%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM126+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Tue Sep 29 09:39:37 AM UTC 2026
% Result : Theorem 7.73s 1.95s
% Output : Refutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 111 ( 21 unt; 6 def)
% Number of atoms : 329 ( 94 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 351 ( 133 ~; 143 |; 58 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 259 ( 0 sgn 205 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
=> ( X0 = X2
& X1 = X3 ) )
& ( ( X0 = X2
& X1 = X3 )
=> vapp(X0,X1) = vapp(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-app') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( X0 = X3
& X1 = vapp(X2,X4) )
=> ( ( ( visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
=> visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X2)
| visFreeVar(X3,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f53,axiom,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X2,varrow(X0,X4))
& vtcheck(X1,X3,X0) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-app') ).
fof(f54,axiom,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X3,X4,X5,X6] :
( X0 = vabs(X3,X5,X4)
& X1 = varrow(X5,X6)
& vtcheck(vbind(X3,X5,X2),X4,X6) )
| ? [X7,X4,X8] :
( X0 = vapp(X7,X4)
& vtcheck(X2,X7,varrow(X8,X1))
& vtcheck(X2,X4,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-inv') ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,ve1app)
& vtcheck(X2,ve1app,X3) )
=> vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-app-IH1') ).
fof(f58,axiom,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,ve2app)
& vtcheck(X2,ve2app,X3) )
=> vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-app-IH2') ).
fof(f59,conjecture,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(X2,vapp(ve1app,ve2app),X3) )
=> vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-app') ).
fof(f60,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(X2,vapp(ve1app,ve2app),X3) )
=> vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) ) ) ),
inference(rectify,[],[f54]) ).
fof(f65,plain,
? [X0,X1,X2,X3] :
( ~ vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
& ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(X2,vapp(ve1app,ve2app),X3) ),
inference(ennf_transformation,[],[f60]) ).
fof(f66,plain,
? [X0,X1,X2,X3] :
( ~ vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3)
& ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(X2,vapp(ve1app,ve2app),X3) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),ve2app,X3)
| visFreeVar(X0,ve2app)
| ~ vtcheck(X2,ve2app,X3) ),
inference(ennf_transformation,[],[f58]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),ve2app,X3)
| visFreeVar(X0,ve2app)
| ~ vtcheck(X2,ve2app,X3) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),ve1app,X3)
| visFreeVar(X0,ve1app)
| ~ vtcheck(X2,ve1app,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),ve1app,X3)
| visFreeVar(X0,ve1app)
| ~ vtcheck(X2,ve1app,X3) ),
inference(flattening,[],[f69]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X2)
& ~ visFreeVar(X3,X4) ) )
& ( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X2)
& ~ visFreeVar(X3,X4) ) )
& ( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(flattening,[],[f80]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ vtcheck(X2,X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ vtcheck(X2,X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f89,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0) ),
inference(flattening,[],[f88]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X2
& X1 = X3 )
| vapp(X0,X1) != vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
| X0 != X2
| X1 != X3 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X2
& X1 = X3 )
| vapp(X0,X1) != vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
| X0 != X2
| X1 != X3 ) ),
inference(flattening,[],[f105]) ).
fof(f129,definition,
! [X0,X1,X2] :
( ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ sP5(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| sP5(X0,X1,X2)
| ~ vtcheck(X2,X0,X1) ),
inference(definition_folding,[],[f87,f129]) ).
