%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM124+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 : n005.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 35.48s 4.93s
% Output : CNFRefutation 35.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 101 ( 22 unt; 4 def)
% Number of atoms : 321 ( 108 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 377 ( 157 ~; 156 |; 37 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 316 ( 304 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [VVar0,VExp0,Vx,Vv] :
( ( VExp0 = vvar(Vx)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> Vx = Vv )
& ( Vx = Vv
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f12,axiom,
! [VVar0,VExp0,Ve1,Vv,Ve2] :
( ( VExp0 = vapp(Ve1,Ve2)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1) ) )
& ( ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1) )
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Vv,Ve] :
( vgensym(Ve) = Vv
=> ~ visFreeVar(Vv,Ve) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [Vx,Vy,VVar0,VExp0,VExp1,RESULT,Ve] :
( ( VExp1 = vvar(Vy)
& VExp0 = Ve
& VVar0 = Vx )
=> ( Vx = Vy
=> ( RESULT = vsubst(VVar0,VExp0,VExp1)
=> RESULT = Ve ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [VVar0,VExp0,VExp1,RESULT,Ve1,Vx,Ve,Ve2] :
( ( VExp1 = vapp(Ve1,Ve2)
& VExp0 = Ve
& VVar0 = Vx )
=> ( RESULT = vsubst(VVar0,VExp0,VExp1)
=> RESULT = vapp(vsubst(Vx,Ve,Ve1),vsubst(Vx,Ve,Ve2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [Ve] : valphaEquivalent(Ve,Ve),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [Ve2,Ve1] :
( valphaEquivalent(Ve1,Ve2)
=> valphaEquivalent(Ve2,Ve1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [Ve2,Ve1,Ve3] :
( ( valphaEquivalent(Ve2,Ve3)
& valphaEquivalent(Ve1,Ve2) )
=> valphaEquivalent(Ve1,Ve3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [VS,Vx,Vy,Ve] :
( ~ visFreeVar(Vy,Ve)
=> valphaEquivalent(vabs(Vx,VS,Ve),vabs(Vy,VS,vsubst(Vx,vvar(Vy),Ve))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [Ve,VC,Ve1,VT] :
( ( valphaEquivalent(Ve,Ve1)
& vtcheck(VC,Ve,VT) )
=> vtcheck(VC,Ve1,VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [Ve,Vx,Ve1] :
( ( valphaEquivalent(Ve,Ve1)
& ~ visFreeVar(Vx,Ve) )
=> ~ visFreeVar(Vx,Ve1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [Vx,VS,VC,Vy,VS1,Ve1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,Ve1),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,Ve1))
& Vx != Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,Ve1),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,conjecture,
! [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(f65,negated_conjecture,
~ ! [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) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f93,plain,
! [VVar0,VExp0,Vx,Vv] :
( ( ( Vx = Vv
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| Vx != Vv ) )
| VExp0 != vvar(Vx)
| VVar0 != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X0,X2)
| X3 != X1
| X2 != vvar(X3)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f96,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(f97,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)],[f96]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 != X1
| ~ visFreeVar(X0,X2)
| X2 != vabs(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [VVar0,VExp0,Ve1,Vv,Ve2] :
( ( ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1)
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| ( ~ visFreeVar(Vv,Ve2)
& ~ visFreeVar(Vv,Ve1) ) ) )
| VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X3)
| X2 != vapp(X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X4)
| X2 != vapp(X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f154,plain,
! [Vv,Ve] :
( ~ visFreeVar(Vv,Ve)
| vgensym(Ve) != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f155,plain,
! [X0,X1] :
( ~ visFreeVar(X1,X0)
| vgensym(X0) != X1 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
! [Vx,Vy,VVar0,VExp0,VExp1,RESULT,Ve] :
( RESULT = Ve
| RESULT != vsubst(VVar0,VExp0,VExp1)
| Vx != Vy
| VExp1 != vvar(Vy)
| VExp0 != Ve
