TSTP Solution File: SWW102+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWW102+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 0.17s 0.50s
% Output   : Refutation 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SWW102+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun Jun  5 10:27:23 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.50  
% 0.17/0.50  SPASS V 3.9 
% 0.17/0.50  SPASS beiseite: Proof found.
% 0.17/0.50  % SZS status Theorem
% 0.17/0.50  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.17/0.50  SPASS derived 789 clauses, backtracked 219 clauses, performed 8 splits and kept 586 clauses.
% 0.17/0.50  SPASS allocated 98197 KBytes.
% 0.17/0.50  SPASS spent	0:00:00.17 on the problem.
% 0.17/0.50  		0:00:00.04 for the input.
% 0.17/0.50  		0:00:00.04 for the FLOTTER CNF translation.
% 0.17/0.50  		0:00:00.01 for inferences.
% 0.17/0.50  		0:00:00.00 for the backtracking.
% 0.17/0.50  		0:00:00.06 for the reduction.
% 0.17/0.50  
% 0.17/0.50  
% 0.17/0.50  Here is a proof with depth 5, length 158 :
% 0.17/0.50  % SZS output start Refutation
% 0.17/0.50  1[0:Inp] ||  -> d(true__dfg)*.
% 0.17/0.50  2[0:Inp] ||  -> d(false__dfg)*.
% 0.17/0.50  4[0:Inp] ||  -> equal(false__dfg,false1)**.
% 0.17/0.50  5[0:Inp] || equal(true__dfg,false__dfg)** -> .
% 0.17/0.50  6[0:Inp] || equal(true__dfg,err)** -> .
% 0.17/0.50  7[0:Inp] || equal(false__dfg,err)** -> .
% 0.17/0.50  8[0:Inp] ||  -> equal(not1(false__dfg),true__dfg)**.
% 0.17/0.50  9[0:Inp] ||  -> equal(not1(true__dfg),false__dfg)**.
% 0.17/0.50  10[0:Inp] d(u) ||  -> SkP2(u)*.
% 0.17/0.50  11[0:Inp] SkP2(u) ||  -> d(u)*.
% 0.17/0.50  12[0:Inp] ||  -> equal(lazy_impl(false__dfg,u),true__dfg)**.
% 0.17/0.50  13[0:Inp] ||  -> equal(lazy_and1(false__dfg,u),false__dfg)**.
% 0.17/0.50  14[0:Inp] ||  -> equal(phi(f7(skc3)),false2)**.
% 0.17/0.50  15[0:Inp] || equal(not1(skc2),not2(skc2))** -> .
% 0.17/0.50  16[0:Inp] || equal(u,false__dfg) -> bool(u)*.
% 0.17/0.50  17[0:Inp] || equal(u,true__dfg) -> bool(u)*.
% 0.17/0.50  24[0:Inp] ||  -> SkP2(u) equal(phi(u),err)**.
% 0.17/0.50  25[0:Inp] ||  -> bool(u) equal(prop(u),false__dfg)**.
% 0.17/0.50  26[0:Inp] ||  -> equal(lazy_impl(true__dfg,u),phi(u))**.
% 0.17/0.50  28[0:Inp] || forallprefers(f7(u),f7(skc3))* -> .
% 0.17/0.50  29[0:Inp] ||  -> equal(impl(u,false2),not2(u))**.
% 0.17/0.50  34[0:Inp] SkP2(u) ||  -> equal(phi(u),u)**.
% 0.17/0.50  36[0:Inp] bool(u) ||  -> equal(prop(u),true__dfg)**.
% 0.17/0.50  37[0:Inp] ||  -> equal(lazy_impl(prop(u),u),f7(u))**.
% 0.17/0.50  38[0:Inp] ||  -> bool(u) equal(phi(u),not1(u))**.
% 0.17/0.50  39[0:Inp] d(u) ||  -> d(v) forallprefers(v,u)*.
% 0.17/0.50  42[0:Inp] ||  -> equal(impl(u,v),phi(u))** bool(u).
% 0.17/0.50  43[0:Inp] bool(u) ||  -> equal(impl(false__dfg,u),true__dfg)**.
% 0.17/0.50  44[0:Inp] bool(u) ||  -> equal(impl(true__dfg,u),u)**.
