%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM136+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 01:03:39 PM UTC 2026
% Result : Theorem 80.38s 16.15s
% Output : Proof 80.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 12 unt; 0 def)
% Number of atoms : 191 ( 75 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 191 ( 65 ~; 82 |; 32 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 226 ( 19 sgn 141 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,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',qtd25) ).
fof(f53_nnf,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(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [VC,Ve,VT] :
( ( vtcheck(VC,sk72(Ve,VT,VC),sk73(Ve,VT,VC))
& vtcheck(VC,sk71(Ve,VT,VC),varrow(sk73(Ve,VT,VC),VT))
& Ve = vapp(sk71(Ve,VT,VC),sk72(Ve,VT,VC)) )
| ( vtcheck(vbind(sk67(Ve,VT,VC),sk69(Ve,VT,VC),VC),sk68(Ve,VT,VC),sk70(Ve,VT,VC))
& VT = varrow(sk69(Ve,VT,VC),sk70(Ve,VT,VC))
& Ve = vabs(sk67(Ve,VT,VC),sk69(Ve,VT,VC),sk68(Ve,VT,VC)) )
| ( vlookup(sk66(Ve,VT,VC),VC) = vsomeType(VT)
& Ve = vvar(sk66(Ve,VT,VC)) )
| ~ vtcheck(VC,Ve,VT) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk66,sk67,sk68,sk69,sk70,sk71,sk72,sk73])],[f53_nnf]) ).
cnf(c307,plain,
( X0 = vapp(sk71(X0,X1,X2),sk72(X0,X1,X2))
| vtcheck(vbind(sk67(X0,X1,X2),sk69(X0,X1,X2),X2),sk68(X0,X1,X2),sk70(X0,X1,X2))
| X0 = vvar(sk66(X0,X1,X2))
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
fof(f56,conjecture,
! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) )
=> vtcheck(VC,vabs(Vy,VS1,veabs),VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd28) ).
fof(f56_neg,negated_conjecture,
~ ! [Vx,VS,VC,Vy,VS1,VT] :
( ( vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) )
=> vtcheck(VC,vabs(Vy,VS1,veabs),VT) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f56_nnf,plain,
? [Vx,VS,VC,Vy,VS1,VT] :
( ~ vtcheck(VC,vabs(Vy,VS1,veabs),VT)
& vtcheck(vbind(Vx,VS,VC),vabs(Vy,VS1,veabs),VT)
& ~ visFreeVar(Vx,vabs(Vy,VS1,veabs)) ),
inference(nnf_transformation,[status(thm)],[f56_neg]) ).
fof(f56_sk,plain,
( ~ vtcheck(sk76,vabs(sk77,sk78,veabs),sk79)
& vtcheck(vbind(sk74,sk75,sk76),vabs(sk77,sk78,veabs),sk79)
& ~ visFreeVar(sk74,vabs(sk77,sk78,veabs)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk74,sk75,sk76,sk77,sk78,sk79])],[f56_nnf]) ).
cnf(c322,plain,
vtcheck(vbind(sk74,sk75,sk76),vabs(sk77,sk78,veabs),sk79),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(p3230,plain,
( vabs(sk77,sk78,veabs) = vapp(sk71(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)),sk72(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| vtcheck(vbind(sk77,sk78,vbind(sk74,sk75,sk76)),veabs,sk70(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| vabs(sk77,sk78,veabs) = vvar(sk66(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[c307,c322]) ).
fof(f5,axiom,
! [VVar0,VTyp0,VExp0,VExp1,VExp2] : vabs(VVar0,VTyp0,VExp0) != vapp(VExp1,VExp2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd5) ).
fof(f5_nnf,plain,
! [VVar0,VTyp0,VExp0,VExp1,VExp2] : vabs(VVar0,VTyp0,VExp0) != vapp(VExp1,VExp2),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [VVar0,VTyp0,VExp0,VExp1,VExp2] : vabs(VVar0,VTyp0,VExp0) != vapp(VExp1,VExp2),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p3680,plain,
( vtcheck(vbind(sk77,sk78,vbind(sk74,sk75,sk76)),veabs,sk70(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| vabs(sk77,sk78,veabs) = vvar(sk66(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p3230,c11]) ).
fof(f26,axiom,
! [Vy,VTy,Vx,VTx,VC,Ve,VT] :
( ( vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
& Vx != Vy )
=> vtcheck(vbind(Vy,VTy,vbind(Vx,VTx,VC)),Ve,VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd14) ).