fof(f140,plain,
( ~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16)
& ~ visFreeVar(sK13,vapp(ve1app,ve2app))
& vtcheck(sK15,vapp(ve1app,ve2app),sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16)],[f66]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ sP5(X0,X1,X2) ),
inference(nnf_transformation,[],[f129]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vapp(X3,X4) = X0
& vtcheck(X2,X3,varrow(X5,X1))
& vtcheck(X2,X4,X5) )
| ~ sP5(X0,X1,X2) ),
inference(rectify,[],[f157]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( vapp(sK43(X0,X1,X2),sK44(X0,X1,X2)) = X0
& vtcheck(X2,sK43(X0,X1,X2),varrow(sK45(X0,X1,X2),X1))
& vtcheck(X2,sK44(X0,X1,X2),sK45(X0,X1,X2)) )
| ~ sP5(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43,sK44,sK45]),skolemize(X3,sK43(X0,X1,X2)),skolemize(X4,sK44(X0,X1,X2)),skolemize(X5,sK45(X0,X1,X2))],[f158]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ( vvar(sK46(X0,X1,X2)) = X0
& vsomeType(X1) = vlookup(sK46(X0,X1,X2),X2) )
| ( vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X0
& varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1
& vtcheck(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X2),sK48(X0,X1,X2),sK50(X0,X1,X2)) )
| sP5(X0,X1,X2)
| ~ vtcheck(X2,X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49,sK50]),skolemize(X3,sK46(X0,X1,X2)),skolemize(X4,sK47(X0,X1,X2)),skolemize(X5,sK48(X0,X1,X2)),skolemize(X6,sK49(X0,X1,X2)),skolemize(X7,sK50(X0,X1,X2))],[f130]) ).
fof(f186,plain,
vtcheck(sK15,vapp(ve1app,ve2app),sK16),
inference(cnf_transformation,[],[f140]) ).
fof(f187,plain,
~ visFreeVar(sK13,vapp(ve1app,ve2app)),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
~ vtcheck(vbind(sK13,sK14,sK15),vapp(ve1app,ve2app),sK16),
inference(cnf_transformation,[],[f140]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),ve2app,X3)
| visFreeVar(X0,ve2app)
| ~ vtcheck(X2,ve2app,X3) ),
inference(cnf_transformation,[],[f68]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),ve1app,X3)
| visFreeVar(X0,ve1app)
| ~ vtcheck(X2,ve1app,X3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f227,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X0,X1)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f228,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f229,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f235,plain,
! [X2,X0,X1] :
( vtcheck(X2,sK44(X0,X1,X2),sK45(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f236,plain,
! [X2,X0,X1] :
( vtcheck(X2,sK43(X0,X1,X2),varrow(sK45(X0,X1,X2),X1))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vapp(sK43(X0,X1,X2),sK44(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f243,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X0
| vvar(sK46(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
fof(f244,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f280,plain,
! [X2,X3,X0,X1,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[],[f6]) ).
fof(f281,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f106]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f106]) ).
fof(f322,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f229]) ).
fof(f323,plain,
! [X2,X3,X4] :
( ~ visFreeVar(X3,X2)
| visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f322]) ).
fof(f324,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f228]) ).
fof(f325,plain,
! [X2,X3,X4] :
( ~ visFreeVar(X3,X4)
| visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f324]) ).
fof(f326,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X3,X1)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f227]) ).
fof(f327,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f326]) ).
fof(f415,plain,
! [X0] :
( visFreeVar(sK13,X0)
| ~ visFreeVar(sK13,vapp(vapp(ve1app,ve2app),X0)) ),
inference(resolution,[],[f327,f187]) ).
fof(f428,plain,
! [X0,X1] :
( visFreeVar(sK13,vapp(X0,X1))
| ~ visFreeVar(sK13,vapp(vapp(ve1app,ve2app),X0)) ),
inference(resolution,[],[f415,f323]) ).
fof(f448,plain,
~ visFreeVar(sK13,vapp(vapp(ve1app,ve2app),ve1app)),
inference(resolution,[],[f428,f187]) ).
fof(f796,plain,
! [X0] :
( ~ vtcheck(vbind(sK13,sK14,sK15),ve1app,varrow(X0,sK16))
| ~ vtcheck(vbind(sK13,sK14,sK15),ve2app,X0) ),
inference(resolution,[],[f244,f188]) ).
fof(f798,plain,
! [X0] :
( ~ vtcheck(vbind(sK13,sK14,sK15),ve2app,X0)
| visFreeVar(sK13,ve1app)
| ~ vtcheck(sK15,ve1app,varrow(X0,sK16)) ),
inference(resolution,[],[f796,f190]) ).
fof(f801,definition,
( spl91_1
<=> visFreeVar(sK13,ve1app) ),
introduced(definition,[new_symbols(definition,[spl91_1])],[avatar_definition]) ).
