TSTP Solution File: SWC379-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC379-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 22:03:41 EDT 2022
% Result : Unsatisfiable 2.05s 2.28s
% Output : Refutation 2.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC379-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 11 18:56:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.05/2.28
% 2.05/2.28 SPASS V 3.9
% 2.05/2.28 SPASS beiseite: Proof found.
% 2.05/2.28 % SZS status Theorem
% 2.05/2.28 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.05/2.28 SPASS derived 4319 clauses, backtracked 1387 clauses, performed 37 splits and kept 3715 clauses.
% 2.05/2.28 SPASS allocated 81699 KBytes.
% 2.05/2.28 SPASS spent 0:00:01.93 on the problem.
% 2.05/2.28 0:00:00.04 for the input.
% 2.05/2.28 0:00:00.00 for the FLOTTER CNF translation.
% 2.05/2.28 0:00:00.05 for inferences.
% 2.05/2.28 0:00:00.03 for the backtracking.
% 2.05/2.28 0:00:01.66 for the reduction.
% 2.05/2.28
% 2.05/2.28
% 2.05/2.28 Here is a proof with depth 2, length 117 :
% 2.05/2.28 % SZS output start Refutation
% 2.05/2.28 2[0:Inp] || -> ssList(sk2)*.
% 2.05/2.28 5[0:Inp] || -> equal(sk4,sk2)**.
% 2.05/2.28 6[0:Inp] || -> equal(sk3,sk1)**.
% 2.05/2.28 7[0:Inp] ssItem(u) || memberP(sk4,u)* -> memberP(sk3,u) ssItem(sk5(u)).
% 2.05/2.28 8[0:Inp] ssItem(u) || memberP(sk4,u) -> memberP(sk3,u) memberP(sk4,sk5(u))*.
% 2.05/2.28 9[0:Inp] ssItem(u) || memberP(sk4,u) -> memberP(sk3,u) leq(sk5(u),u)*.
% 2.05/2.28 10[0:Inp] ssItem(u) || equal(sk5(u),u) memberP(sk4,u)* -> memberP(sk3,u).
% 2.05/2.28 11[0:Inp] ssItem(u) || memberP(sk3,u) -> memberP(sk4,u)*.
% 2.05/2.28 12[0:Inp] ssItem(u) ssItem(v) || memberP(sk3,u) memberP(sk4,v) leq(v,u)* -> equal(u,v).
% 2.05/2.28 13[0:Inp] || -> ssItem(sk6)*.
% 2.05/2.28 14[0:Inp] || -> memberP(sk1,sk6) memberP(sk2,sk6)*.
% 2.05/2.28 15[0:Inp] ssItem(u) || memberP(sk2,u) leq(u,sk6)* -> memberP(sk1,sk6) equal(sk6,u).
% 2.05/2.28 16[0:Inp] || memberP(sk2,sk6)* memberP(sk1,sk6) -> ssItem(sk7).
% 2.05/2.28 17[0:Inp] || memberP(sk2,sk6) memberP(sk1,sk6) -> memberP(sk2,sk7)*.
% 2.05/2.28 18[0:Inp] || memberP(sk2,sk6) memberP(sk1,sk6) -> leq(sk7,sk6)*.
% 2.05/2.28 19[0:Inp] || equal(sk7,sk6) memberP(sk2,sk6)* memberP(sk1,sk6) -> .
% 2.05/2.28 90[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.05/2.28 91[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 2.05/2.28 104[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 2.05/2.28 105[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 2.05/2.28 176[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 2.05/2.28 196[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).
% 2.05/2.28 198[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)* -> .
% 2.05/2.28 207[0:Rew:5.0,11.2,6.0,11.1] ssItem(u) || memberP(sk1,u) -> memberP(sk2,u)*.
% 2.05/2.28 208[0:Rew:6.0,7.2,5.0,7.1] ssItem(u) || memberP(sk2,u)* -> ssItem(sk5(u)) memberP(sk1,u).
% 2.05/2.28 209[0:Rew:6.0,9.2,5.0,9.1] ssItem(u) || memberP(sk2,u) -> memberP(sk1,u) leq(sk5(u),u)*.
% 2.05/2.28 210[0:Rew:5.0,8.3,6.0,8.2,5.0,8.1] ssItem(u) || memberP(sk2,u) -> memberP(sk1,u) memberP(sk2,sk5(u))*.
% 2.05/2.28 211[0:Rew:6.0,10.3,5.0,10.2] ssItem(u) || memberP(sk2,u)* equal(sk5(u),u) -> memberP(sk1,u).
% 2.05/2.28 212[0:Rew:5.0,12.3,6.0,12.2] ssItem(u) ssItem(v) || leq(u,v)* memberP(sk2,u) memberP(sk1,v) -> equal(v,u).
% 2.05/2.28 220[0:Res:13.0,212.0] ssItem(u) || memberP(sk1,sk6) memberP(sk2,u) leq(u,sk6)* -> equal(sk6,u).
% 2.05/2.28 231[0:Res:13.0,211.0] || equal(sk5(sk6),sk6) memberP(sk2,sk6)* -> memberP(sk1,sk6).
