TSTP Solution File: SWW101+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 : Thu Jul 21 01:27:56 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 5 03:17:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 738 clauses, backtracked 221 clauses, performed 7 splits and kept 500 clauses.
% 0.19/0.51 SPASS allocated 98181 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.04 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 5, length 129 :
% 0.19/0.51 % SZS output start Refutation
% 0.19/0.51 1[0:Inp] || -> d(true__dfg)*.
% 0.19/0.51 2[0:Inp] || -> d(false__dfg)*.
% 0.19/0.51 4[0:Inp] || -> equal(false__dfg,false1)**.
% 0.19/0.51 5[0:Inp] || equal(false2,false1)** -> .
% 0.19/0.51 6[0:Inp] || equal(true__dfg,false__dfg)** -> .
% 0.19/0.51 7[0:Inp] || equal(true__dfg,err)** -> .
% 0.19/0.51 9[0:Inp] || -> equal(not1(false__dfg),true__dfg)**.
% 0.19/0.51 10[0:Inp] || -> equal(not1(true__dfg),false__dfg)**.
% 0.19/0.51 11[0:Inp] d(u) || -> SkP2(u)*.
% 0.19/0.51 13[0:Inp] || -> equal(lazy_impl(false__dfg,u),true__dfg)**.
% 0.19/0.51 15[0:Inp] || -> equal(phi(f7(skc1)),false2)**.
% 0.19/0.51 16[0:Inp] || equal(u,false__dfg) -> bool(u)*.
% 0.19/0.51 17[0:Inp] || equal(u,true__dfg) -> bool(u)*.
% 0.19/0.51 24[0:Inp] || -> SkP2(u) equal(phi(u),err)**.
% 0.19/0.51 25[0:Inp] || -> bool(u) equal(prop(u),false__dfg)**.
% 0.19/0.51 26[0:Inp] || -> equal(lazy_impl(true__dfg,u),phi(u))**.
% 0.19/0.51 28[0:Inp] || forallprefers(f7(u),f7(skc1))* -> .
% 0.19/0.51 34[0:Inp] SkP2(u) || -> equal(phi(u),u)**.
% 0.19/0.51 36[0:Inp] bool(u) || -> equal(prop(u),true__dfg)**.
% 0.19/0.51 37[0:Inp] || -> equal(lazy_impl(prop(u),u),f7(u))**.
% 0.19/0.51 38[0:Inp] || -> bool(u) equal(phi(u),not1(u))**.
% 0.19/0.51 47[0:Inp] bool(u) || -> equal(and1(false__dfg,u),false__dfg)**.
% 0.19/0.51 50[0:Inp] || -> equal(or1(u,v),phi(u))** bool(u).
% 0.19/0.51 52[0:Inp] bool(u) || -> equal(or1(false__dfg,u),u)**.
% 0.19/0.51 55[0:Inp] bool(u) || -> equal(u,false__dfg) equal(u,true__dfg)*.
% 0.19/0.51 59[0:Inp] || equal(u,false__dfg) equal(v,true__dfg) -> forallprefers(u,v)*.
% 0.19/0.51 86[0:Rew:4.0,2.0] || -> d(false1)*.
% 0.19/0.51 87[0:Rew:4.0,10.0] || -> equal(not1(true__dfg),false1)**.
% 0.19/0.51 88[0:Rew:4.0,9.0] || -> equal(not1(false1),true__dfg)**.
% 0.19/0.51 90[0:Rew:4.0,6.0] || equal(true__dfg,false1)** -> .
% 0.19/0.51 92[0:Rew:4.0,13.0] || -> equal(lazy_impl(false1,u),true__dfg)**.
% 0.19/0.51 93[0:Rew:4.0,25.1] || -> bool(u) equal(prop(u),false1)**.
% 0.19/0.51 94[0:Rew:4.0,16.0] || equal(u,false1) -> bool(u)*.
% 0.19/0.51 96[0:Rew:4.0,52.1] bool(u) || -> equal(or1(false1,u),u)**.