fof(f803,plain,
( visFreeVar(sK13,ve1app)
| ~ spl91_1 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f805,definition,
( spl91_2
<=> ! [X0] :
( ~ vtcheck(vbind(sK13,sK14,sK15),ve2app,X0)
| ~ vtcheck(sK15,ve1app,varrow(X0,sK16)) ) ),
introduced(definition,[new_symbols(definition,[spl91_2])],[avatar_definition]) ).
fof(f806,plain,
( ! [X0] :
( ~ vtcheck(sK15,ve1app,varrow(X0,sK16))
| ~ vtcheck(vbind(sK13,sK14,sK15),ve2app,X0) )
| ~ spl91_2 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f807,plain,
( spl91_1
| spl91_2 ),
inference(avatar_split_clause,[],[f798,f805,f801]) ).
fof(f1136,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| vvar(sK46(X0,X1,X2)) = X0
| vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X0
| vapp(sK43(X0,X1,X2),sK44(X0,X1,X2)) = X0 ),
inference(resolution,[],[f243,f237]) ).
fof(f2314,plain,
( vapp(ve1app,ve2app) = vvar(sK46(vapp(ve1app,ve2app),sK16,sK15))
| vapp(ve1app,ve2app) = vabs(sK47(vapp(ve1app,ve2app),sK16,sK15),sK49(vapp(ve1app,ve2app),sK16,sK15),sK48(vapp(ve1app,ve2app),sK16,sK15))
| vapp(ve1app,ve2app) = vapp(sK43(vapp(ve1app,ve2app),sK16,sK15),sK44(vapp(ve1app,ve2app),sK16,sK15)) ),
inference(resolution,[],[f1136,f186]) ).
fof(f2332,plain,
( vapp(ve1app,ve2app) = vabs(sK47(vapp(ve1app,ve2app),sK16,sK15),sK49(vapp(ve1app,ve2app),sK16,sK15),sK48(vapp(ve1app,ve2app),sK16,sK15))
| vapp(ve1app,ve2app) = vapp(sK43(vapp(ve1app,ve2app),sK16,sK15),sK44(vapp(ve1app,ve2app),sK16,sK15)) ),
inference(forward_subsumption_resolution,[],[f2314,f281]) ).
fof(f2335,plain,
vapp(ve1app,ve2app) = vapp(sK43(vapp(ve1app,ve2app),sK16,sK15),sK44(vapp(ve1app,ve2app),sK16,sK15)),
inference(forward_subsumption_resolution,[],[f2332,f280]) ).
fof(f3010,plain,
! [X0,X1] :
( vapp(X0,X1) != vapp(ve1app,ve2app)
| sK44(vapp(ve1app,ve2app),sK16,sK15) = X1 ),
inference(superposition,[],[f283,f2335]) ).
fof(f3012,plain,
! [X0,X1] :
( vapp(X0,X1) != vapp(ve1app,ve2app)
| sK43(vapp(ve1app,ve2app),sK16,sK15) = X0 ),
inference(superposition,[],[f284,f2335]) ).
fof(f3136,definition,
( spl91_12
<=> visFreeVar(sK13,ve2app) ),
introduced(definition,[new_symbols(definition,[spl91_12])],[avatar_definition]) ).
fof(f3137,plain,
( ~ visFreeVar(sK13,ve2app)
| spl91_12 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f3138,plain,
( visFreeVar(sK13,ve2app)
| ~ spl91_12 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f3143,plain,
( ! [X0] : visFreeVar(sK13,vapp(X0,ve2app))
| ~ spl91_12 ),
inference(resolution,[],[f3138,f325]) ).
fof(f3149,plain,
( $false
| ~ spl91_12 ),
inference(resolution,[],[f3143,f187]) ).
fof(f3178,plain,
~ spl91_12,
inference(avatar_contradiction_clause,[],[f3149]) ).
fof(f3221,plain,
( ! [X0] : visFreeVar(sK13,vapp(X0,ve1app))
| ~ spl91_1 ),
inference(resolution,[],[f803,f325]) ).
fof(f3243,plain,
( $false
| ~ spl91_1 ),
inference(resolution,[],[f3221,f448]) ).
fof(f3254,plain,
~ spl91_1,
inference(avatar_contradiction_clause,[],[f3243]) ).
fof(f5528,plain,
ve2app = sK44(vapp(ve1app,ve2app),sK16,sK15),
inference(equality_resolution,[],[f3010]) ).