% 2.05/2.28 233[0:Res:13.0,210.0] || memberP(sk2,sk6) -> memberP(sk1,sk6) memberP(sk2,sk5(sk6))*.
% 2.05/2.28 234[0:Res:13.0,209.0] || memberP(sk2,sk6) -> memberP(sk1,sk6) leq(sk5(sk6),sk6)*.
% 2.05/2.28 240[0:Res:13.0,208.0] || memberP(sk2,sk6)* -> memberP(sk1,sk6) ssItem(sk5(sk6)).
% 2.05/2.28 251[0:Res:13.0,207.0] || memberP(sk1,sk6) -> memberP(sk2,sk6)*.
% 2.05/2.28 261[0:Res:13.0,90.0] || memberP(nil,sk6)* -> .
% 2.05/2.28 408[0:Res:2.0,91.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 2.05/2.28 423[0:Res:2.0,196.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 2.05/2.28 464[0:Res:2.0,105.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 2.05/2.28 498[0:MRR:251.0,14.0] || -> memberP(sk2,sk6)*.
% 2.05/2.28 499[0:MRR:16.0,498.0] || memberP(sk1,sk6)* -> ssItem(sk7).
% 2.05/2.28 500[0:MRR:18.0,498.0] || memberP(sk1,sk6) -> leq(sk7,sk6)*.
% 2.05/2.28 501[0:MRR:17.0,498.0] || memberP(sk1,sk6) -> memberP(sk2,sk7)*.
% 2.05/2.28 502[0:MRR:19.1,498.0] || memberP(sk1,sk6)* equal(sk7,sk6) -> .
% 2.05/2.28 503[0:MRR:240.0,498.0] || -> ssItem(sk5(sk6)) memberP(sk1,sk6)*.
% 2.05/2.28 504[0:MRR:233.0,498.0] || -> memberP(sk1,sk6) memberP(sk2,sk5(sk6))*.
% 2.05/2.28 505[0:MRR:234.0,498.0] || -> memberP(sk1,sk6) leq(sk5(sk6),sk6)*.
% 2.05/2.28 506[0:MRR:231.1,498.0] || equal(sk5(sk6),sk6) -> memberP(sk1,sk6)*.
% 2.05/2.28 509[0:MRR:220.1,15.3] ssItem(u) || leq(u,sk6)* memberP(sk2,u) -> equal(sk6,u).
% 2.05/2.28 511[1:Spt:91.1] || -> ssItem(u)*.
% 2.05/2.28 515[1:MRR:90.0,511.0] || memberP(nil,u)* -> .
% 2.05/2.28 562[1:MRR:509.0,511.0] || leq(u,sk6)* memberP(sk2,u) -> equal(sk6,u).
% 2.05/2.28 716[2:Spt:423.5] || -> equal(nil,sk2)**.
% 2.05/2.28 770[2:Rew:716.0,515.0] || memberP(sk2,u)* -> .
% 2.05/2.28 793[2:UnC:770.0,498.0] || -> .
% 2.05/2.28 868[2:Spt:793.0,423.5,716.0] || equal(nil,sk2)** -> .
% 2.05/2.28 869[2:Spt:793.0,423.0,423.1,423.2,423.3,423.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.05/2.28 883[3:Spt:501.0] || memberP(sk1,sk6)* -> .
% 2.05/2.28 884[3:MRR:505.0,883.0] || -> leq(sk5(sk6),sk6)*.
% 2.05/2.28 885[3:MRR:504.0,883.0] || -> memberP(sk2,sk5(sk6))*.
% 2.05/2.28 886[3:MRR:506.1,883.0] || equal(sk5(sk6),sk6)** -> .
% 2.05/2.28 1017[3:Res:884.0,562.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.05/2.28 1018[3:MRR:1017.0,1017.1,885.0,886.0] || -> .
% 2.05/2.28 1019[3:Spt:1018.0,501.0,883.0] || -> memberP(sk1,sk6)*.
% 2.05/2.28 1020[3:Spt:1018.0,501.1] || -> memberP(sk2,sk7)*.
% 2.05/2.28 1021[3:MRR:500.0,1019.0] || -> leq(sk7,sk6)*.
% 2.05/2.28 1022[3:MRR:502.0,1019.0] || equal(sk7,sk6)** -> .
% 2.05/2.28 1052[3:Res:1021.0,562.0] || memberP(sk2,sk7)* -> equal(sk7,sk6).
% 2.05/2.28 1053[3:MRR:1052.0,1020.0] || -> equal(sk7,sk6)**.
% 2.05/2.28 1054[3:MRR:1053.0,1022.0] || -> .
% 2.05/2.28 1055[1:Spt:1054.0,91.0,91.2] ssList(u) || -> duplicatefreeP(u)*.
% 2.05/2.28 1060[1:MRR:198.1,1055.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 2.05/2.28 1073[2:Spt:408.0] || -> ssItem(u)*.
% 2.05/2.28 1084[2:MRR:90.0,1073.0] || memberP(nil,u)* -> .
