%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM135+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 : n017.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 12:10:27 PM UTC 2026
% Result : Theorem 11.11s 1.88s
% Output : CNFRefutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 119 ( 16 unt; 11 def)
% Number of atoms : 398 ( 196 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 449 ( 170 ~; 175 |; 69 &)
% ( 12 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-4 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 341 ( 287 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [VVar0,VVar1] :
( ( VVar0 = VVar1
=> vvar(VVar0) = vvar(VVar1) )
& ( vvar(VVar0) = vvar(VVar1)
=> VVar0 = VVar1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [VVar0,VVar1,VTyp0,VExp0] : vvar(VVar0) != vabs(VVar1,VTyp0,VExp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [VVar0,VExp0,VExp1] : vvar(VVar0) != vapp(VExp0,VExp1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f16,axiom,
! [VTyp0,VTyp1] :
( ( VTyp0 = VTyp1
=> vsomeType(VTyp0) = vsomeType(VTyp1) )
& ( vsomeType(VTyp0) = vsomeType(VTyp1)
=> VTyp0 = VTyp1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [VC,Vx,Vy,VVar0,VCtx0,RESULT,VTy] :
( ( VCtx0 = vbind(Vy,VTy,VC)
& VVar0 = Vx )
=> ( Vx = Vy
=> ( RESULT = vlookup(VVar0,VCtx0)
=> RESULT = vsomeType(VTy) ) ) ),
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(f30,axiom,
! [Ve,Vx,VVar0,VExp0,VExp1,RESULT,Vy] :
( ( VExp1 = vvar(Vy)
& VExp0 = Ve
& VVar0 = Vx )
=> ( Vx != Vy
=> ( RESULT = vsubst(VVar0,VExp0,VExp1)
=> RESULT = vvar(Vy) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [Ve,VT,VC] :
( vtcheck(VC,Ve,VT)
=> ( ? [Ve1,Ve2,VS] :
( vtcheck(VC,Ve2,VS)
& vtcheck(VC,Ve1,varrow(VS,VT))
& Ve = vapp(Ve1,Ve2) )
| ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] :
( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [Vx,VS,VC,Ve,VT] :
( ( vtcheck(vbind(Vx,VS,VC),Ve,VT)
& ~ visFreeVar(Vx,Ve) )
=> vtcheck(VC,Ve,VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,conjecture,
! [VT,VC,Vx,Ve,Vy,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vvar(Vy),VT2)
& vtcheck(VC,Ve,VT) )
=> vtcheck(VC,vsubst(Vx,Ve,vvar(Vy)),VT2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
~ ! [VT,VC,Vx,Ve,Vy,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vvar(Vy),VT2)
& vtcheck(VC,Ve,VT) )
=> vtcheck(VC,vsubst(Vx,Ve,vvar(Vy)),VT2) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,plain,
! [VVar0,VVar1] :
( ( vvar(VVar0) = vvar(VVar1)
| VVar0 != VVar1 )
& ( VVar0 = VVar1
| vvar(VVar0) != vvar(VVar1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f61,plain,
( ! [VVar0,VVar1] :
( vvar(VVar0) = vvar(VVar1)
| VVar0 != VVar1 )
& ! [VVar0,VVar1] :
( VVar0 = VVar1
| vvar(VVar0) != vvar(VVar1) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f75,plain,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f76,plain,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f87,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(f88,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X0,X2)
| X3 != X1
| X2 != vvar(X3)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ visFreeVar(X0,X2)
| X2 != vvar(X3)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,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(f91,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)],[f90]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 != X1
| ~ visFreeVar(X0,X2)
| X2 != vabs(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f111,plain,
! [VTyp0,VTyp1] :
( ( vsomeType(VTyp0) = vsomeType(VTyp1)
| VTyp0 != VTyp1 )
& ( VTyp0 = VTyp1
| vsomeType(VTyp0) != vsomeType(VTyp1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f112,plain,
( ! [VTyp0,VTyp1] :
( vsomeType(VTyp0) = vsomeType(VTyp1)
| VTyp0 != VTyp1 )
& ! [VTyp0,VTyp1] :
( VTyp0 = VTyp1
| vsomeType(VTyp0) != vsomeType(VTyp1) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f128,plain,
! [VC,Vx,Vy,VVar0,VCtx0,RESULT,VTy] :
( RESULT = vsomeType(VTy)
| RESULT != vlookup(VVar0,VCtx0)
| Vx != Vy
| VCtx0 != vbind(Vy,VTy,VC)
| VVar0 != Vx ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f129,plain,
! [Vx,Vy,VVar0,VCtx0,VTy] :
( ! [RESULT] :
( RESULT = vsomeType(VTy)
| RESULT != vlookup(VVar0,VCtx0) )
| Vx != Vy
| ! [VC] : VCtx0 != vbind(Vy,VTy,VC)
| VVar0 != Vx ),
inference(miniscoping,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X6 = vsomeType(X4)
| X6 != vlookup(X0,X2)
| X1 != X3
| X2 != vbind(X3,X4,X5)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f150,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(f151,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)],[f150]) ).