| VVar0 != Vx ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f157,plain,
! [Vx,Vy,VVar0,VExp0,VExp1,Ve] :
( ! [RESULT] :
( RESULT = Ve
| RESULT != vsubst(VVar0,VExp0,VExp1) )
| Vx != Vy
| VExp1 != vvar(Vy)
| VExp0 != Ve
| VVar0 != Vx ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X6 = X3
| X6 != vsubst(X0,X2,X4)
| X1 != X5
| X4 != vvar(X5)
| X2 != X3
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f162,plain,
! [VVar0,VExp0,VExp1,RESULT,Ve1,Vx,Ve,Ve2] :
( RESULT = vapp(vsubst(Vx,Ve,Ve1),vsubst(Vx,Ve,Ve2))
| RESULT != vsubst(VVar0,VExp0,VExp1)
| VExp1 != vapp(Ve1,Ve2)
| VExp0 != Ve
| VVar0 != Vx ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f163,plain,
! [VVar0,VExp0,VExp1,Ve1,Vx,Ve,Ve2] :
( ! [RESULT] :
( RESULT = vapp(vsubst(Vx,Ve,Ve1),vsubst(Vx,Ve,Ve2))
| RESULT != vsubst(VVar0,VExp0,VExp1) )
| VExp1 != vapp(Ve1,Ve2)
| VExp0 != Ve
| VVar0 != Vx ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( X7 = vapp(vsubst(X1,X3,X5),vsubst(X1,X3,X6))
| X7 != vsubst(X0,X2,X4)
| X4 != vapp(X5,X6)
| X2 != X3
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f253,plain,
! [X0] : valphaEquivalent(X0,X0),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f254,plain,
! [Ve2,Ve1] :
( valphaEquivalent(Ve2,Ve1)
| ~ valphaEquivalent(Ve1,Ve2) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f255,plain,
! [X0,X1] :
( valphaEquivalent(X1,X0)
| ~ valphaEquivalent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [Ve2,Ve1,Ve3] :
( valphaEquivalent(Ve1,Ve3)
| ~ valphaEquivalent(Ve2,Ve3)
| ~ valphaEquivalent(Ve1,Ve2) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f257,plain,
! [Ve1,Ve3] :
( valphaEquivalent(Ve1,Ve3)
| ! [Ve2] :
( ~ valphaEquivalent(Ve2,Ve3)
| ~ valphaEquivalent(Ve1,Ve2) ) ),
inference(miniscoping,[status(thm)],[f256]) ).
fof(f258,plain,
! [X0,X1,X2] :
( valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X1,X2)
| ~ valphaEquivalent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [VS,Vx,Vy,Ve] :
( valphaEquivalent(vabs(Vx,VS,Ve),vabs(Vy,VS,vsubst(Vx,vvar(Vy),Ve)))
| visFreeVar(Vy,Ve) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f260,plain,
! [Vy,Ve] :
( ! [VS,Vx] : valphaEquivalent(vabs(Vx,VS,Ve),vabs(Vy,VS,vsubst(Vx,vvar(Vy),Ve)))
| visFreeVar(Vy,Ve) ),
inference(miniscoping,[status(thm)],[f259]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( valphaEquivalent(vabs(X2,X3,X1),vabs(X0,X3,vsubst(X2,vvar(X0),X1)))
| visFreeVar(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f262,plain,
! [Ve,VC,Ve1,VT] :
( vtcheck(VC,Ve1,VT)
| ~ valphaEquivalent(Ve,Ve1)
| ~ vtcheck(VC,Ve,VT) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f263,plain,
! [VC,Ve1,VT] :
( vtcheck(VC,Ve1,VT)
| ! [Ve] :
( ~ valphaEquivalent(Ve,Ve1)
| ~ vtcheck(VC,Ve,VT) ) ),
inference(miniscoping,[status(thm)],[f262]) ).
fof(f264,plain,
! [X0,X1,X2,X3] :
( vtcheck(X0,X3,X2)
| ~ valphaEquivalent(X1,X3)
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f265,plain,
! [Ve,Vx,Ve1] :
( ~ visFreeVar(Vx,Ve1)
| ~ valphaEquivalent(Ve,Ve1)
| visFreeVar(Vx,Ve) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f266,plain,
! [Vx,Ve1] :
( ~ visFreeVar(Vx,Ve1)
| ! [Ve] :
( ~ valphaEquivalent(Ve,Ve1)
| visFreeVar(Vx,Ve) ) ),
inference(miniscoping,[status(thm)],[f265]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ visFreeVar(X0,X2)
| ~ valphaEquivalent(X1,X2)
| visFreeVar(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f274,plain,
! [Vx,VS,VC,Vy,VS1,Ve1,VT] :
( vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,Ve1),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,Ve1),VT)
| visFreeVar(Vx,vabs(Vy,VS1,Ve1))
| Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f275,plain,
! [Vx,VC,Vy,VS1,Ve1,VT] :
( ! [VS] : vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,Ve1),VT)
| ~ vtcheck(VC,vabs(Vy,VS1,Ve1),VT)
| visFreeVar(Vx,vabs(Vy,VS1,Ve1))
| Vx = Vy ),
inference(miniscoping,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X6,X4),vabs(X1,X2,X3),X5)
| ~ vtcheck(X4,vabs(X1,X2,X3),X5)
| visFreeVar(X0,vabs(X1,X2,X3))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f277,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)],[f65]) ).