fof(f5581,plain,
( vtcheck(sK15,ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15))
| ~ sP5(vapp(ve1app,ve2app),sK16,sK15) ),
inference(superposition,[],[f235,f5528]) ).
fof(f5583,definition,
( spl91_36
<=> sP5(vapp(ve1app,ve2app),sK16,sK15) ),
introduced(definition,[new_symbols(definition,[spl91_36])],[avatar_definition]) ).
fof(f5584,plain,
( sP5(vapp(ve1app,ve2app),sK16,sK15)
| ~ spl91_36 ),
inference(avatar_component_clause,[],[f5583]) ).
fof(f5585,plain,
( ~ sP5(vapp(ve1app,ve2app),sK16,sK15)
| spl91_36 ),
inference(avatar_component_clause,[],[f5583]) ).
fof(f5587,definition,
( spl91_37
<=> vtcheck(sK15,ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl91_37])],[avatar_definition]) ).
fof(f5589,plain,
( vtcheck(sK15,ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15))
| ~ spl91_37 ),
inference(avatar_component_clause,[],[f5587]) ).
fof(f5590,plain,
( ~ spl91_36
| spl91_37 ),
inference(avatar_split_clause,[],[f5581,f5587,f5583]) ).
fof(f5605,plain,
( vapp(ve1app,ve2app) = vabs(sK47(vapp(ve1app,ve2app),sK16,sK15),sK49(vapp(ve1app,ve2app),sK16,sK15),sK48(vapp(ve1app,ve2app),sK16,sK15))
| vapp(ve1app,ve2app) = vvar(sK46(vapp(ve1app,ve2app),sK16,sK15))
| ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16)
| spl91_36 ),
inference(resolution,[],[f5585,f243]) ).
fof(f5610,plain,
( vapp(ve1app,ve2app) = vvar(sK46(vapp(ve1app,ve2app),sK16,sK15))
| ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16)
| spl91_36 ),
inference(forward_subsumption_resolution,[],[f5605,f280]) ).
fof(f5622,plain,
( ~ vtcheck(sK15,vapp(ve1app,ve2app),sK16)
| spl91_36 ),
inference(forward_subsumption_resolution,[],[f5610,f281]) ).
fof(f5625,plain,
( $false
| spl91_36 ),
inference(forward_subsumption_resolution,[],[f5622,f186]) ).
fof(f5626,plain,
spl91_36,
inference(avatar_contradiction_clause,[],[f5625]) ).
fof(f5753,plain,
ve1app = sK43(vapp(ve1app,ve2app),sK16,sK15),
inference(equality_resolution,[],[f3012]) ).
fof(f5821,plain,
( vtcheck(sK15,ve1app,varrow(sK45(vapp(ve1app,ve2app),sK16,sK15),sK16))
| ~ sP5(vapp(ve1app,ve2app),sK16,sK15) ),
inference(superposition,[],[f236,f5753]) ).
fof(f5822,plain,
( vtcheck(sK15,ve1app,varrow(sK45(vapp(ve1app,ve2app),sK16,sK15),sK16))
| ~ spl91_36 ),
inference(forward_subsumption_resolution,[],[f5821,f5584]) ).
fof(f5843,plain,
( ~ vtcheck(vbind(sK13,sK14,sK15),ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15))
| ~ spl91_2
| ~ spl91_36 ),
inference(resolution,[],[f5822,f806]) ).
fof(f5866,plain,
( visFreeVar(sK13,ve2app)
| ~ vtcheck(sK15,ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15))
| ~ spl91_2
| ~ spl91_36 ),
inference(resolution,[],[f5843,f189]) ).
fof(f5869,plain,
( ~ vtcheck(sK15,ve2app,sK45(vapp(ve1app,ve2app),sK16,sK15))
| ~ spl91_2
| spl91_12
| ~ spl91_36 ),
inference(forward_subsumption_resolution,[],[f5866,f3137]) ).
fof(f5870,plain,
( $false
| ~ spl91_2
| spl91_12
| ~ spl91_36
| ~ spl91_37 ),
inference(forward_subsumption_resolution,[],[f5869,f5589]) ).