fof(f152,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)],[f151]) ).
fof(f153,plain,
! [Ve,Vx,VVar0,VExp0,VExp1,RESULT,Vy] :
( RESULT = vvar(Vy)
| RESULT != vsubst(VVar0,VExp0,VExp1)
| Vx = Vy
| VExp1 != vvar(Vy)
| VExp0 != Ve
| VVar0 != Vx ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f154,plain,
! [Vx,VVar0,VExp0,VExp1,Vy] :
( ! [RESULT] :
( RESULT = vvar(Vy)
| RESULT != vsubst(VVar0,VExp0,VExp1) )
| Vx = Vy
| VExp1 != vvar(Vy)
| ! [Ve] : VExp0 != Ve
| VVar0 != Vx ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X6 = vvar(X5)
| X6 != vsubst(X0,X2,X4)
| X1 = X5
| X4 != vvar(X5)
| X2 != X3
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f239,plain,
! [Ve,VT,VC] :
( ? [Ve1,Ve2,VS] :
( vtcheck(VC,Ve2,VS)
& vtcheck(VC,Ve1,varrow(VS,VT))
& Ve = vapp(Ve1,Ve2) )
| ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] :
( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) )
| ~ vtcheck(VC,Ve,VT) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f240,definition,
! [Ve,VT,VC] :
( sP3_prd(VC,VT,Ve)
<=> ( ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] :
( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f241,plain,
! [Ve,VT,VC] :
( ? [Ve1,Ve2,VS] :
( vtcheck(VC,Ve2,VS)
& vtcheck(VC,Ve1,varrow(VS,VT))
& Ve = vapp(Ve1,Ve2) )
| sP3_prd(VC,VT,Ve)
| ~ vtcheck(VC,Ve,VT) ),
inference(formula_renaming,[status(thm)],[f239,f240]) ).
fof(f242,plain,
! [Ve,VT,VC] :
( ? [Ve2,VS] :
( vtcheck(VC,Ve2,VS)
& ? [Ve1] :
( vtcheck(VC,Ve1,varrow(VS,VT))
& Ve = vapp(Ve1,Ve2) ) )
| sP3_prd(VC,VT,Ve)
| ~ vtcheck(VC,Ve,VT) ),
inference(miniscoping,[status(thm)],[f241]) ).
fof(f243,plain,
! [Ve,VT,VC] :
( ( vtcheck(VC,sK18_skl(VC,VT,Ve),sK19_skl(VC,VT,Ve))
& vtcheck(VC,sK20_skl(VC,VT,Ve),varrow(sK19_skl(VC,VT,Ve),VT))
& Ve = vapp(sK20_skl(VC,VT,Ve),sK18_skl(VC,VT,Ve)) )
| sP3_prd(VC,VT,Ve)
| ~ vtcheck(VC,Ve,VT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl]),skolemize(Ve2,sK18_skl(VC,VT,Ve)),skolemize(VS,sK19_skl(VC,VT,Ve)),skolemize(Ve1,sK20_skl(VC,VT,Ve))],[f242]) ).
fof(f244,plain,
! [X0,X1,X2] :
( X1 = vapp(sK20_skl(X0,X2,X1),sK18_skl(X0,X2,X1))
| sP3_prd(X0,X2,X1)
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f243]) ).