% 0.19/0.51 97[0:Rew:38.1,50.0] || -> bool(u) equal(or1(u,v),not1(u))**.
% 0.19/0.51 99[0:Rew:4.0,47.1] bool(u) || -> equal(and1(false1,u),false1)**.
% 0.19/0.51 105[0:Rew:4.0,55.1] bool(u) || -> equal(u,true__dfg)* equal(u,false1).
% 0.19/0.51 110[0:Rew:4.0,59.0] || equal(u,true__dfg) equal(v,false1) -> forallprefers(v,u)*.
% 0.19/0.51 121[0:Res:105.1,5.0] bool(false2) || -> equal(true__dfg,false2)**.
% 0.19/0.51 133[0:SpR:24.1,15.0] || -> SkP2(f7(skc1))* equal(err,false2).
% 0.19/0.51 135[1:Spt:133.1] || -> equal(err,false2)**.
% 0.19/0.51 138[1:Rew:135.0,7.0] || equal(true__dfg,false2)** -> .
% 0.19/0.51 154[0:SpR:36.1,37.0] bool(u) || -> equal(lazy_impl(true__dfg,u),f7(u))**.
% 0.19/0.51 155[0:SpR:93.1,37.0] || -> bool(u) equal(lazy_impl(false1,u),f7(u))**.
% 0.19/0.51 156[0:Rew:92.0,155.1] || -> bool(u) equal(f7(u),true__dfg)**.
% 0.19/0.51 157[0:Rew:26.0,154.1] bool(u) || -> equal(phi(u),f7(u))**.
% 0.19/0.51 158[0:SpR:156.1,15.0] || -> bool(skc1) equal(phi(true__dfg),false2)**.
% 0.19/0.51 166[0:SpR:34.1,15.0] SkP2(f7(skc1)) || -> equal(f7(skc1),false2)**.
% 0.19/0.51 169[0:SpR:34.1,158.1] SkP2(true__dfg) || -> bool(skc1)* equal(true__dfg,false2).
% 0.19/0.51 170[0:SSi:169.0,11.0,1.1] || -> bool(skc1)* equal(true__dfg,false2).
% 0.19/0.51 171[1:MRR:170.1,138.0] || -> bool(skc1)*.
% 0.19/0.51 176[0:SpR:38.1,15.0] || -> bool(f7(skc1)) equal(not1(f7(skc1)),false2)**.
% 0.19/0.51 186[0:SpR:156.1,176.1] || -> bool(skc1) bool(f7(skc1))* equal(not1(true__dfg),false2).
% 0.19/0.51 203[0:SpR:97.1,96.1] bool(u) || -> bool(false1) equal(not1(false1),u)*.
% 0.19/0.51 207[0:Rew:88.0,203.2] bool(u) || -> bool(false1)* equal(true__dfg,u)*.
% 0.19/0.51 213[2:Spt:207.0,207.2] bool(u) || -> equal(true__dfg,u)*.
% 0.19/0.51 215[2:EmS:213.0,171.0] || -> equal(true__dfg,skc1)**.
% 0.19/0.51 217[2:EmS:213.0,94.1] || equal(u,false1) -> equal(true__dfg,u)*.
% 0.19/0.51 221[2:Rew:215.0,90.0] || equal(skc1,false1)** -> .
% 0.19/0.51 243[2:Rew:215.0,217.1] || equal(u,false1) -> equal(skc1,u)*.
% 0.19/0.51 305[2:SpR:243.1,99.1] bool(u) || equal(and1(false1,u),false1)** -> equal(skc1,false1).
% 0.19/0.51 353[2:Rew:99.1,305.1] bool(u) || equal(false1,false1) -> equal(skc1,false1)**.
% 0.19/0.51 354[2:Obv:353.1] bool(u) || -> equal(skc1,false1)**.
% 0.19/0.51 355[2:MRR:354.1,221.0] bool(u) || -> .
% 0.19/0.51 356[2:UnC:355.0,171.0] || -> .
% 0.19/0.51 357[2:Spt:356.0,207.1] || -> bool(false1)*.
