%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM125+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:10:26 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 7 unt; 5 def)
% Number of atoms : 148 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 166 ( 70 ~; 64 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 129 ( 117 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [VT,VVar0,VExp0,Vx,Vv,Ve] :
( ( VExp0 = vabs(Vx,VT,Ve)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> ( visFreeVar(Vv,Ve)
& Vx != Vv ) )
& ( ( visFreeVar(Vv,Ve)
& Vx != Vv )
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs))
& Vx != Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs))
& Vx = Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,conjecture,
! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
~ ! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
inference(negated_conjecture,[status(cth)],[f60]) ).
fof(f92,plain,
! [VT,VVar0,VExp0,Vx,Vv,Ve] :
( ( ( ( visFreeVar(Vv,Ve)
& Vx != Vv )
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| ~ visFreeVar(Vv,Ve)
| Vx = Vv ) )
| VExp0 != vabs(Vx,VT,Ve)
| VVar0 != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f93,plain,
! [VVar0,VExp0,Vx,Vv,Ve] :
( ( ( ( visFreeVar(Vv,Ve)
& Vx != Vv )
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| ~ visFreeVar(Vv,Ve)
| Vx = Vv ) )
| ! [VT] : VExp0 != vabs(Vx,VT,Ve)
| VVar0 != Vv ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4,X5] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X5)
| X3 = X1
| X2 != vabs(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 != X1
| ~ visFreeVar(X0,X2)
| X2 != vabs(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4,X5] :
( visFreeVar(X1,X5)
| ~ visFreeVar(X0,X2)
| X2 != vabs(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f258,plain,
! [Vx,VS,VC,Vy,VS1,VT] :
( vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,veabs),VT)
| visFreeVar(Vx,vabs(Vy,VS1,veabs))
| Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f259,plain,
! [Vx,VC,Vy,VS1,VT] :
( ! [VS] : vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,veabs),VT)
| visFreeVar(Vx,vabs(Vy,VS1,veabs))
| Vx = Vy ),
inference(miniscoping,[status(thm)],[f258]) ).
fof(f260,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X5,X3),vabs(X1,X2,veabs),X4)
| ~ vtcheck(X3,vabs(X1,X2,veabs),X4)
| visFreeVar(X0,vabs(X1,X2,veabs))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f261,plain,
! [Vx,VS,VC,Vy,VS1,VT] :
( vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,veabs),VT)
| visFreeVar(Vx,vabs(Vy,VS1,veabs))
| Vx != Vy ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f262,plain,
! [Vx,VC,Vy,VS1,VT] :
( ! [VS] : vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,veabs),VT)
| visFreeVar(Vx,vabs(Vy,VS1,veabs))
| Vx != Vy ),
inference(miniscoping,[status(thm)],[f261]) ).
fof(f263,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X5,X3),vabs(X1,X2,veabs),X4)
| ~ vtcheck(X3,vabs(X1,X2,veabs),X4)
| visFreeVar(X0,vabs(X1,X2,veabs))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f262]) ).
fof(f264,plain,
? [Vx,VS,VC,Vy,VS1,VT] :
( ~ vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f265,plain,
? [Vx,VC,Vy,VS1,VT] :
( ? [VS] : ~ vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) ),
inference(miniscoping,[status(thm)],[f264]) ).
fof(f266,plain,
( ~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK23_skl,sK24_skl,veabs),sK25_skl)
& vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl)
& ~ visFreeVar(sK21_skl,vabs(sK23_skl,sK24_skl,veabs)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(Vx,sK21_skl),skolemize(VC,sK22_skl),skolemize(Vy,sK23_skl),skolemize(VS1,sK24_skl),skolemize(VT,sK25_skl),skolemize(VS,sK26_skl)],[f265]) ).
fof(f267,plain,
~ visFreeVar(sK21_skl,vabs(sK23_skl,sK24_skl,veabs)),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f268,plain,
vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f420,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X1,vabs(X0,X3,X2))
| ~ visFreeVar(X1,X2)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f421,plain,
! [X0,X1,X2] : ~ visFreeVar(X0,vabs(X0,X1,X2)),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(f422,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X0,X3)
| ~ visFreeVar(X0,vabs(X1,X2,X3)) ),
inference(destructive_equality_resolution,[status(thm)],[f96]) ).
fof(f465,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X4,X2),vabs(X0,X1,veabs),X3)
| ~ vtcheck(X2,vabs(X0,X1,veabs),X3)
| visFreeVar(X0,vabs(X0,X1,veabs)) ),
inference(destructive_equality_resolution,[status(thm)],[f263]) ).
fof(f489,plain,
( ~ visFreeVar(sK21_skl,veabs)
| sK23_skl = sK21_skl ),
inference(resolution,[status(thm)],[f420,f267]) ).
fof(f492,definition,
( sQ0_spl
<=> sK23_skl = sK21_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ0_spl
| sK23_skl = sK21_skl ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,definition,
( sQ1_spl
<=> visFreeVar(sK21_skl,veabs) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ1_spl
| ~ visFreeVar(sK21_skl,veabs) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f489,f492,f495]) ).
fof(f501,plain,
( ~ sQ0_spl
| ~ vtcheck(vbind(sK23_skl,sK26_skl,sK22_skl),vabs(sK23_skl,sK24_skl,veabs),sK25_skl) ),
inference(backward_demodulation,[status(thm)],[f493,f269]) ).
fof(f651,definition,
( sQ5_spl
<=> visFreeVar(sK23_skl,vabs(sK23_skl,sK24_skl,veabs)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f652,plain,
( ~ sQ5_spl
| visFreeVar(sK23_skl,vabs(sK23_skl,sK24_skl,veabs)) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,definition,
( sQ6_spl
<=> vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( sQ6_spl
| ~ vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl) ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f658,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f268]) ).
fof(f659,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f658]) ).
fof(f660,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f652,f421]) ).
fof(f661,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f662,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X1,X4,X0),vabs(X1,X2,veabs),X3)
| ~ vtcheck(X0,vabs(X1,X2,veabs),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f421]) ).
fof(f758,plain,
( ~ vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl)
| visFreeVar(sK21_skl,vabs(sK23_skl,sK24_skl,veabs))
| sK21_skl = sK23_skl ),
inference(resolution,[status(thm)],[f269,f260]) ).
fof(f759,definition,
( sQ7_spl
<=> visFreeVar(sK21_skl,vabs(sK23_skl,sK24_skl,veabs)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ7_spl
| visFreeVar(sK21_skl,vabs(sK23_skl,sK24_skl,veabs)) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,plain,
( ~ sQ6_spl
| sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f758,f492,f759,f654]) ).
fof(f765,plain,
( ~ sQ0_spl
| ~ vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl) ),
inference(resolution,[status(thm)],[f501,f662]) ).
fof(f767,plain,
( ~ sQ0_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f765,f654,f492]) ).
fof(f771,plain,
( ~ sQ7_spl
| visFreeVar(sK21_skl,veabs) ),
inference(resolution,[status(thm)],[f760,f422]) ).
fof(f772,plain,
( ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f771,f497]) ).
fof(f773,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f772]) ).
fof(f774,plain,
$false,
inference(sat_refutation,[status(thm)],[f498,f659,f661,f762,f767,f773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM125+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:22:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.122230 seconds
% 0.14/0.50 % CPU time: 0.221136 seconds
% 0.14/0.50 % Total memory used: 49.306 MB
% 0.14/0.50 % Net memory used: 49.139 MB
%------------------------------------------------------------------------------