% 0.17/0.50  49[0:Inp] ||  -> equal(lazy_and1(u,v),phi(u))** bool(u).
% 0.17/0.50  55[0:Inp] bool(u) ||  -> equal(u,false__dfg) equal(u,true__dfg)*.
% 0.17/0.50  59[0:Inp] || equal(u,false__dfg) equal(v,true__dfg) -> forallprefers(u,v)*.
% 0.17/0.50  86[0:Rew:4.0,2.0] ||  -> d(false1)*.
% 0.17/0.50  87[0:Rew:4.0,9.0] ||  -> equal(not1(true__dfg),false1)**.
% 0.17/0.50  88[0:Rew:4.0,8.0] ||  -> equal(not1(false1),true__dfg)**.
% 0.17/0.50  89[0:Rew:4.0,7.0] || equal(false1,err)** -> .
% 0.17/0.50  90[0:Rew:4.0,5.0] || equal(true__dfg,false1)** -> .
% 0.17/0.50  91[0:Rew:4.0,13.0] ||  -> equal(lazy_and1(false1,u),false1)**.
% 0.17/0.50  92[0:Rew:4.0,12.0] ||  -> equal(lazy_impl(false1,u),true__dfg)**.
% 0.17/0.50  93[0:Rew:4.0,25.1] ||  -> bool(u) equal(prop(u),false1)**.
% 0.17/0.50  94[0:Rew:4.0,16.0] || equal(u,false1) -> bool(u)*.
% 0.17/0.50  98[0:Rew:38.1,49.0] ||  -> bool(u) equal(lazy_and1(u,v),not1(u))**.
% 0.17/0.50  102[0:Rew:4.0,43.1] bool(u) ||  -> equal(impl(false1,u),true__dfg)**.
% 0.17/0.50  103[0:Rew:38.1,42.0] ||  -> bool(u) equal(impl(u,v),not1(u))**.
% 0.17/0.50  105[0:Rew:4.0,55.1] bool(u) ||  -> equal(u,true__dfg)* equal(u,false1).
% 0.17/0.50  110[0:Rew:4.0,59.0] || equal(u,true__dfg) equal(v,false1) -> forallprefers(v,u)*.
% 0.17/0.50  128[0:SpR:24.1,14.0] ||  -> SkP2(f7(skc3))* equal(false2,err).
% 0.17/0.50  130[1:Spt:128.1] ||  -> equal(false2,err)**.
% 0.17/0.50  131[1:Rew:130.0,14.0] ||  -> equal(phi(f7(skc3)),err)**.
% 0.17/0.50  132[1:Rew:130.0,29.0] ||  -> equal(impl(u,err),not2(u))**.
% 0.17/0.50  141[0:SpR:36.1,37.0] bool(u) ||  -> equal(lazy_impl(true__dfg,u),f7(u))**.
% 0.17/0.50  142[0:SpR:93.1,37.0] ||  -> bool(u) equal(lazy_impl(false1,u),f7(u))**.
% 0.17/0.50  143[0:Rew:92.0,142.1] ||  -> bool(u) equal(f7(u),true__dfg)**.
% 0.17/0.50  144[0:Rew:26.0,141.1] bool(u) ||  -> equal(phi(u),f7(u))**.
% 0.17/0.50  148[1:SpR:143.1,131.0] ||  -> bool(skc3) equal(phi(true__dfg),err)**.
% 0.17/0.50  153[1:SpR:148.1,34.1] SkP2(true__dfg) ||  -> bool(skc3)* equal(true__dfg,err).
% 0.17/0.50  155[1:SSi:153.0,10.0,1.1] ||  -> bool(skc3)* equal(true__dfg,err).
% 0.17/0.50  156[1:MRR:155.1,6.0] ||  -> bool(skc3)*.
% 0.17/0.50  189[0:SpR:144.1,24.1] bool(u) ||  -> SkP2(u) equal(f7(u),err)**.
% 0.17/0.50  190[0:SpR:144.1,34.1] bool(u) SkP2(u) ||  -> equal(f7(u),u)**.
% 0.17/0.50  193[1:SpR:144.1,131.0] bool(f7(skc3)) ||  -> equal(f7(f7(skc3)),err)**.
