%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU015+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:47:04 PM UTC 2026
% Result : Theorem 4.33s 1.61s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 187 ( 32 unt; 10 def)
% Number of atoms : 708 ( 127 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 896 ( 375 ~; 413 |; 72 &)
% ( 16 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 153 ( 1 sgn 136 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f10,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f27,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f29,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f32,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f33,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(relation_composition(X1,X0))
& subset(relation_rng(X1),relation_dom(X0)) )
=> one_to_one(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
fof(f34,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(relation_composition(X1,X0))
& relation_rng(X1) = relation_dom(X0) )
=> ( one_to_one(X1)
& one_to_one(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(relation_composition(X1,X0))
& relation_rng(X1) = relation_dom(X0) )
=> ( one_to_one(X1)
& one_to_one(X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f41,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f55]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( one_to_one(X1)
| ~ one_to_one(relation_composition(X1,X0))
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( one_to_one(X1)
| ~ one_to_one(relation_composition(X1,X0))
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ( ~ one_to_one(X1)
| ~ one_to_one(X0) )
& one_to_one(relation_composition(X1,X0))
& relation_rng(X1) = relation_dom(X0)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ( ~ one_to_one(X1)
| ~ one_to_one(X0) )
& one_to_one(relation_composition(X1,X0))
& relation_rng(X1) = relation_dom(X0)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f75]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1) )
| ~ in(sK0(X0,X1),X1) )
& ( ( in(sK1(X0,X1),relation_dom(X0))
& sK0(X0,X1) = apply(X0,sK1(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK2(X0,X5),relation_dom(X0))
& apply(X0,sK2(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f84]) ).
fof(f86,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK3(X0) != sK4(X0)
& in(sK3(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0))
& apply(X0,sK3(X0)) = apply(X0,sK4(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f87]) ).
fof(f99,plain,
( ( ~ one_to_one(sK15)
| ~ one_to_one(sK14) )
& one_to_one(relation_composition(sK15,sK14))
& relation_dom(sK14) = relation_rng(sK15)
& relation(sK15)
& function(sK15)
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f76]) ).
fof(f103,plain,
! [X0,X1,X5] :
( apply(X0,sK2(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f104,plain,
! [X0,X1,X5] :
( in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f109,plain,
! [X3,X0,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| X3 = X4
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f110,plain,
! [X0] :
( ~ relation(X0)
| apply(X0,sK3(X0)) = apply(X0,sK4(X0))
| one_to_one(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f111,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f112,plain,
! [X0] :
( in(sK3(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f113,plain,
! [X0] :
( sK3(X0) != sK4(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f114,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f120,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f147,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f153,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f154,plain,
! [X0,X1] :
( ~ subset(relation_rng(X1),relation_dom(X0))
| ~ one_to_one(relation_composition(X1,X0))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f155,plain,
function(sK14),
inference(cnf_transformation,[],[f99]) ).
fof(f156,plain,
relation(sK14),
inference(cnf_transformation,[],[f99]) ).
fof(f157,plain,
function(sK15),
inference(cnf_transformation,[],[f99]) ).
fof(f158,plain,
relation(sK15),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
relation_dom(sK14) = relation_rng(sK15),
inference(cnf_transformation,[],[f99]) ).
fof(f160,plain,
one_to_one(relation_composition(sK15,sK14)),
inference(cnf_transformation,[],[f99]) ).
fof(f161,plain,
( ~ one_to_one(sK15)
| ~ one_to_one(sK14) ),
inference(cnf_transformation,[],[f99]) ).
fof(f169,plain,
! [X0,X5] :
( in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f170,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK2(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f103]) ).
fof(f171,definition,
sF16 = relation_composition(sK15,sK14),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f172,plain,
relation_composition(sK15,sK14) = sF16,
inference(reorient_equations,[],[f171]) ).
fof(f173,plain,
one_to_one(sF16),
inference(definition_folding,[],[f160,f172]) ).
fof(f174,definition,
sF17 = relation_dom(sK14),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f175,plain,
relation_dom(sK14) = sF17,
inference(reorient_equations,[],[f174]) ).
fof(f176,definition,
sF18 = relation_rng(sK15),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f177,plain,
relation_rng(sK15) = sF18,
inference(reorient_equations,[],[f176]) ).
fof(f178,plain,
sF17 = sF18,
inference(definition_folding,[],[f159,f177,f175]) ).