fof(f5871,plain,
( ~ spl91_2
| spl91_12
| ~ spl91_36
| ~ spl91_37 ),
inference(avatar_contradiction_clause,[],[f5870]) ).
cnf(s1,plain,
( spl91_1
| spl91_2 ),
inference(sat_conversion,[],[f807]) ).
cnf(s16,plain,
~ spl91_12,
inference(sat_conversion,[],[f3178]) ).
cnf(s18,plain,
~ spl91_1,
inference(sat_conversion,[],[f3254]) ).
cnf(s88,plain,
( ~ spl91_36
| spl91_37 ),
inference(sat_conversion,[],[f5590]) ).
cnf(s91,plain,
spl91_36,
inference(sat_conversion,[],[f5626]) ).
cnf(s97,plain,
( ~ spl91_2
| spl91_12
| ~ spl91_36
| ~ spl91_37 ),
inference(sat_conversion,[],[f5871]) ).
cnf(s98,plain,
spl91_37,
inference(rat,[],[s88,s91]) ).
cnf(s120,plain,
~ spl91_2,
inference(rat,[],[s97,s98,s91,s16]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s1,s120,s18]) ).
fof(f5872,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM126+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:57:57 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.73/1.95 % (123111)Detected formulas, will run a generic FOF schedule.
% 7.73/1.95 % (123124)dis-21_1_sil=8000:lcm=predicate:random_seed=1831673718:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.73/1.95 % (123118)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2701911608:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.73/1.95 % (123124)Instruction limit reached!
% 7.73/1.95 % (123124)------------------------------
% 7.73/1.95 % (123124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123124)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123124)Termination reason: Instruction limit
% 7.73/1.95 % (123124)Termination phase: Saturation
% 7.73/1.95 % (123124)Time elapsed: 0.044 s
% 7.73/1.95 % (123124)Peak memory usage: 90 MB
% 7.73/1.95 % (123124)Instructions burned: 131 (million)
% 7.73/1.95 % (123120)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3422602775:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.73/1.95 % (123121)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=641534345:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.73/1.95 % (123122)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3468408911:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.73/1.95 % (123119)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3007399673:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.73/1.95 % (123123)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3050242248:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.73/1.95 % (123121)Refutation not found, incomplete strategy
% 7.73/1.95 % (123121)------------------------------
% 7.73/1.95 % (123121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123121)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123121)Termination reason: Refutation not found, incomplete strategy
% 7.73/1.95 % (123121)Time elapsed: 0.003 s
% 7.73/1.95 % (123121)Peak memory usage: 88 MB
% 7.73/1.95 % (123121)Instructions burned: 2 (million)
% 7.73/1.95 % (123122)Instruction limit reached!
% 7.73/1.95 % (123122)------------------------------
% 7.73/1.95 % (123122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123122)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123122)Termination reason: Instruction limit
% 7.73/1.95 % (123122)Termination phase: Saturation
% 7.73/1.95 % (123122)Time elapsed: 0.086 s
% 7.73/1.95 % (123122)Peak memory usage: 88 MB
% 7.73/1.95 % (123122)Instructions burned: 120 (million)
% 7.73/1.95 % (123127)lrs+10_1_sil=8000:sp=occurrence:random_seed=960347232:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.73/1.95 % (123123)Instruction limit reached!
% 7.73/1.95 % (123123)------------------------------
% 7.73/1.95 % (123123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123123)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123123)Termination reason: Instruction limit
% 7.73/1.95 % (123123)Termination phase: Saturation
% 7.73/1.95 % (123123)Time elapsed: 0.143 s
% 7.73/1.95 % (123123)Peak memory usage: 90 MB
% 7.73/1.95 % (123123)Instructions burned: 139 (million)
% 7.73/1.95 % (123127)Instruction limit reached!
% 7.73/1.95 % (123127)------------------------------
% 7.73/1.95 % (123127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123127)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123127)Termination reason: Instruction limit
% 7.73/1.95 % (123127)Termination phase: Saturation
% 7.73/1.95 % (123127)Time elapsed: 0.112 s
% 7.73/1.95 % (123127)Peak memory usage: 89 MB
% 7.73/1.95 % (123127)Instructions burned: 287 (million)
% 7.73/1.95 % (123133)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2149324314:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 7.73/1.95 % (123135)lrs+1011_1_sil=32000:sp=occurrence:random_seed=239281250:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 7.73/1.95 % (123121)------------------------------
% 7.73/1.95 % (123121)------------------------------
% 7.73/1.95 % (123137)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2611771022:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.73/1.95 % (123133)Instruction limit reached!