% 0.19/0.51 380[0:SpR:157.1,15.0] bool(f7(skc1)) || -> equal(f7(f7(skc1)),false2)**.
% 0.19/0.51 382[0:SpR:157.1,34.1] bool(u) SkP2(u) || -> equal(f7(u),u)**.
% 0.19/0.51 414[0:SoR:380.0,17.1] || equal(f7(skc1),true__dfg) -> equal(f7(f7(skc1)),false2)**.
% 0.19/0.51 417[1:EmS:105.0,171.0] || -> equal(true__dfg,skc1)** equal(skc1,false1).
% 0.19/0.51 420[3:Spt:417.0] || -> equal(true__dfg,skc1)**.
% 0.19/0.51 421[3:Rew:420.0,1.0] || -> d(skc1)*.
% 0.19/0.51 423[3:Rew:420.0,138.0] || equal(skc1,false2)** -> .
% 0.19/0.51 445[3:Rew:420.0,414.0] || equal(f7(skc1),skc1) -> equal(f7(f7(skc1)),false2)**.
% 0.19/0.51 595[0:SpR:382.2,15.0] bool(skc1) SkP2(skc1) || -> equal(phi(skc1),false2)**.
% 0.19/0.51 597[3:SpR:382.2,445.1] bool(skc1) SkP2(skc1) || equal(f7(skc1),skc1)** -> equal(f7(skc1),false2).
% 0.19/0.51 611[0:Rew:382.2,595.2,157.1,595.2] bool(skc1) SkP2(skc1) || -> equal(skc1,false2)**.
% 0.19/0.51 653[3:Rew:382.2,597.3,382.2,597.2] bool(skc1) SkP2(skc1) || equal(skc1,skc1)* -> equal(skc1,false2).
% 0.19/0.51 654[3:Obv:653.2] bool(skc1) SkP2(skc1) || -> equal(skc1,false2)**.
% 0.19/0.51 655[3:SSi:654.1,654.0,11.0,171.0,421.0,171.0,421.1] || -> equal(skc1,false2)**.
% 0.19/0.51 656[3:MRR:655.0,423.0] || -> .
% 0.19/0.51 658[3:Spt:656.0,417.0,420.0] || equal(true__dfg,skc1)** -> .
% 0.19/0.51 659[3:Spt:656.0,417.1] || -> equal(skc1,false1)**.
% 0.19/0.51 660[3:Rew:659.0,15.0] || -> equal(phi(f7(false1)),false2)**.
% 0.19/0.51 709[3:SpR:382.2,660.0] bool(false1) SkP2(false1) || -> equal(phi(false1),false2)**.
% 0.19/0.51 712[3:Rew:382.2,709.2,157.1,709.2] bool(false1) SkP2(false1) || -> equal(false2,false1)**.
% 0.19/0.51 713[3:SSi:712.1,712.0,11.0,86.0,357.0,86.0,357.1] || -> equal(false2,false1)**.
% 0.19/0.51 714[3:MRR:713.0,5.0] || -> .
% 0.19/0.51 715[1:Spt:714.0,133.1,135.0] || equal(err,false2)** -> .
% 0.19/0.51 716[1:Spt:714.0,133.0] || -> SkP2(f7(skc1))*.
% 0.19/0.51 730[1:MRR:166.0,716.0] || -> equal(f7(skc1),false2)**.
% 0.19/0.51 733[1:Rew:730.0,28.0] || forallprefers(f7(u),false2)* -> .
% 0.19/0.51 735[1:Rew:730.0,176.0] || -> bool(false2) equal(not1(f7(skc1)),false2)**.
% 0.19/0.51 736[1:Rew:730.0,735.1] || -> bool(false2) equal(not1(false2),false2)**.
% 0.19/0.51 738[0:Rew:87.0,186.2] || -> bool(skc1) bool(f7(skc1))* equal(false2,false1).
% 0.19/0.51 739[1:Rew:730.0,738.1] || -> bool(skc1)* bool(false2) equal(false2,false1).
% 0.19/0.51 740[1:MRR:739.2,94.0] || -> bool(skc1)* bool(false2).
