%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM140+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 : n010.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 12:10:28 PM UTC 2026
% Result : Theorem 8.56s 1.61s
% Output : CNFRefutation 8.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 15 unt; 0 def)
% Number of atoms : 159 ( 54 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 172 ( 70 ~; 66 |; 23 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 168 ( 156 !; 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(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(f56,axiom,
! [Ve2,Ve1] :
( valphaEquivalent(Ve1,Ve2)
=> valphaEquivalent(Ve2,Ve1) ),
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(f61,axiom,
! [Vx,VS,VC,Vy,VS1,Ve1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,Ve1),VT)
& vlookup(Vx,VC) = vnoType
& Vx != Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,Ve1),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,conjecture,
! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& vlookup(Vx,VC) = vnoType
& Vx = Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
~ ! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& vlookup(Vx,VC) = vnoType
& Vx = Vy )
=> vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f91,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(f92,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X0,X2)
| X3 != X1
| X2 != vvar(X3)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f99,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(f100,plain,
! [X0,X1,X2,X3,X4] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X3)
| X2 != vapp(X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X4)
| X2 != vapp(X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f152,plain,
! [Vv,Ve] :
( ~ visFreeVar(Vv,Ve)
| vgensym(Ve) != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f153,plain,
! [X0,X1] :
( ~ visFreeVar(X1,X0)
| vgensym(X0) != X1 ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f252,plain,
! [Ve2,Ve1] :
( valphaEquivalent(Ve2,Ve1)
| ~ valphaEquivalent(Ve1,Ve2) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f253,plain,
! [X0,X1] :
( valphaEquivalent(X1,X0)
| ~ valphaEquivalent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f257,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(f258,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)],[f257]) ).
fof(f259,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)],[f258]) ).
fof(f260,plain,
! [Ve,VC,Ve1,VT] :
( vtcheck(VC,Ve1,VT)
| ~ valphaEquivalent(Ve,Ve1)
| ~ vtcheck(VC,Ve,VT) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f261,plain,
! [VC,Ve1,VT] :
( vtcheck(VC,Ve1,VT)
| ! [Ve] :
( ~ valphaEquivalent(Ve,Ve1)
| ~ vtcheck(VC,Ve,VT) ) ),
inference(miniscoping,[status(thm)],[f260]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( vtcheck(X0,X3,X2)
| ~ valphaEquivalent(X1,X3)
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f266,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)
| vlookup(Vx,VC) != vnoType
| Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f267,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)
| vlookup(Vx,VC) != vnoType
| Vx = Vy ),
inference(miniscoping,[status(thm)],[f266]) ).
fof(f268,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X6,X2),vabs(X1,X3,X4),X5)
| ~ vtcheck(X2,vabs(X1,X3,X4),X5)
| vlookup(X0,X2) != vnoType
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f269,plain,
? [Vx,VS,VC,Vy,VS1,VT] :
( ~ vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& vlookup(Vx,VC) = vnoType
& Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f270,plain,
? [Vx,VC,Vy,VS1,VT] :
( ? [VS] : ~ vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& vlookup(Vx,VC) = vnoType
& Vx = Vy ),
inference(miniscoping,[status(thm)],[f269]) ).
fof(f271,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)
& vlookup(sK21_skl,sK22_skl) = vnoType
& 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)],[f270]) ).
fof(f272,plain,
sK21_skl = sK23_skl,
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f273,plain,
vlookup(sK21_skl,sK22_skl) = vnoType,
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f274,plain,
vtcheck(sK22_skl,vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f275,plain,
~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK23_skl,sK24_skl,veabs),sK25_skl),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f424,plain,
! [X0] : visFreeVar(X0,vvar(X0)),
inference(destructive_equality_resolution,[status(thm)],[f92]) ).
fof(f429,plain,
! [X0,X1,X2] :
( visFreeVar(X0,vapp(X1,X2))
| ~ visFreeVar(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f430,plain,
! [X0,X1,X2] :
( visFreeVar(X0,vapp(X2,X1))
| ~ visFreeVar(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f443,plain,
! [X0] : ~ visFreeVar(vgensym(X0),X0),
inference(destructive_equality_resolution,[status(thm)],[f153]) ).