fof(f180,definition,
( spl19_1
<=> one_to_one(sK14) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f182,plain,
( ~ one_to_one(sK14)
| spl19_1 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f184,definition,
( spl19_2
<=> one_to_one(sK15) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f187,plain,
( ~ spl19_1
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f161,f184,f180]) ).
fof(f188,plain,
relation_rng(sK15) = sF17,
inference(forward_demodulation,[],[f177,f178]) ).
fof(f189,plain,
! [X0] :
( ~ subset(sF17,relation_dom(X0))
| ~ one_to_one(relation_composition(sK15,X0))
| one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f154,f188]) ).
fof(f192,plain,
! [X0] :
( ~ subset(sF17,relation_dom(X0))
| ~ one_to_one(relation_composition(sK15,X0))
| one_to_one(sK15)
| ~ function(sK15)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f189,f158]) ).
fof(f194,plain,
! [X0] :
( ~ subset(sF17,relation_dom(X0))
| ~ one_to_one(relation_composition(sK15,X0))
| one_to_one(sK15)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f192,f157]) ).
fof(f196,definition,
( spl19_3
<=> ! [X0] :
( ~ subset(sF17,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(relation_composition(sK15,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f197,plain,
( ! [X0] :
( ~ subset(sF17,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(relation_composition(sK15,X0)) )
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f198,plain,
( spl19_2
| spl19_3 ),
inference(avatar_split_clause,[],[f194,f196,f184]) ).
fof(f199,plain,
( in(sK3(sK14),sF17)
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f112,f175]) ).
fof(f200,plain,
( in(sK3(sK14),sF17)
| ~ relation(sK14)
| ~ function(sK14)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f199,f182]) ).
fof(f201,plain,
( in(sK3(sK14),sF17)
| ~ function(sK14)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f200,f156]) ).
fof(f202,plain,
( in(sK3(sK14),sF17)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f201,f155]) ).
fof(f203,plain,
( in(sK4(sK14),sF17)
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f111,f175]) ).
fof(f204,plain,
( in(sK4(sK14),sF17)
| ~ relation(sK14)
| ~ function(sK14)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f203,f182]) ).
fof(f205,plain,
( in(sK4(sK14),sF17)
| ~ function(sK14)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f204,f156]) ).
fof(f206,plain,
( in(sK4(sK14),sF17)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f205,f155]) ).
fof(f217,plain,
! [X0] :
( ~ subset(relation_rng(X0),sF17)
| relation_dom(X0) = relation_dom(relation_composition(X0,sK14))
| ~ relation(sK14)
| ~ relation(X0) ),
inference(superposition,[],[f153,f175]) ).
fof(f218,plain,
! [X0] :
( ~ subset(relation_rng(X0),sF17)
| relation_dom(X0) = relation_dom(relation_composition(X0,sK14))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f217,f156]) ).
fof(f220,plain,
( apply(sK14,sK3(sK14)) = apply(sK14,sK4(sK14))
| one_to_one(sK14)
| ~ function(sK14) ),
inference(resolution,[],[f110,f156]) ).
fof(f223,plain,
( apply(sK14,sK3(sK14)) = apply(sK14,sK4(sK14))
| ~ function(sK14)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f220,f182]) ).
fof(f229,plain,
( apply(sK14,sK3(sK14)) = apply(sK14,sK4(sK14))
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f223,f155]) ).
fof(f230,plain,
( function(sF16)
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f120,f172]) ).
fof(f231,plain,
( function(sF16)
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f230,f158]) ).
fof(f232,plain,
( function(sF16)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f231,f157]) ).
fof(f233,plain,
( function(sF16)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f232,f156]) ).
fof(f234,plain,
function(sF16),
inference(forward_subsumption_resolution,[],[f233,f155]) ).
fof(f236,plain,
( relation(sF16)
| ~ relation(sK15)
| ~ relation(sK14) ),
inference(superposition,[],[f114,f172]) ).
fof(f237,plain,
( relation(sF16)
| ~ relation(sK14) ),
inference(forward_subsumption_resolution,[],[f236,f158]) ).
fof(f238,plain,
relation(sF16),
inference(forward_subsumption_resolution,[],[f237,f156]) ).
fof(f239,plain,
( ~ subset(sF17,sF17)
| ~ function(sK14)
| ~ relation(sK14)
| ~ one_to_one(relation_composition(sK15,sK14))
| ~ spl19_3 ),
inference(superposition,[],[f197,f175]) ).