% 0.17/0.50  215[0:SpR:98.1,91.0] ||  -> bool(false1) equal(not1(false1),false1)**.
% 0.17/0.50  218[0:Rew:88.0,215.1] ||  -> bool(false1)* equal(true__dfg,false1).
% 0.17/0.50  219[0:MRR:218.1,90.0] ||  -> bool(false1)*.
% 0.17/0.50  227[1:SpR:103.1,132.0] ||  -> bool(u) equal(not1(u),not2(u))**.
% 0.17/0.50  258[1:SpL:227.1,15.0] || equal(not2(skc2),not2(skc2))* -> bool(skc2).
% 0.17/0.50  259[1:Obv:258.0] ||  -> bool(skc2)*.
% 0.17/0.50  264[0:Res:39.2,28.0] d(f7(skc3)) ||  -> d(f7(u))*.
% 0.17/0.50  266[0:SoR:264.0,11.1] SkP2(f7(skc3)) ||  -> d(f7(u))*.
% 0.17/0.50  285[1:EmS:105.0,259.0] ||  -> equal(true__dfg,skc2)** equal(skc2,false1).
% 0.17/0.50  288[1:EmS:105.0,156.0] ||  -> equal(true__dfg,skc3)** equal(skc3,false1).
% 0.17/0.50  292[2:Spt:285.0] ||  -> equal(true__dfg,skc2)**.
% 0.17/0.50  293[2:Rew:292.0,1.0] ||  -> d(skc2)*.
% 0.17/0.50  296[2:Rew:292.0,6.0] || equal(skc2,err)** -> .
% 0.17/0.50  302[2:Rew:292.0,17.0] || equal(u,skc2) -> bool(u)*.
% 0.17/0.50  322[2:Rew:292.0,288.0] ||  -> equal(skc3,skc2)** equal(skc3,false1).
% 0.17/0.50  335[3:Spt:322.0] ||  -> equal(skc3,skc2)**.
% 0.17/0.50  342[3:Rew:335.0,193.1] bool(f7(skc3)) ||  -> equal(f7(f7(skc2)),err)**.
% 0.17/0.50  396[3:SoR:342.0,302.1] || equal(f7(skc3),skc2) -> equal(f7(f7(skc2)),err)**.
% 0.17/0.50  399[3:Rew:335.0,396.0] || equal(f7(skc2),skc2) -> equal(f7(f7(skc2)),err)**.
% 0.17/0.50  508[3:SpR:190.2,399.1] bool(skc2) SkP2(skc2) || equal(f7(skc2),skc2)** -> equal(f7(skc2),err).
% 0.17/0.50  575[3:Rew:190.2,508.3,190.2,508.2] bool(skc2) SkP2(skc2) || equal(skc2,skc2)* -> equal(skc2,err).
% 0.17/0.50  576[3:Obv:575.2] bool(skc2) SkP2(skc2) ||  -> equal(skc2,err)**.
% 0.17/0.50  577[3:SSi:576.1,576.0,10.0,259.0,293.0,259.0,293.1] ||  -> equal(skc2,err)**.
% 0.17/0.50  578[3:MRR:577.0,296.0] ||  -> .
% 0.17/0.50  580[3:Spt:578.0,322.0,335.0] || equal(skc3,skc2)** -> .
% 0.17/0.50  581[3:Spt:578.0,322.1] ||  -> equal(skc3,false1)**.
% 0.17/0.50  584[3:Rew:581.0,131.0] ||  -> equal(phi(f7(false1)),err)**.
% 0.17/0.50  600[3:SpR:190.2,584.0] bool(false1) SkP2(false1) ||  -> equal(phi(false1),err)**.
% 0.17/0.50  604[3:Rew:190.2,600.2,144.1,600.2] bool(false1) SkP2(false1) ||  -> equal(false1,err)**.
% 0.17/0.50  605[3:SSi:604.1,604.0,10.0,86.0,219.0,86.0,219.1] ||  -> equal(false1,err)**.
% 0.17/0.50  606[3:MRR:605.0,89.0] ||  -> .
% 0.17/0.50  607[2:Spt:606.0,285.0,292.0] || equal(true__dfg,skc2)** -> .