fof(f26_nnf,plain,
! [Vy,VTy,Vx,VTx,VC,Ve,VT] :
( vtcheck(vbind(Vy,VTy,vbind(Vx,VTx,VC)),Ve,VT)
| ~ vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
| Vx = Vy ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [Vx,Vy,VTx,VTy,VC,Ve,VT] :
( vtcheck(vbind(Vy,VTy,vbind(Vx,VTx,VC)),Ve,VT)
| ~ vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
| Vx = Vy ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c90,plain,
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X2 = X0 ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p3682,plain,
( vtcheck(vbind(sk74,sk75,vbind(sk77,sk78,sk76)),veabs,sk70(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| sk77 = sk74
| vabs(sk77,sk78,veabs) = vvar(sk66(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p3680,c90]) ).
fof(f55,axiom,
! [Vx,VS,VC,VT] :
( ( vtcheck(vbind(Vx,VS,VC),veabs,VT)
& ~ visFreeVar(Vx,veabs) )
=> vtcheck(VC,veabs,VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd27) ).
fof(f55_nnf,plain,
! [Vx,VS,VC,VT] :
( vtcheck(VC,veabs,VT)
| ~ vtcheck(vbind(Vx,VS,VC),veabs,VT)
| visFreeVar(Vx,veabs) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [Vx,VS,VC,VT] :
( vtcheck(VC,veabs,VT)
| ~ vtcheck(vbind(Vx,VS,VC),veabs,VT)
| visFreeVar(Vx,veabs) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c320,plain,
( vtcheck(X2,veabs,X3)
| ~ vtcheck(vbind(X0,X1,X2),veabs,X3)
| visFreeVar(X0,veabs) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(p4082,plain,
( vtcheck(vbind(sk77,sk78,sk76),veabs,sk70(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| visFreeVar(sk74,veabs)
| sk77 = sk74
| vabs(sk77,sk78,veabs) = vvar(sk66(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p3682,c320]) ).
fof(f51,axiom,
! [VC,Vx,Ve,VS,VT] :
( vtcheck(vbind(Vx,VS,VC),Ve,VT)
=> vtcheck(VC,vabs(Vx,VS,Ve),varrow(VS,VT)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd23) ).
fof(f51_nnf,plain,
! [VC,Vx,Ve,VS,VT] :
( vtcheck(VC,vabs(Vx,VS,Ve),varrow(VS,VT))
| ~ vtcheck(vbind(Vx,VS,VC),Ve,VT) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [Vx,VS,VC,Ve,VT] :
( vtcheck(VC,vabs(Vx,VS,Ve),varrow(VS,VT))
| ~ vtcheck(vbind(Vx,VS,VC),Ve,VT) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c299,plain,
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p4096,plain,
( vtcheck(sk76,vabs(sk77,sk78,veabs),sk79)
| visFreeVar(sk74,veabs)
| sk77 = sk74
| vabs(sk77,sk78,veabs) = vvar(sk66(vabs(sk77,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p4082,c299]) ).
fof(f7,axiom,
! [Vx,VExp0] :
( VExp0 = vvar(Vx)
=> ~ visValue(VExp0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1) ).
fof(f7_nnf,plain,
! [Vx,VExp0] :
( ~ visValue(VExp0)
| VExp0 != vvar(Vx) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [VExp0,Vx] :
( ~ visValue(VExp0)
| VExp0 != vvar(Vx) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
( ~ visValue(X1)
| X1 != vvar(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p4112,plain,
( ~ visValue(vabs(sk77,sk78,veabs))
| vtcheck(sk76,vabs(sk77,sk78,veabs),sk79)
| visFreeVar(sk74,veabs)
| sk77 = sk74 ),
inference(resolution,[status(thm)],[p4096,c13]) ).
fof(f6,axiom,
! [Vx,VS,Ve,VExp0] :
( VExp0 = vabs(Vx,VS,Ve)
=> visValue(VExp0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).
fof(f6_nnf,plain,
! [Vx,VS,Ve,VExp0] :
( visValue(VExp0)
| VExp0 != vabs(Vx,VS,Ve) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [VExp0,Vx,VS,Ve] :
( visValue(VExp0)
| VExp0 != vabs(Vx,VS,Ve) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c12,plain,
( visValue(X3)
| X3 != vabs(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p341,plain,
visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(p4454,plain,
( vtcheck(sk76,vabs(sk77,sk78,veabs),sk79)
| visFreeVar(sk74,veabs)
| sk77 = sk74 ),
inference(resolution,[status(thm)],[p4112,p341]) ).