fof(f250,plain,
! [Vx,VS,VC,Ve,VT] :
( vtcheck(VC,Ve,VT)
| ~ vtcheck(vbind(Vx,VS,VC),Ve,VT)
| visFreeVar(Vx,Ve) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f251,plain,
! [VC,Ve,VT] :
( vtcheck(VC,Ve,VT)
| ! [Vx] :
( ! [VS] : ~ vtcheck(vbind(Vx,VS,VC),Ve,VT)
| visFreeVar(Vx,Ve) ) ),
inference(miniscoping,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X3,X1,X4)
| ~ vtcheck(vbind(X0,X2,X3),X1,X4)
| visFreeVar(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f256,plain,
? [VT,VC,Vx,Ve,Vy,VT2] :
( ~ vtcheck(VC,vsubst(Vx,Ve,vvar(Vy)),VT2)
& vtcheck(vbind(Vx,VT,VC),vvar(Vy),VT2)
& vtcheck(VC,Ve,VT) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f257,plain,
? [VC,Vx,Ve,Vy,VT2] :
( ~ vtcheck(VC,vsubst(Vx,Ve,vvar(Vy)),VT2)
& ? [VT] :
( vtcheck(vbind(Vx,VT,VC),vvar(Vy),VT2)
& vtcheck(VC,Ve,VT) ) ),
inference(miniscoping,[status(thm)],[f256]) ).
fof(f258,plain,
( ~ vtcheck(sK21_skl,vsubst(sK22_skl,sK23_skl,vvar(sK24_skl)),sK25_skl)
& vtcheck(vbind(sK22_skl,sK26_skl,sK21_skl),vvar(sK24_skl),sK25_skl)
& vtcheck(sK21_skl,sK23_skl,sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(VC,sK21_skl),skolemize(Vx,sK22_skl),skolemize(Ve,sK23_skl),skolemize(Vy,sK24_skl),skolemize(VT2,sK25_skl),skolemize(VT,sK26_skl)],[f257]) ).
fof(f259,plain,
vtcheck(sK21_skl,sK23_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f260,plain,
vtcheck(vbind(sK22_skl,sK26_skl,sK21_skl),vvar(sK24_skl),sK25_skl),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f261,plain,
~ vtcheck(sK21_skl,vsubst(sK22_skl,sK23_skl,vvar(sK24_skl)),sK25_skl),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f299,definition,
! [Ve,VT,VC,Vx] :
( sP7_prd(Vx,VC,VT,Ve)
<=> ( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f300,plain,
! [Ve,VT,VC] :
( sP3_prd(VC,VT,Ve)
<=> ( ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] : sP7_prd(Vx,VC,VT,Ve) ) ),
inference(formula_renaming,[status(thm)],[f240,f299]) ).
fof(f301,plain,
! [Ve,VT,VC] :
( ( ( ! [Vx,Ve2,VT1,VT2] :
( ~ vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
| VT != varrow(VT1,VT2)
| Ve != vabs(Vx,VT1,Ve2) )
& ! [Vx] : ~ sP7_prd(Vx,VC,VT,Ve) )
| sP3_prd(VC,VT,Ve) )
& ( ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] : sP7_prd(Vx,VC,VT,Ve)
| ~ sP3_prd(VC,VT,Ve) ) ),
inference(NNF_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
( ! [Ve,VT,VC] :
( ( ! [Vx,Ve2,VT1,VT2] :
( ~ vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
| VT != varrow(VT1,VT2)
| Ve != vabs(Vx,VT1,Ve2) )
& ! [Vx] : ~ sP7_prd(Vx,VC,VT,Ve) )
| sP3_prd(VC,VT,Ve) )
& ! [Ve,VT,VC] :
( ? [Vx,Ve2,VT1,VT2] :
( vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
& VT = varrow(VT1,VT2)
& Ve = vabs(Vx,VT1,Ve2) )
| ? [Vx] : sP7_prd(Vx,VC,VT,Ve)
| ~ sP3_prd(VC,VT,Ve) ) ),
inference(miniscoping,[status(thm)],[f301]) ).
fof(f303,plain,
( ! [Ve,VT,VC] :
( ( ! [Vx,Ve2,VT1,VT2] :
( ~ vtcheck(vbind(Vx,VT1,VC),Ve2,VT2)
| VT != varrow(VT1,VT2)
| Ve != vabs(Vx,VT1,Ve2) )
& ! [Vx] : ~ sP7_prd(Vx,VC,VT,Ve) )
| sP3_prd(VC,VT,Ve) )
& ! [Ve,VT,VC] :
( ( vtcheck(vbind(sK45_skl(VC,VT,Ve),sK47_skl(VC,VT,Ve),VC),sK46_skl(VC,VT,Ve),sK48_skl(VC,VT,Ve))
& VT = varrow(sK47_skl(VC,VT,Ve),sK48_skl(VC,VT,Ve))
& Ve = vabs(sK45_skl(VC,VT,Ve),sK47_skl(VC,VT,Ve),sK46_skl(VC,VT,Ve)) )
| sP7_prd(sK44_skl(VC,VT,Ve),VC,VT,Ve)
| ~ sP3_prd(VC,VT,Ve) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl,sK45_skl,sK46_skl,sK47_skl,sK48_skl]),skolemize(Vx,sK44_skl(VC,VT,Ve)),skolemize(Vx,sK45_skl(VC,VT,Ve)),skolemize(Ve2,sK46_skl(VC,VT,Ve)),skolemize(VT1,sK47_skl(VC,VT,Ve)),skolemize(VT2,sK48_skl(VC,VT,Ve))],[f302]) ).
