%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 7 unt; 4 def)
% Number of atoms : 158 ( 41 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 187 ( 80 ~; 77 |; 18 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 183 ( 169 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [Ve,Vx,VVar0,VExp0,VExp1,RESULT,Vy,VT,Ve1] :
( ( VExp1 = vabs(Vy,VT,Ve1)
& VExp0 = Ve
& VVar0 = Vx )
=> ( Vx = Vy
=> ( RESULT = vsubst(VVar0,VExp0,VExp1)
=> RESULT = vabs(Vy,VT,Ve1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [VT,VC,Vx,Ve,Vy,VS,Ve1,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,Ve1),VT2)
& vtcheck(VC,Ve,VT)
& Vx = Vy )
=> vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,Ve1)),VT2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT)
& ~ visFreeVar(Vy,Ve)
& Vx != Vy )
=> vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT)
& visFreeVar(Vy,Ve)
& Vx != Vy )
=> vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,conjecture,
! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT) )
=> vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
~ ! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( ( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT) )
=> vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f163,plain,
! [Ve,Vx,VVar0,VExp0,VExp1,RESULT,Vy,VT,Ve1] :
( RESULT = vabs(Vy,VT,Ve1)
| RESULT != vsubst(VVar0,VExp0,VExp1)
| Vx != Vy
| VExp1 != vabs(Vy,VT,Ve1)
| VExp0 != Ve
| VVar0 != Vx ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f164,plain,
! [Vx,VVar0,VExp0,VExp1,Vy,VT,Ve1] :
( ! [RESULT] :
( RESULT = vabs(Vy,VT,Ve1)
| RESULT != vsubst(VVar0,VExp0,VExp1) )
| Vx != Vy
| VExp1 != vabs(Vy,VT,Ve1)
| ! [Ve] : VExp0 != Ve
| VVar0 != Vx ),
inference(miniscoping,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( X8 = vabs(X5,X6,X7)
| X8 != vsubst(X0,X2,X4)
| X1 != X5
| X4 != vabs(X5,X6,X7)
| X2 != X3
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f263,plain,
! [VT,VC,Vx,Ve,Vy,VS,Ve1,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,Ve1)),VT2)
| ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,Ve1),VT2)
| ~ vtcheck(VC,Ve,VT)
| Vx != Vy ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f264,plain,
! [VC,Vx,Ve,Vy,VS,Ve1,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,Ve1)),VT2)
| ! [VT] :
( ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,Ve1),VT2)
| ~ vtcheck(VC,Ve,VT)
| Vx != Vy ) ),
inference(miniscoping,[status(thm)],[f263]) ).
fof(f265,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(X2,vsubst(X0,X3,vabs(X1,X5,X6)),X7)
| ~ vtcheck(vbind(X0,X4,X2),vabs(X1,X5,X6),X7)
| ~ vtcheck(X2,X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f266,plain,
! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
| ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
| ~ vtcheck(VC,Ve,VT)
| visFreeVar(Vy,Ve)
| Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f267,plain,
! [VC,Vx,Ve,Vy,VS,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
| ! [VT] :
( ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
| ~ vtcheck(VC,Ve,VT)
| visFreeVar(Vy,Ve)
| Vx = Vy ) ),
inference(miniscoping,[status(thm)],[f266]) ).
fof(f268,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X3,vsubst(X0,X2,vabs(X1,X5,veabs)),X6)
| ~ vtcheck(vbind(X0,X4,X3),vabs(X1,X5,veabs),X6)
| ~ vtcheck(X3,X2,X4)
| visFreeVar(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f269,plain,
! [VT,VC,Vx,Ve,Vy,VS,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
| ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
| ~ vtcheck(VC,Ve,VT)
| ~ visFreeVar(Vy,Ve)
| Vx = Vy ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f270,plain,
! [VC,Vx,Ve,Vy,VS,VT2] :
( vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
| ! [VT] :
( ~ vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
| ~ vtcheck(VC,Ve,VT)
| ~ visFreeVar(Vy,Ve)
| Vx = Vy ) ),
inference(miniscoping,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X3,vsubst(X0,X2,vabs(X1,X5,veabs)),X6)
| ~ vtcheck(vbind(X0,X4,X3),vabs(X1,X5,veabs),X6)
| ~ vtcheck(X3,X2,X4)
| ~ visFreeVar(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f272,plain,
? [VT,VC,Vx,Ve,Vy,VS,VT2] :
( ~ vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
& vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f273,plain,
? [VC,Vx,Ve,Vy,VS,VT2] :
( ~ vtcheck(VC,vsubst(Vx,Ve,vabs(Vy,VS,veabs)),VT2)
& ? [VT] :
( vtcheck(vbind(Vx,VT,VC),vabs(Vy,VS,veabs),VT2)
& vtcheck(VC,Ve,VT) ) ),
inference(miniscoping,[status(thm)],[f272]) ).