% 0.19/0.51 760[2:Spt:740.0] || -> bool(skc1)*.
% 0.19/0.51 761[2:MRR:611.0,760.0] SkP2(skc1) || -> equal(skc1,false2)**.
% 0.19/0.51 771[3:Spt:736.0] || -> bool(false2)*.
% 0.19/0.51 772[3:MRR:121.0,771.0] || -> equal(true__dfg,false2)**.
% 0.19/0.51 786[3:Rew:772.0,110.0] || equal(u,false2) equal(v,false1) -> forallprefers(v,u)*.
% 0.19/0.51 821[0:SpR:24.1,157.1] bool(u) || -> SkP2(u) equal(f7(u),err)**.
% 0.19/0.51 893[3:Res:786.2,733.0] || equal(false2,false2) equal(f7(u),false1)** -> .
% 0.19/0.51 896[3:Obv:893.0] || equal(f7(u),false1)** -> .
% 0.19/0.51 900[3:SpL:382.2,896.0] bool(u) SkP2(u) || equal(u,false1)* -> .
% 0.19/0.51 902[3:MRR:900.0,94.1] SkP2(u) || equal(u,false1)* -> .
% 0.19/0.51 906[3:EmS:902.0,11.1] d(u) || equal(u,false1)* -> .
% 0.19/0.51 913[3:EmS:906.0,86.0] || equal(false1,false1)* -> .
% 0.19/0.51 914[3:Obv:913.0] || -> .
% 0.19/0.51 915[3:Spt:914.0,736.0,771.0] || bool(false2)* -> .
% 0.19/0.51 916[3:Spt:914.0,736.1] || -> equal(not1(false2),false2)**.
% 0.19/0.51 924[1:SpR:730.0,821.2] bool(skc1) || -> SkP2(skc1)* equal(err,false2).
% 0.19/0.51 927[2:SSi:924.0,760.0] || -> SkP2(skc1)* equal(err,false2).
% 0.19/0.51 928[2:MRR:927.1,715.0] || -> SkP2(skc1)*.
% 0.19/0.51 929[2:MRR:761.0,928.0] || -> equal(skc1,false2)**.
% 0.19/0.51 930[2:Rew:929.0,760.0] || -> bool(false2)*.
% 0.19/0.51 933[3:MRR:930.0,915.0] || -> .
% 0.19/0.51 934[2:Spt:933.0,740.0,760.0] || bool(skc1)* -> .
% 0.19/0.51 935[2:Spt:933.0,740.1] || -> bool(false2)*.
% 0.19/0.51 936[2:MRR:121.0,935.0] || -> equal(true__dfg,false2)**.
% 0.19/0.51 951[2:Rew:936.0,110.0] || equal(u,false2) equal(v,false1) -> forallprefers(v,u)*.
% 0.19/0.51 1038[2:Res:951.2,733.0] || equal(false2,false2) equal(f7(u),false1)** -> .
% 0.19/0.51 1041[2:Obv:1038.0] || equal(f7(u),false1)** -> .
% 0.19/0.51 1045[2:SpL:382.2,1041.0] bool(u) SkP2(u) || equal(u,false1)* -> .
% 0.19/0.51 1048[2:MRR:1045.0,94.1] SkP2(u) || equal(u,false1)* -> .
% 0.19/0.51 1052[2:EmS:1048.0,11.1] d(u) || equal(u,false1)* -> .
% 0.19/0.51 1059[2:EmS:1052.0,86.0] || equal(false1,false1)* -> .
% 0.19/0.51 1060[2:Obv:1059.0] || -> .
% 0.19/0.51 % SZS output end Refutation
% 0.19/0.52 Formulae used in the proof : false_true_err_in_d def_false1 false1_false2 distinct_false_true_err not1_axiom2 not1_axiom3 def_phi lazy_impl_axiom2 def_false2 def_bool prop_false lazy_impl_axiom3 prop_true def_f7 not1_axiom1 and1_axiom3 or1_axiom1 or1_axiom4 def_forallprefers
% 0.19/0.52
%------------------------------------------------------------------------------