cnf(c323,plain,
~ vtcheck(sk76,vabs(sk77,sk78,veabs),sk79),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(p4464,plain,
( visFreeVar(sk74,veabs)
| sk77 = sk74 ),
inference(resolution,[status(thm)],[p4454,c323]) ).
fof(f10,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',isFreeVar1) ).
fof(f10_nnf,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(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [VVar0,Vv,VExp0,Vx,VT,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(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c17,plain,
( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4
| X2 != vabs(X3,X0,X5)
| X1 != X4 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p352,plain,
( visFreeVar(X4,X0)
| ~ visFreeVar(X4,X3)
| X1 = X4
| X0 != vabs(X1,X2,X3) ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(p1085,plain,
( visFreeVar(X1,vabs(X0,X3,X2))
| ~ visFreeVar(X1,X2)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[p352]) ).
cnf(p4467,plain,
( visFreeVar(sk74,vabs(X0,X1,veabs))
| X0 = sk74
| sk77 = sk74 ),
inference(resolution,[status(thm)],[p4464,p1085]) ).
cnf(c321,plain,
~ visFreeVar(sk74,vabs(sk77,sk78,veabs)),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(p4537,plain,
( sk77 = sk74
| sk77 = sk74 ),
inference(resolution,[status(thm)],[p4467,c321]) ).
cnf(p4541,plain,
sk77 = sk74,
inference(factoring,[status(thm)],[p4537]) ).
cnf(p4566,plain,
( vtcheck(vbind(sk74,sk78,vbind(sk74,sk75,sk76)),veabs,sk70(vabs(sk74,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| vabs(sk74,sk78,veabs) = vvar(sk66(vabs(sk74,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(demodulation,[status(thm)],[p4541,p3680]) ).
fof(f25,axiom,
! [Vy,VTy,Vx,VTx,VC,Ve,VT] :
( ( vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
& Vx = Vy )
=> vtcheck(vbind(Vx,VTx,VC),Ve,VT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd13) ).
fof(f25_nnf,plain,
! [Vy,VTy,Vx,VTx,VC,Ve,VT] :
( vtcheck(vbind(Vx,VTx,VC),Ve,VT)
| ~ vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
| Vx != Vy ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Vx,Vy,VTx,VTy,VC,Ve,VT] :
( vtcheck(vbind(Vx,VTx,VC),Ve,VT)
| ~ vtcheck(vbind(Vx,VTx,vbind(Vy,VTy,VC)),Ve,VT)
| Vx != Vy ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c89,plain,
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X2 != X0 ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p909,plain,
( vtcheck(vbind(X0,X1,X3),X4,X5)
| ~ vtcheck(vbind(X0,X1,vbind(X0,X2,X3)),X4,X5) ),
inference(equality_resolution,[status(thm)],[c89]) ).
cnf(p4689,plain,
( vtcheck(vbind(sk74,sk78,sk76),veabs,sk70(vabs(sk74,sk78,veabs),sk79,vbind(sk74,sk75,sk76)))
| vabs(sk74,sk78,veabs) = vvar(sk66(vabs(sk74,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p4566,p909]) ).
cnf(p4691,plain,
( vtcheck(sk76,vabs(sk74,sk78,veabs),sk79)
| vabs(sk74,sk78,veabs) = vvar(sk66(vabs(sk74,sk78,veabs),sk79,vbind(sk74,sk75,sk76))) ),
inference(resolution,[status(thm)],[p4689,c299]) ).
cnf(p4713,plain,
( ~ visValue(vabs(sk74,sk78,veabs))
| vtcheck(sk76,vabs(sk74,sk78,veabs),sk79) ),
inference(resolution,[status(thm)],[p4691,c13]) ).
cnf(p5057,plain,
vtcheck(sk76,vabs(sk74,sk78,veabs),sk79),
inference(resolution,[status(thm)],[p4713,p341]) ).
cnf(p4543,plain,
~ vtcheck(sk76,vabs(sk74,sk78,veabs),sk79),
inference(demodulation,[status(thm)],[p4541,c323]) ).
cnf(p5075,plain,
$false,
inference(resolution,[status(thm)],[p5057,p4543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM136+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/5.87 % Computer : n013.cluster.edu
% 0.17/5.87 % Model : x86_64 x86_64
% 0.17/5.87 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.87 % Memory : 8046.5625MB
% 0.17/5.87 % OS : Linux 6.8.0-71-generic
% 0.17/5.87 % CPULimit : 300
% 0.17/5.87 % WCLimit : 300
% 0.17/5.87 % DateTime : Fri Sep 25 07:55:43 UTC 2026
% 0.17/5.87 % CPUTime :
% 0.17/5.88 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 80.38/16.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.38/16.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------