fof(f304,plain,
! [X0,X1,X2] :
( X2 = vabs(sK45_skl(X0,X1,X2),sK47_skl(X0,X1,X2),sK46_skl(X0,X1,X2))
| sP7_prd(sK44_skl(X0,X1,X2),X0,X1,X2)
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f339,plain,
! [Ve,VT,VC,Vx] :
( ( vlookup(Vx,VC) != vsomeType(VT)
| Ve != vvar(Vx)
| sP7_prd(Vx,VC,VT,Ve) )
& ( ( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) )
| ~ sP7_prd(Vx,VC,VT,Ve) ) ),
inference(NNF_transformation,[status(thm)],[f299]) ).
fof(f340,plain,
( ! [Ve,VT,VC,Vx] :
( vlookup(Vx,VC) != vsomeType(VT)
| Ve != vvar(Vx)
| sP7_prd(Vx,VC,VT,Ve) )
& ! [Ve,VT,VC,Vx] :
( ( vlookup(Vx,VC) = vsomeType(VT)
& Ve = vvar(Vx) )
| ~ sP7_prd(Vx,VC,VT,Ve) ) ),
inference(miniscoping,[status(thm)],[f339]) ).
fof(f341,plain,
! [X0,X1,X2,X3] :
( X3 = vvar(X0)
| ~ sP7_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f340]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( vlookup(X0,X1) = vsomeType(X2)
| ~ sP7_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f340]) ).
fof(f410,plain,
! [X0] : visFreeVar(X0,vvar(X0)),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f411,plain,
! [X0,X1] :
( X1 = X0
| ~ visFreeVar(X0,vvar(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f89]) ).
fof(f413,plain,
! [X0,X1,X2] : ~ visFreeVar(X0,vabs(X0,X1,X2)),
inference(destructive_equality_resolution,[status(thm)],[f93]) ).
fof(f422,plain,
! [X0,X1,X2] : vlookup(X0,vbind(X0,X1,X2)) = vsomeType(X1),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f430,plain,
! [X0,X1] : vsubst(X0,X1,vvar(X0)) = X1,
inference(destructive_equality_resolution,[status(thm)],[f152]) ).
fof(f431,plain,
! [X0,X1,X2] :
( vsubst(X0,X2,vvar(X1)) = vvar(X1)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f484,plain,
( sK22_skl = sK24_skl
| ~ vtcheck(sK21_skl,vvar(sK24_skl),sK25_skl) ),
inference(paramodulation,[status(thm)],[f431,f261]) ).
fof(f488,definition,
( sQ0_spl
<=> vtcheck(sK21_skl,vvar(sK24_skl),sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f491,definition,
( sQ1_spl
<=> sK22_skl = sK24_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ1_spl
| sK22_skl = sK24_skl ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f484,f488,f491]) ).
fof(f495,plain,
( vtcheck(sK21_skl,vvar(sK24_skl),sK25_skl)
| visFreeVar(sK22_skl,vvar(sK24_skl)) ),
inference(resolution,[status(thm)],[f252,f260]) ).
fof(f496,definition,
( sQ2_spl
<=> visFreeVar(sK22_skl,vvar(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( ~ sQ2_spl
| visFreeVar(sK22_skl,vvar(sK24_skl)) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f498,plain,
( sQ2_spl
| ~ visFreeVar(sK22_skl,vvar(sK24_skl)) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f495,f496,f488]) ).
fof(f516,plain,
( vvar(sK24_skl) = vapp(sK20_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK18_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)))
| sP3_prd(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
inference(resolution,[status(thm)],[f244,f260]) ).
fof(f518,definition,
( sQ5_spl
<=> sP3_prd(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ5_spl
| sP3_prd(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,definition,
( sQ6_spl
<=> vvar(sK24_skl) = vapp(sK20_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK18_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ6_spl
| vvar(sK24_skl) = vapp(sK20_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK18_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl))) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f516,f518,f521]) ).
fof(f532,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f76]) ).