fof(f240,plain,
( ~ function(sK14)
| ~ relation(sK14)
| ~ one_to_one(relation_composition(sK15,sK14))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f239,f147]) ).
fof(f241,plain,
( ~ relation(sK14)
| ~ one_to_one(relation_composition(sK15,sK14))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f240,f155]) ).
fof(f242,plain,
( ~ one_to_one(relation_composition(sK15,sK14))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f241,f156]) ).
fof(f243,plain,
( ~ one_to_one(sF16)
| ~ spl19_3 ),
inference(forward_demodulation,[],[f242,f172]) ).
fof(f244,plain,
( $false
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f243,f173]) ).
fof(f245,plain,
~ spl19_3,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f247,plain,
! [X0] :
( ~ in(X0,sF17)
| apply(sK15,sK2(sK15,X0)) = X0
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f170,f188]) ).
fof(f248,plain,
! [X0] :
( ~ in(X0,sF17)
| apply(sK15,sK2(sK15,X0)) = X0
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f247,f158]) ).
fof(f249,plain,
! [X0] :
( ~ in(X0,sF17)
| apply(sK15,sK2(sK15,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f248,f157]) ).
fof(f273,plain,
( sK4(sK14) = apply(sK15,sK2(sK15,sK4(sK14)))
| spl19_1 ),
inference(resolution,[],[f249,f206]) ).
fof(f274,plain,
( sK3(sK14) = apply(sK15,sK2(sK15,sK3(sK14)))
| spl19_1 ),
inference(resolution,[],[f249,f202]) ).
fof(f276,plain,
( ~ subset(sF17,sF17)
| relation_dom(sK15) = relation_dom(relation_composition(sK15,sK14))
| ~ relation(sK15) ),
inference(superposition,[],[f218,f188]) ).
fof(f277,plain,
( relation_dom(sK15) = relation_dom(relation_composition(sK15,sK14))
| ~ relation(sK15) ),
inference(forward_subsumption_resolution,[],[f276,f147]) ).
fof(f278,plain,
relation_dom(sK15) = relation_dom(relation_composition(sK15,sK14)),
inference(forward_subsumption_resolution,[],[f277,f158]) ).
fof(f279,plain,
relation_dom(sK15) = relation_dom(sF16),
inference(forward_demodulation,[],[f278,f172]) ).
fof(f334,definition,
( spl19_7
<=> in(sK2(sK15,sK3(sK14)),relation_dom(sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_7])],[avatar_definition]) ).
fof(f335,plain,
( in(sK2(sK15,sK3(sK14)),relation_dom(sK15))
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f336,plain,
( ~ in(sK2(sK15,sK3(sK14)),relation_dom(sK15))
| spl19_7 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f342,plain,
( ~ in(sK3(sK14),relation_rng(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| spl19_7 ),
inference(resolution,[],[f336,f169]) ).
fof(f343,plain,
( ~ in(sK3(sK14),relation_rng(sK15))
| ~ function(sK15)
| spl19_7 ),
inference(forward_subsumption_resolution,[],[f342,f158]) ).
fof(f344,plain,
( ~ in(sK3(sK14),relation_rng(sK15))
| spl19_7 ),
inference(forward_subsumption_resolution,[],[f343,f157]) ).
fof(f345,plain,
( ~ in(sK3(sK14),sF17)
| spl19_7 ),
inference(forward_demodulation,[],[f344,f188]) ).
fof(f346,plain,
( $false
| spl19_1
| spl19_7 ),
inference(forward_subsumption_resolution,[],[f345,f202]) ).
fof(f347,plain,
( spl19_1
| spl19_7 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f349,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK3(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK3(sK14))))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK15)
| ~ function(sK15) )
| ~ spl19_7 ),
inference(resolution,[],[f335,f149]) ).
fof(f350,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK3(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK3(sK14))))
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK15) )
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f349,f158]) ).
fof(f351,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK3(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK3(sK14))))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f350,f157]) ).
fof(f352,plain,
( ! [X0] :
( ~ relation(X0)
| apply(relation_composition(sK15,X0),sK2(sK15,sK3(sK14))) = apply(X0,sK3(sK14))
| ~ function(X0) )
| spl19_1
| ~ spl19_7 ),
inference(forward_demodulation,[],[f351,f274]) ).