% 7.73/1.95 % (123133)------------------------------
% 7.73/1.95 % (123133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123133)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123133)Termination reason: Instruction limit
% 7.73/1.95 % (123133)Termination phase: Saturation
% 7.73/1.95 % (123133)Time elapsed: 0.142 s
% 7.73/1.95 % (123133)Peak memory usage: 91 MB
% 7.73/1.95 % (123133)Instructions burned: 157 (million)
% 7.73/1.95 % (123137)Instruction limit reached!
% 7.73/1.95 % (123137)------------------------------
% 7.73/1.95 % (123137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123137)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123137)Termination reason: Instruction limit
% 7.73/1.95 % (123137)Termination phase: Saturation
% 7.73/1.95 % (123137)Time elapsed: 0.114 s
% 7.73/1.95 % (123137)Peak memory usage: 91 MB
% 7.73/1.95 % (123137)Instructions burned: 248 (million)
% 7.73/1.95 % (123143)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1948774580:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 7.73/1.95 % (123143)Refutation not found, incomplete strategy
% 7.73/1.95 % (123143)------------------------------
% 7.73/1.95 % (123143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123143)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123143)Termination reason: Refutation not found, incomplete strategy
% 7.73/1.95 % (123143)Time elapsed: 0.012 s
% 7.73/1.95 % (123143)Peak memory usage: 88 MB
% 7.73/1.95 % (123143)Instructions burned: 11 (million)
% 7.73/1.95 % (123144)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=664633187:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 7.73/1.95 % (123148)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1356508333:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 7.73/1.95 % (123135)First to succeed.
% 7.73/1.95 % (123135)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-123111"
% 7.73/1.95 % (123148)Instruction limit reached!
% 7.73/1.95 % (123148)------------------------------
% 7.73/1.95 % (123148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123148)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123148)Termination reason: Instruction limit
% 7.73/1.95 % (123148)Termination phase: Saturation
% 7.73/1.95 % (123148)Time elapsed: 0.067 s
% 7.73/1.95 % (123148)Peak memory usage: 89 MB
% 7.73/1.95 % (123148)Instructions burned: 113 (million)
% 7.73/1.95 % (123152)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1796293135:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 7.73/1.95 % (123152)Instruction limit reached!
% 7.73/1.95 % (123152)------------------------------
% 7.73/1.95 % (123152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/1.95 % (123152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/1.95 % (123152)CaDiCaL version: 2.1.3
% 7.73/1.95 % (123152)Termination reason: Instruction limit
% 7.73/1.95 % (123152)Termination phase: Saturation
% 7.73/1.95 % (123152)Time elapsed: 0.054 s
% 7.73/1.95 % (123152)Peak memory usage: 89 MB
% 7.73/1.95 % (123152)Instructions burned: 129 (million)
% 7.73/1.95 % (123143)------------------------------
% 7.73/1.95 % (123143)------------------------------
% 7.73/1.95 % (123118)Also succeeded, but the first one will report.
% 7.73/1.95 % (123119)Also succeeded, but the first one will report.
% 7.73/1.95 % (123135)Refutation found. Thanks to Tanya!
% 7.73/1.95 % SZS status Theorem for theBenchmark
% 7.73/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 10.00/2.25 % (123135)------------------------------
% 10.00/2.25 % (123135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.00/2.25 % (123135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.00/2.25 % (123135)CaDiCaL version: 2.1.3
% 10.00/2.25 % (123135)Termination reason: Refutation
% 10.00/2.25 % (123135)Time elapsed: 0.314 s
% 10.00/2.25 % (123135)Peak memory usage: 92 MB
% 10.00/2.25 % (123135)Instructions burned: 298 (million)
% 10.00/2.25 % (123135)------------------------------
% 10.00/2.25 % (123135)------------------------------
% 10.00/2.25 % (123111)Success in time 1.316 s
% 10.00/2.25 % Vampire exiting
%------------------------------------------------------------------------------