fof(f533,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f565,plain,
( ~ sQ5_spl
| vvar(sK24_skl) = vabs(sK45_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK47_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK46_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)))
| sP7_prd(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
inference(resolution,[status(thm)],[f519,f304]) ).
fof(f566,definition,
( sQ15_spl
<=> sP7_prd(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ15_spl
| sP7_prd(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,definition,
( sQ16_spl
<=> vvar(sK24_skl) = vabs(sK45_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK47_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK46_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( ~ sQ16_spl
| vvar(sK24_skl) = vabs(sK45_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK47_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),sK46_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl))) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f572,plain,
( ~ sQ5_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f565,f566,f569,f518]) ).
fof(f573,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f75]) ).
fof(f574,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f908,plain,
( ~ sQ2_spl
| sK24_skl = sK22_skl ),
inference(resolution,[status(thm)],[f411,f497]) ).
fof(f914,plain,
( ~ sQ2_spl
| ~ vtcheck(sK21_skl,vsubst(sK22_skl,sK23_skl,vvar(sK22_skl)),sK25_skl) ),
inference(backward_demodulation,[status(thm)],[f908,f261]) ).
fof(f915,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sP7_prd(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK24_skl)),vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl)) ),
inference(backward_demodulation,[status(thm)],[f908,f567]) ).
fof(f916,plain,
( ~ sQ2_spl
| ~ vtcheck(sK21_skl,sK23_skl,sK25_skl) ),
inference(forward_demodulation,[status(thm)],[f430,f914]) ).
fof(f917,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sP7_prd(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl)),vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl)) ),
inference(forward_demodulation,[status(thm)],[f908,f915]) ).
fof(f1175,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| vvar(sK22_skl) = vvar(sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl))) ),
inference(resolution,[status(thm)],[f917,f341]) ).
fof(f1212,definition,
( sQ23_spl
<=> sK23_skl = sK23_skl ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1214,plain,
( sQ23_spl
| sK23_skl != sK23_skl ),
inference(component_clause,[status(thm)],[f1212]) ).
fof(f1539,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1214]) ).
fof(f1540,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1539]) ).
fof(f1724,definition,
! [X0] :
( sQ28_spl
<=> visFreeVar(sK79_skl(vnoExp,sK23_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1725,plain,
! [X0] :
( ~ sQ28_spl
| visFreeVar(sK79_skl(vnoExp,sK23_skl),X0) ),
inference(component_clause,[status(thm)],[f1724]) ).
fof(f1735,plain,
( ~ sQ28_spl
| $false ),
inference(resolution,[status(thm)],[f1725,f413]) ).
fof(f1741,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1735]) ).
fof(f1749,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sK22_skl = sK44_skl(vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl)) ),
inference(resolution,[status(thm)],[f1175,f62]) ).
fof(f1787,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sP7_prd(sK22_skl,vbind(sK22_skl,sK26_skl,sK21_skl),sK25_skl,vvar(sK22_skl)) ),
inference(backward_demodulation,[status(thm)],[f1749,f917]) ).
fof(f2583,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| vlookup(sK22_skl,vbind(sK22_skl,sK26_skl,sK21_skl)) = vsomeType(sK25_skl) ),
inference(resolution,[status(thm)],[f342,f1787]) ).
fof(f2586,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| vsomeType(sK26_skl) = vsomeType(sK25_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f2583]) ).
fof(f2588,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sK26_skl = sK25_skl ),
inference(resolution,[status(thm)],[f2586,f113]) ).
fof(f2603,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| vtcheck(sK21_skl,sK23_skl,sK25_skl) ),
inference(backward_demodulation,[status(thm)],[f2588,f259]) ).
fof(f2609,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2603,f916]) ).
fof(f2610,plain,
( ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f2609]) ).
fof(f2612,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ visFreeVar(sK22_skl,vvar(sK22_skl)) ),
inference(backward_demodulation,[status(thm)],[f492,f498]) ).
fof(f2618,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2612,f410]) ).
fof(f2619,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2618]) ).
fof(f2620,plain,
$false,
inference(sat_refutation,[status(thm)],[f494,f499,f524,f533,f572,f574,f1540,f1741,f2610,f2619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM135+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:13:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.40 % Drodi V4.1.1
% 11.11/1.88 % Refutation found
% 11.11/1.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.11/1.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.11/1.93 % Elapsed time: 1.563317 seconds
% 11.11/1.93 % CPU time: 11.724579 seconds
% 11.11/1.93 % Total memory used: 215.498 MB
% 11.11/1.93 % Net memory used: 206.135 MB
%------------------------------------------------------------------------------