fof(f274,plain,
( ~ vtcheck(sK21_skl,vsubst(sK22_skl,sK23_skl,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl)
& vtcheck(vbind(sK22_skl,sK27_skl,sK21_skl),vabs(sK24_skl,sK25_skl,veabs),sK26_skl)
& vtcheck(sK21_skl,sK23_skl,sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(VC,sK21_skl),skolemize(Vx,sK22_skl),skolemize(Ve,sK23_skl),skolemize(Vy,sK24_skl),skolemize(VS,sK25_skl),skolemize(VT2,sK26_skl),skolemize(VT,sK27_skl)],[f273]) ).
fof(f275,plain,
vtcheck(sK21_skl,sK23_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
vtcheck(vbind(sK22_skl,sK27_skl,sK21_skl),vabs(sK24_skl,sK25_skl,veabs),sK26_skl),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,plain,
~ vtcheck(sK21_skl,vsubst(sK22_skl,sK23_skl,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f449,plain,
! [X0,X1,X2,X3] : vsubst(X0,X1,vabs(X0,X2,X3)) = vabs(X0,X2,X3),
inference(destructive_equality_resolution,[status(thm)],[f165]) ).
fof(f473,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X0,vsubst(X3,X1,vabs(X3,X4,X5)),X6)
| ~ vtcheck(vbind(X3,X2,X0),vabs(X3,X4,X5),X6)
| ~ vtcheck(X0,X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f265]) ).
fof(f500,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X0,vabs(X3,X4,X5),X6)
| ~ vtcheck(vbind(X3,X2,X0),vabs(X3,X4,X5),X6)
| ~ vtcheck(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f449,f473]) ).
fof(f502,definition,
( sQ0_spl
<=> sK22_skl = sK24_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( ~ sQ0_spl
| sK22_skl = sK24_skl ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f509,plain,
( ~ sQ0_spl
| ~ vtcheck(sK21_skl,vsubst(sK24_skl,sK23_skl,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f277]) ).
fof(f510,plain,
( ~ sQ0_spl
| vtcheck(vbind(sK24_skl,sK27_skl,sK21_skl),vabs(sK24_skl,sK25_skl,veabs),sK26_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f276]) ).
fof(f511,plain,
( ~ sQ0_spl
| ~ vtcheck(sK21_skl,vabs(sK24_skl,sK25_skl,veabs),sK26_skl) ),
inference(forward_demodulation,[status(thm)],[f449,f509]) ).
fof(f534,plain,
! [X0] :
( ~ sQ0_spl
| vtcheck(sK21_skl,vabs(sK24_skl,sK25_skl,veabs),sK26_skl)
| ~ vtcheck(sK21_skl,X0,sK27_skl) ),
inference(resolution,[status(thm)],[f510,f500]) ).
fof(f542,definition,
! [X0] :
( sQ4_spl
<=> ~ vtcheck(sK21_skl,X0,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f543,plain,
! [X0] :
( ~ sQ4_spl
| ~ vtcheck(sK21_skl,X0,sK27_skl) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ5_spl
<=> vtcheck(sK21_skl,vabs(sK24_skl,sK25_skl,veabs),sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ5_spl
| vtcheck(sK21_skl,vabs(sK24_skl,sK25_skl,veabs),sK26_skl) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,plain,
( ~ sQ0_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f534,f542,f545,f502]) ).
fof(f549,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f275,f543]) ).
fof(f550,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f511]) ).
fof(f552,plain,
( ~ sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f574,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X2,vsubst(X0,X3,vabs(X1,X5,veabs)),X6)
| ~ vtcheck(vbind(X0,X4,X2),vabs(X1,X5,veabs),X6)
| ~ vtcheck(X2,X3,X4)
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f268]) ).
fof(f575,plain,
! [X0] :
( vtcheck(sK21_skl,vsubst(sK22_skl,X0,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl)
| ~ vtcheck(sK21_skl,X0,sK27_skl)
| sK22_skl = sK24_skl ),
inference(resolution,[status(thm)],[f276,f574]) ).
fof(f576,definition,
! [X0] :
( sQ6_spl
<=> ( vtcheck(sK21_skl,vsubst(sK22_skl,X0,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl)
| ~ vtcheck(sK21_skl,X0,sK27_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f577,plain,
! [X0] :
( ~ sQ6_spl
| vtcheck(sK21_skl,vsubst(sK22_skl,X0,vabs(sK24_skl,sK25_skl,veabs)),sK26_skl)
| ~ vtcheck(sK21_skl,X0,sK27_skl) ),
inference(component_clause,[status(thm)],[f576]) ).
fof(f579,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f575,f502,f576]) ).
fof(f595,plain,
( ~ sQ6_spl
| ~ vtcheck(sK21_skl,sK23_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f577,f277]) ).
fof(f596,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f275]) ).
fof(f597,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f598,plain,
$false,
inference(sat_refutation,[status(thm)],[f548,f550,f552,f579,f597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 14:19:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.062545 seconds
% 0.10/0.43 % CPU time: 0.185705 seconds
% 0.10/0.43 % Total memory used: 105.150 MB
% 0.10/0.43 % Net memory used: 104.908 MB
%------------------------------------------------------------------------------