fof(f278,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)],[f277]) ).
fof(f279,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))
& sK21_skl = sK23_skl ),
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)],[f278]) ).
fof(f280,plain,
sK21_skl = sK23_skl,
inference(cnf_transformation,[status(thm)],[f279]) ).
fof(f282,plain,
vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f279]) ).
fof(f283,plain,
~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f279]) ).
fof(f432,plain,
! [X0] : visFreeVar(X0,vvar(X0)),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f435,plain,
! [X0,X1,X2] : ~ visFreeVar(X0,vabs(X0,X1,X2)),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f437,plain,
! [X0,X1,X2] :
( visFreeVar(X0,vapp(X1,X2))
| ~ visFreeVar(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f102]) ).
fof(f438,plain,
! [X0,X1,X2] :
( visFreeVar(X0,vapp(X2,X1))
| ~ visFreeVar(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f103]) ).
fof(f451,plain,
! [X0] : ~ visFreeVar(vgensym(X0),X0),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f452,plain,
! [X0,X1] : vsubst(X0,X1,vvar(X0)) = X1,
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f454,plain,
! [X0,X1,X2,X3] : vsubst(X0,X1,vapp(X2,X3)) = vapp(vsubst(X0,X1,X2),vsubst(X0,X1,X3)),
inference(destructive_equality_resolution,[status(thm)],[f164]) ).
fof(f496,plain,
vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl),
inference(forward_demodulation,[status(thm)],[f280,f282]) ).
fof(f497,plain,
~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK21_skl,sK24_skl,veabs),sK25_skl),
inference(forward_demodulation,[status(thm)],[f280,f283]) ).
fof(f509,plain,
! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1),
inference(resolution,[status(thm)],[f451,f438]) ).
fof(f510,plain,
! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0),
inference(resolution,[status(thm)],[f451,f437]) ).
fof(f516,plain,
! [X0,X1,X2] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0),
inference(resolution,[status(thm)],[f510,f437]) ).
fof(f518,plain,
! [X0,X1,X2] :
( ~ valphaEquivalent(X2,X1)
| valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X0,X1) ),
inference(resolution,[status(thm)],[f258,f255]) ).
fof(f599,plain,
! [X0] :
( ~ valphaEquivalent(X0,vabs(sK21_skl,sK24_skl,veabs))
| ~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),X0,sK25_skl) ),
inference(resolution,[status(thm)],[f264,f497]) ).
fof(f708,plain,
! [X0,X1,X2] :
( ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs))
| ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f276,f599]) ).
fof(f715,definition,
( sQ1_spl
<=> visFreeVar(sK21_skl,vabs(sK21_skl,sK24_skl,veabs)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ1_spl
| visFreeVar(sK21_skl,vabs(sK21_skl,sK24_skl,veabs)) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,definition,
( sQ2_spl
<=> vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f720,plain,
( sQ2_spl
| ~ vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl) ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f722,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f720,f496]) ).
fof(f723,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f890,plain,
! [X0,X1,X2,X3] :
( ~ valphaEquivalent(vabs(sK21_skl,sK24_skl,veabs),X3)
| ~ valphaEquivalent(vabs(X0,X1,X2),X3)
| ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f708,f518]) ).
fof(f907,plain,
! [X0,X1,X2,X3,X4] :
( ~ valphaEquivalent(X4,vabs(X0,X1,X2))
| ~ vtcheck(sK22_skl,X4,sK25_skl)
| ~ valphaEquivalent(vabs(sK21_skl,sK24_skl,veabs),X3)
| ~ valphaEquivalent(vabs(X0,X1,X2),X3)
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f890,f264]) ).
fof(f1025,plain,
! [X0,X1,X2] :
( ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs))
| ~ vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl)
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(X0,X1,X2))
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f907,f255]) ).