fof(f487,plain,
vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl),
inference(forward_demodulation,[status(thm)],[f272,f274]) ).
fof(f488,plain,
~ vtcheck(vbind(sK21_skl,sK26_skl,sK22_skl),vabs(sK21_skl,sK24_skl,veabs),sK25_skl),
inference(forward_demodulation,[status(thm)],[f272,f275]) ).
fof(f514,plain,
! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0),
inference(resolution,[status(thm)],[f429,f443]) ).
fof(f516,plain,
! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1),
inference(resolution,[status(thm)],[f430,f443]) ).
fof(f532,plain,
! [X0,X1,X2] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0),
inference(resolution,[status(thm)],[f514,f429]) ).
fof(f1077,plain,
! [X0,X1,X2,X3] : ~ visFreeVar(vgensym(vapp(vapp(vapp(X0,X1),X2),X3)),X0),
inference(resolution,[status(thm)],[f532,f429]) ).
fof(f1763,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)],[f262,f488]) ).
fof(f1937,plain,
! [X0,X1,X2] :
( ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| vlookup(sK21_skl,sK22_skl) != vnoType
| sK21_skl = X0
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs)) ),
inference(resolution,[status(thm)],[f1763,f268]) ).
fof(f1940,plain,
! [X0,X1,X2] :
( ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| vnoType != vnoType
| sK21_skl = X0
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs)) ),
inference(forward_demodulation,[status(thm)],[f273,f1937]) ).
fof(f1941,plain,
! [X0,X1,X2] :
( ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| sK21_skl = X0
| ~ valphaEquivalent(vabs(X0,X1,X2),vabs(sK21_skl,sK24_skl,veabs)) ),
inference(trivial_equality_resolution,[status(thm)],[f1940]) ).
fof(f2384,plain,
! [X0,X1,X2] :
( ~ valphaEquivalent(vabs(sK21_skl,sK24_skl,veabs),vabs(X0,X1,X2))
| ~ vtcheck(sK22_skl,vabs(X0,X1,X2),sK25_skl)
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f1941,f253]) ).
fof(f2494,plain,
! [X0] :
( visFreeVar(X0,veabs)
| ~ vtcheck(sK22_skl,vabs(X0,sK24_skl,vsubst(sK21_skl,vvar(X0),veabs)),sK25_skl)
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f2384,f259]) ).
fof(f2502,plain,
! [X0,X1] :
( ~ valphaEquivalent(X1,vabs(X0,sK24_skl,vsubst(sK21_skl,vvar(X0),veabs)))
| ~ vtcheck(sK22_skl,X1,sK25_skl)
| visFreeVar(X0,veabs)
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f2494,f262]) ).
fof(f3582,plain,
! [X0] :
( visFreeVar(X0,veabs)
| ~ vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl)
| visFreeVar(X0,veabs)
| sK21_skl = X0 ),
inference(resolution,[status(thm)],[f2502,f259]) ).
fof(f3590,plain,
! [X0] :
( ~ vtcheck(sK22_skl,vabs(sK21_skl,sK24_skl,veabs),sK25_skl)
| visFreeVar(X0,veabs)
| sK21_skl = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f3582]) ).
fof(f3591,plain,
! [X0] :
( visFreeVar(X0,veabs)
| sK21_skl = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f3590,f487]) ).
fof(f3613,plain,
! [X0] : sK21_skl = vgensym(vapp(X0,veabs)),
inference(resolution,[status(thm)],[f3591,f516]) ).
fof(f3622,plain,
! [X0] : ~ visFreeVar(sK21_skl,X0),
inference(paramodulation,[status(thm)],[f3613,f1077]) ).
fof(f3635,plain,
$false,
inference(resolution,[status(thm)],[f3622,f424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM140+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 : n010.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 14:18:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 8.56/1.61 % Refutation found
% 8.56/1.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.56/1.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.49/1.65 % Elapsed time: 1.258362 seconds
% 8.49/1.65 % CPU time: 9.600036 seconds
% 8.49/1.65 % Total memory used: 199.495 MB
% 8.49/1.65 % Net memory used: 190.149 MB
%------------------------------------------------------------------------------