% 0.17/0.50  608[2:Spt:606.0,285.1] ||  -> equal(skc2,false1)**.
% 0.17/0.50  627[1:SpR:190.2,131.0] bool(skc3) SkP2(skc3) ||  -> equal(phi(skc3),err)**.
% 0.17/0.50  630[1:Rew:190.2,627.2,144.1,627.2] bool(skc3) SkP2(skc3) ||  -> equal(skc3,err)**.
% 0.17/0.50  631[1:SSi:630.0,156.0] SkP2(skc3) ||  -> equal(skc3,err)**.
% 0.17/0.50  644[3:Spt:288.0] ||  -> equal(true__dfg,skc3)**.
% 0.17/0.50  646[3:Rew:644.0,1.0] ||  -> d(skc3)*.
% 0.17/0.50  648[3:Rew:644.0,6.0] || equal(skc3,err)** -> .
% 0.17/0.50  671[3:MRR:631.1,648.0] SkP2(skc3) ||  -> .
% 0.17/0.50  674[3:SoR:671.0,10.1] d(skc3) ||  -> .
% 0.17/0.50  675[3:SSi:674.0,156.0,646.0] ||  -> .
% 0.17/0.50  676[3:Spt:675.0,288.0,644.0] || equal(true__dfg,skc3)** -> .
% 0.17/0.50  677[3:Spt:675.0,288.1] ||  -> equal(skc3,false1)**.
% 0.17/0.50  678[3:Rew:677.0,131.0] ||  -> equal(phi(f7(false1)),err)**.
% 0.17/0.50  711[3:SpR:190.2,678.0] bool(false1) SkP2(false1) ||  -> equal(phi(false1),err)**.
% 0.17/0.50  713[3:Rew:190.2,711.2,144.1,711.2] bool(false1) SkP2(false1) ||  -> equal(false1,err)**.
% 0.17/0.50  714[3:SSi:713.1,713.0,10.0,86.0,219.0,86.0,219.1] ||  -> equal(false1,err)**.
% 0.17/0.50  715[3:MRR:714.0,89.0] ||  -> .
% 0.17/0.50  716[1:Spt:715.0,128.1,130.0] || equal(false2,err)** -> .
% 0.17/0.50  717[1:Spt:715.0,128.0] ||  -> SkP2(f7(skc3))*.
% 0.17/0.50  718[1:MRR:266.0,717.0] ||  -> d(f7(u))*.
% 0.17/0.50  724[0:SpR:14.0,34.1] SkP2(f7(skc3)) ||  -> equal(f7(skc3),false2)**.
% 0.17/0.50  727[0:SpR:190.2,14.0] bool(skc3) SkP2(skc3) ||  -> equal(phi(skc3),false2)**.
% 0.17/0.50  729[1:SSi:724.0,718.0,717.0] ||  -> equal(f7(skc3),false2)**.
% 0.17/0.50  730[1:Rew:729.0,717.0] ||  -> SkP2(false2)*.
% 0.17/0.50  732[1:Rew:729.0,28.0] || forallprefers(f7(u),false2)* -> .
% 0.17/0.50  736[0:Rew:190.2,727.2,144.1,727.2] bool(skc3) SkP2(skc3) ||  -> equal(skc3,false2)**.
% 0.17/0.50  741[1:SpR:729.0,189.2] bool(skc3) ||  -> SkP2(skc3)* equal(false2,err).
% 0.17/0.50  743[1:SpR:729.0,718.0] ||  -> d(false2)*.
% 0.17/0.50  745[1:MRR:741.2,716.0] bool(skc3) ||  -> SkP2(skc3)*.
% 0.17/0.50  746[1:MRR:736.1,745.1] bool(skc3) ||  -> equal(skc3,false2)**.
% 0.17/0.50  765[1:SpR:143.1,729.0] ||  -> bool(skc3)* equal(true__dfg,false2).
% 0.17/0.50  769[2:Spt:765.1] ||  -> equal(true__dfg,false2)**.
% 0.17/0.50  784[2:Rew:769.0,110.0] || equal(u,false2) equal(v,false1) -> forallprefers(v,u)*.
% 0.17/0.50  845[0:SpR:103.1,29.0] ||  -> bool(u) equal(not1(u),not2(u))**.