fof(f1045,definition,
! [X0,X1,X2] :
( sQ10_spl
<=> ( ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs))
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(X0,X1,X2))
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs))
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(X0,X1,X2))
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(component_clause,[status(thm)],[f1045]) ).
fof(f1048,plain,
( ~ sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1025,f1045,f718]) ).
fof(f1052,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs))
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1046,f253]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| ~ valphaEquivalent(vabs(sK21_skl,sK24_skl,veabs),vabs(X0,X1,X2))
| visFreeVar(sK21_skl,vabs(X0,X1,X2))
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f1052,f255]) ).
fof(f1399,plain,
! [X0,X1,X2,X3,X4] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(X2,X3)),X4)),vsubst(X0,X1,X2)),
inference(paramodulation,[status(thm)],[f454,f516]) ).
fof(f3429,plain,
! [X0,X1,X2,X3] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(vvar(X0),X2)),X3)),X1),
inference(paramodulation,[status(thm)],[f452,f1399]) ).
fof(f3436,plain,
! [X0,X1,X2,X3,X4] : ~ visFreeVar(vgensym(vapp(vsubst(X0,vapp(X1,X2),vapp(vvar(X0),X3)),X4)),X1),
inference(resolution,[status(thm)],[f3429,f437]) ).
fof(f4332,plain,
! [X0] :
( ~ sQ10_spl
| visFreeVar(sK21_skl,vabs(X0,sK24_skl,vsubst(sK21_skl,vvar(X0),veabs)))
| sK21_skl = X0
| visFreeVar(X0,veabs) ),
inference(resolution,[status(thm)],[f261,f1105]) ).
fof(f4520,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ valphaEquivalent(X1,vabs(X0,sK24_skl,vsubst(sK21_skl,vvar(X0),veabs)))
| visFreeVar(sK21_skl,X1)
| sK21_skl = X0
| visFreeVar(X0,veabs) ),
inference(resolution,[status(thm)],[f4332,f267]) ).
fof(f4537,plain,
! [X0] :
( ~ sQ10_spl
| visFreeVar(X0,veabs)
| visFreeVar(sK21_skl,vabs(sK21_skl,sK24_skl,veabs))
| sK21_skl = X0
| visFreeVar(X0,veabs) ),
inference(resolution,[status(thm)],[f4520,f261]) ).
fof(f4549,definition,
! [X0] :
( sQ57_spl
<=> ( visFreeVar(X0,veabs)
| sK21_skl = X0
| visFreeVar(X0,veabs) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f4550,plain,
! [X0] :
( ~ sQ57_spl
| visFreeVar(X0,veabs)
| sK21_skl = X0
| visFreeVar(X0,veabs) ),
inference(component_clause,[status(thm)],[f4549]) ).
fof(f4552,plain,
( ~ sQ10_spl
| sQ1_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f4537,f4549,f715,f1045]) ).
fof(f4553,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f716,f435]) ).
fof(f4554,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f4553]) ).
fof(f4555,plain,
! [X0] :
( ~ sQ57_spl
| sK21_skl = X0
| visFreeVar(X0,veabs) ),
inference(duplicate_literals_removal,[status(thm)],[f4550]) ).
fof(f4627,plain,
! [X0] :
( ~ sQ57_spl
| sK21_skl = vgensym(vapp(X0,veabs)) ),
inference(resolution,[status(thm)],[f4555,f509]) ).
fof(f4668,plain,
! [X0] :
( ~ sQ57_spl
| ~ visFreeVar(sK21_skl,X0) ),
inference(paramodulation,[status(thm)],[f4627,f3436]) ).
fof(f4714,plain,
( ~ sQ57_spl
| $false ),
inference(resolution,[status(thm)],[f4668,f432]) ).
fof(f4722,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f4714]) ).
fof(f4723,plain,
$false,
inference(sat_refutation,[status(thm)],[f723,f1048,f4552,f4554,f4722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM124+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:17:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.16/0.40 % Drodi V4.1.1
% 35.48/4.93 % Refutation found
% 35.48/4.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 35.48/4.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 35.48/5.00 % Elapsed time: 4.604146 seconds
% 35.48/5.00 % CPU time: 36.102148 seconds
% 35.48/5.00 % Total memory used: 334.519 MB
% 35.48/5.00 % Net memory used: 306.715 MB
%------------------------------------------------------------------------------