% 2.05/2.28 1133[2:MRR:509.0,1073.0] || leq(u,sk6)* memberP(sk2,u) -> equal(sk6,u).
% 2.05/2.28 1275[3:Spt:423.5] || -> equal(nil,sk2)**.
% 2.05/2.28 1338[3:Rew:1275.0,1084.0] || memberP(sk2,u)* -> .
% 2.05/2.28 1351[3:UnC:1338.0,498.0] || -> .
% 2.05/2.28 1428[3:Spt:1351.0,423.5,1275.0] || equal(nil,sk2)** -> .
% 2.05/2.28 1429[3:Spt:1351.0,423.0,423.1,423.2,423.3,423.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.05/2.28 1445[4:Spt:500.0] || memberP(sk1,sk6)* -> .
% 2.05/2.28 1446[4:MRR:504.0,1445.0] || -> memberP(sk2,sk5(sk6))*.
% 2.05/2.28 1447[4:MRR:505.0,1445.0] || -> leq(sk5(sk6),sk6)*.
% 2.05/2.28 1448[4:MRR:506.1,1445.0] || equal(sk5(sk6),sk6)** -> .
% 2.05/2.28 1576[4:Res:1447.0,1133.0] || memberP(sk2,sk5(sk6))* -> equal(sk5(sk6),sk6).
% 2.05/2.28 1577[4:MRR:1576.0,1576.1,1446.0,1448.0] || -> .
% 2.05/2.28 1578[4:Spt:1577.0,500.0,1445.0] || -> memberP(sk1,sk6)*.
% 2.05/2.28 1579[4:Spt:1577.0,500.1] || -> leq(sk7,sk6)*.
% 2.05/2.28 1580[4:MRR:501.0,1578.0] || -> memberP(sk2,sk7)*.
% 2.05/2.28 1581[4:MRR:502.0,1578.0] || equal(sk7,sk6)** -> .
% 2.05/2.28 1601[4:Res:1579.0,1133.0] || memberP(sk2,sk7)* -> equal(sk7,sk6).
% 2.05/2.28 1602[4:MRR:1601.0,1601.1,1580.0,1581.0] || -> .
% 2.05/2.28 1603[2:Spt:1602.0,408.1] || -> duplicatefreeP(sk2)*.
% 2.05/2.28 1605[3:Spt:423.5] || -> equal(nil,sk2)**.
% 2.05/2.28 1668[3:Rew:1605.0,261.0] || memberP(sk2,sk6)* -> .
% 2.05/2.28 1699[3:MRR:1668.0,498.0] || -> .
% 2.05/2.28 1778[3:Spt:1699.0,423.5,1605.0] || equal(nil,sk2)** -> .
% 2.05/2.28 1779[3:Spt:1699.0,423.0,423.1,423.2,423.3,423.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.05/2.28 1796[4:Spt:503.1] || -> memberP(sk1,sk6)*.
% 2.05/2.28 1797[4:MRR:499.0,1796.0] || -> ssItem(sk7)*.
% 2.05/2.28 1798[4:MRR:501.0,1796.0] || -> memberP(sk2,sk7)*.
% 2.05/2.28 1799[4:MRR:500.0,1796.0] || -> leq(sk7,sk6)*.
% 2.05/2.28 1800[4:MRR:502.0,1796.0] || equal(sk7,sk6)** -> .
% 2.05/2.28 5150[0:SpR:176.3,104.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 2.05/2.28 5197[0:Obv:5150.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 2.05/2.28 5198[0:SSi:5197.2,105.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 2.05/2.28 5574[4:Res:1799.0,212.2] ssItem(sk7) ssItem(sk6) || memberP(sk2,sk7)* memberP(sk1,sk6) -> equal(sk7,sk6).
% 2.05/2.28 5583[4:SSi:5574.1,5574.0,13.0,1797.0] || memberP(sk2,sk7)* memberP(sk1,sk6) -> equal(sk7,sk6).
% 2.05/2.28 5584[4:MRR:5583.0,5583.1,5583.2,1798.0,1796.0,1800.0] || -> .
% 2.05/2.28 5593[4:Spt:5584.0,503.1,1796.0] || memberP(sk1,sk6)* -> .
% 2.05/2.28 5594[4:Spt:5584.0,503.0] || -> ssItem(sk5(sk6))*.
% 2.05/2.28 6675[1:EqR:1060.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 2.05/2.28 6702[1:SSi:6675.0,104.2,104.2,105.2,105.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 2.05/2.28 6703[1:MRR:5198.3,6702.1] ssList(u) ssItem(v) ssList(w) || -> .
% 2.05/2.28 6706[1:Con:6703.2] ssList(u) ssItem(v) || -> .
% 2.05/2.28 6707[1:MRR:464.1,6706.0] ssItem(u) || -> .
% 2.05/2.28 6708[4:UnC:6707.0,5594.0] || -> .
% 2.05/2.28 % SZS output end Refutation
% 2.14/2.39 Formulae used in the proof : co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_12 co1_13 co1_14 co1_15 co1_16 co1_17 co1_18 co1_19 clause71 clause72 clause85 clause86 clause157 clause177 clause179
% 2.14/2.39
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