% 0.17/0.50  870[0:SpL:845.1,15.0] || equal(not2(skc2),not2(skc2))* -> bool(skc2).
% 0.17/0.50  871[0:Obv:870.0] ||  -> bool(skc2)*.
% 0.17/0.50  930[2:Res:784.2,732.0] || equal(false2,false2) equal(f7(u),false1)** -> .
% 0.17/0.50  934[2:Obv:930.0] || equal(f7(u),false1)** -> .
% 0.17/0.50  937[2:SpL:190.2,934.0] bool(u) SkP2(u) || equal(u,false1)* -> .
% 0.34/0.51  941[2:MRR:937.0,94.1] SkP2(u) || equal(u,false1)* -> .
% 0.34/0.51  945[2:EmS:941.0,10.1] d(u) || equal(u,false1)* -> .
% 0.34/0.51  951[2:EmS:945.0,86.0] || equal(false1,false1)* -> .
% 0.34/0.51  953[2:Obv:951.0] ||  -> .
% 0.34/0.51  954[2:Spt:953.0,765.1,769.0] || equal(true__dfg,false2)** -> .
% 0.34/0.51  955[2:Spt:953.0,765.0] ||  -> bool(skc3)*.
% 0.34/0.51  956[2:MRR:746.0,955.0] ||  -> equal(skc3,false2)**.
% 0.34/0.51  958[2:Rew:956.0,955.0] ||  -> bool(false2)*.
% 0.34/0.51  993[0:SpR:102.1,29.0] bool(false2) ||  -> equal(not2(false1),true__dfg)**.
% 0.34/0.51  996[2:SSi:993.0,730.0,743.0,958.0] ||  -> equal(not2(false1),true__dfg)**.
% 0.34/0.51  997[0:SpR:44.1,29.0] bool(false2) ||  -> equal(not2(true__dfg),false2)**.
% 0.34/0.51  1000[2:SSi:997.0,730.0,743.0,958.0] ||  -> equal(not2(true__dfg),false2)**.
% 0.34/0.51  1009[2:EmS:105.0,958.0] ||  -> equal(true__dfg,false2)** equal(false2,false1).
% 0.34/0.51  1011[0:EmS:105.0,871.0] ||  -> equal(true__dfg,skc2)** equal(skc2,false1).
% 0.34/0.51  1016[2:MRR:1009.0,954.0] ||  -> equal(false2,false1)**.
% 0.34/0.51  1031[2:Rew:1016.0,1000.0] ||  -> equal(not2(true__dfg),false1)**.
% 0.34/0.51  1056[3:Spt:1011.0] ||  -> equal(true__dfg,skc2)**.
% 0.34/0.51  1062[3:Rew:1056.0,87.0] ||  -> equal(not1(skc2),false1)**.
% 0.34/0.51  1075[3:Rew:1056.0,1031.0] ||  -> equal(not2(skc2),false1)**.
% 0.34/0.51  1084[3:Rew:1062.0,15.0] || equal(not2(skc2),false1)** -> .
% 0.34/0.51  1085[3:Rew:1075.0,1084.0] || equal(false1,false1)* -> .
% 0.34/0.51  1086[3:Obv:1085.0] ||  -> .
% 0.34/0.51  1088[3:Spt:1086.0,1011.0,1056.0] || equal(true__dfg,skc2)** -> .
% 0.34/0.51  1089[3:Spt:1086.0,1011.1] ||  -> equal(skc2,false1)**.
% 0.34/0.51  1092[3:Rew:88.0,15.0,996.0,15.0,1089.0,15.0] || equal(true__dfg,true__dfg)* -> .
% 0.34/0.51  1093[3:Obv:1092.0] ||  -> .
% 0.34/0.51  % SZS output end Refutation
% 0.34/0.51  Formulae used in the proof : false_true_err_in_d def_false1 distinct_false_true_err not1_axiom2 not1_axiom3 def_phi lazy_impl_axiom2 lazy_and1_axiom2 def_false2 not1_not2 def_bool prop_false lazy_impl_axiom3 def_not2 prop_true def_f7 not1_axiom1 def_forallprefers impl_axiom1 impl_axiom3 impl_axiom4 lazy_and1_axiom1
% 0.34/0.51  
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