk1,sk5)* -> .
% 7.23/7.43 6863[3:MRR:6861.0,8.0] || -> .
% 7.23/7.43 6864[1:Spt:6863.0,86.0,86.2] ssList(u) || -> duplicatefreeP(u)*.
% 7.23/7.43 6877[1:MRR:193.1,6864.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 7.23/7.43 6954[2:Spt:394.0] || -> ssItem(u)*.
% 7.23/7.43 7089[2:MRR:100.1,6954.0] ssList(u) || -> ssList(cons(v,u))*.
% 7.23/7.43 7111[2:MRR:6877.1,6954.0] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(y,x)),u)* -> .
% 7.23/7.43 7145[2:MRR:171.2,6954.0] ssList(u) ssList(v) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 7.23/7.43 9499[2:SpR:7145.2,99.2] ssList(u) ssList(v) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 7.23/7.43 9542[2:Obv:9499.0] ssList(u) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 7.23/7.43 9543[2:SSi:9542.1,7089.1] ssList(u) ssList(v) || -> ssList(cons(w,app(u,v)))*.
% 7.23/7.43 10944[2:EqR:7111.4] ssList(app(app(u,cons(v,w)),cons(v,x))) ssList(u) ssList(w) ssList(x) || -> .
% 7.23/7.43 10972[2:SSi:10944.0,99.1,99.1,7089.2,7089.2] ssList(u) ssList(v) ssList(w) || -> .
% 7.23/7.43 10984[2:MRR:9543.2,10972.2] ssList(u) ssList(v) || -> .
% 7.23/7.43 10998[2:Con:10984.1] ssList(u) || -> .
% 7.23/7.43 10999[2:UnC:10998.0,2.0] || -> .
% 7.23/7.43 11026[2:Spt:10999.0,394.1] || -> duplicatefreeP(sk2)*.
% 7.23/7.43 11028[3:Spt:409.5] || -> equal(nil,sk2)**.
% 7.23/7.43 11145[3:Rew:11028.0,204.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 7.23/7.43 11201[3:Obv:11145.0] || -> equal(nil,sk1)**.
% 7.23/7.43 11202[3:Rew:11028.0,11201.0] || -> equal(sk2,sk1)**.
% 8.31/8.51 11208[3:Rew:11202.0,9.0] || memberP(sk1,sk5)* -> .
% 8.31/8.51 11328[3:MRR:11208.0,8.0] || -> .
% 8.31/8.51 11547[3:Spt:11328.0,409.5,11028.0] || equal(nil,sk2)** -> .
% 8.31/8.51 11548[3:Spt:11328.0,409.0,409.1,409.2,409.3,409.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 8.31/8.51 11589[4:Spt:202.0] || neq(sk2,nil)* -> .
% 8.31/8.51 11679[4:Res:448.2,11589.0] ssList(nil) || -> equal(nil,sk2)**.
% 8.31/8.51 11680[4:SSi:11679.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0] || -> equal(nil,sk2)**.
% 8.31/8.51 11681[4:MRR:11680.0,11547.0] || -> .
% 8.31/8.51 11682[4:Spt:11681.0,202.0,11589.0] || -> neq(sk2,nil)*.
% 8.31/8.51 11683[4:Spt:11681.0,202.1] || -> ssList(sk7)*.
% 8.31/8.51 11684[4:MRR:203.0,11682.0] || -> ssItem(sk6)*.
% 8.31/8.51 15039[0:SpR:171.3,99.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 8.31/8.51 15075[0:Obv:15039.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.31/8.51 15076[0:SSi:15075.2,100.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 8.31/8.51 17632[1:EqR:6877.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 8.31/8.51 17662[1:SSi:17632.0,99.2,99.2,100.2,100.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 8.31/8.51 17663[1:MRR:15076.3,17662.1] ssList(u) ssItem(v) ssList(w) || -> .
% 8.31/8.51 17666[1:Con:17663.2] ssList(u) ssItem(v) || -> .
% 8.31/8.51 17667[1:MRR:450.1,17666.0] ssItem(u) || -> .
% 8.31/8.51 17668[4:UnC:17667.0,11684.0] || -> .
% 8.31/8.51 % SZS output end Refutation
% 8.31/8.51 Formulae used in the proof : co1_2 co1_5 co1_6 co1_8 co1_9 co1_10 co1_11 co1_12 co1_13 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause85 clause86 clause100 clause102 clause116 clause120 clause138 clause140 clause141 clause157 clause161 clause177 clause179
% 8.31/8.51
%------------------------------------------------------------------------------