fof(f362,definition,
( spl19_9
<=> in(sK2(sK15,sK4(sK14)),relation_dom(sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
fof(f363,plain,
( in(sK2(sK15,sK4(sK14)),relation_dom(sK15))
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f364,plain,
( ~ in(sK2(sK15,sK4(sK14)),relation_dom(sK15))
| spl19_9 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f366,definition,
( spl19_10
<=> sK2(sK15,sK4(sK14)) = sK2(sK15,sK3(sK14)) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f368,plain,
( sK2(sK15,sK4(sK14)) = sK2(sK15,sK3(sK14))
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f370,definition,
( spl19_11
<=> sK3(sK14) = sK4(sK14) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f371,plain,
( sK3(sK14) = sK4(sK14)
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f372,plain,
( sK3(sK14) != sK4(sK14)
| spl19_11 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f385,plain,
( ~ in(sK4(sK14),relation_rng(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| spl19_9 ),
inference(resolution,[],[f364,f169]) ).
fof(f386,plain,
( ~ in(sK4(sK14),relation_rng(sK15))
| ~ function(sK15)
| spl19_9 ),
inference(forward_subsumption_resolution,[],[f385,f158]) ).
fof(f387,plain,
( ~ in(sK4(sK14),relation_rng(sK15))
| spl19_9 ),
inference(forward_subsumption_resolution,[],[f386,f157]) ).
fof(f388,plain,
( ~ in(sK4(sK14),sF17)
| spl19_9 ),
inference(forward_demodulation,[],[f387,f188]) ).
fof(f389,plain,
( $false
| spl19_1
| spl19_9 ),
inference(forward_subsumption_resolution,[],[f388,f206]) ).
fof(f390,plain,
( spl19_1
| spl19_9 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f393,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK4(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK4(sK14))))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK15)
| ~ function(sK15) )
| ~ spl19_9 ),
inference(resolution,[],[f363,f149]) ).
fof(f394,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK4(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK4(sK14))))
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK15) )
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f393,f158]) ).
fof(f395,plain,
( ! [X0] :
( apply(relation_composition(sK15,X0),sK2(sK15,sK4(sK14))) = apply(X0,apply(sK15,sK2(sK15,sK4(sK14))))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f394,f157]) ).
fof(f396,plain,
( ! [X0] :
( ~ relation(X0)
| apply(relation_composition(sK15,X0),sK2(sK15,sK4(sK14))) = apply(X0,sK4(sK14))
| ~ function(X0) )
| spl19_1
| ~ spl19_9 ),
inference(forward_demodulation,[],[f395,f273]) ).
fof(f400,plain,
( apply(sK14,sK3(sK14)) = apply(relation_composition(sK15,sK14),sK2(sK15,sK3(sK14)))
| ~ function(sK14)
| spl19_1
| ~ spl19_7 ),
inference(resolution,[],[f352,f156]) ).
fof(f405,plain,
( apply(sK14,sK3(sK14)) = apply(relation_composition(sK15,sK14),sK2(sK15,sK3(sK14)))
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f400,f155]) ).
fof(f406,plain,
( apply(sK14,sK3(sK14)) = apply(sF16,sK2(sK15,sK3(sK14)))
| spl19_1
| ~ spl19_7 ),
inference(forward_demodulation,[],[f405,f172]) ).
fof(f409,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(sK2(sK15,sK3(sK14)),relation_dom(sF16))
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0
| ~ one_to_one(sF16)
| ~ relation(sF16)
| ~ function(sF16) )
| spl19_1
| ~ spl19_7 ),
inference(superposition,[],[f109,f406]) ).
fof(f410,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(sK2(sK15,sK3(sK14)),relation_dom(sF16))
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0
| ~ relation(sF16)
| ~ function(sF16) )
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f409,f173]) ).
fof(f413,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(sK2(sK15,sK3(sK14)),relation_dom(sF16))
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0
| ~ function(sF16) )
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f410,f238]) ).
fof(f416,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(sK2(sK15,sK3(sK14)),relation_dom(sF16))
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0 )
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f413,f234]) ).
fof(f419,plain,
( ! [X0] :
( ~ in(sK2(sK15,sK3(sK14)),relation_dom(sK15))
| apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0 )
| spl19_1
| ~ spl19_7 ),
inference(forward_demodulation,[],[f416,f279]) ).
fof(f422,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(X0,relation_dom(sF16))
| sK2(sK15,sK3(sK14)) = X0 )
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f419,f335]) ).
fof(f424,plain,
( ! [X0] :
( apply(sK14,sK3(sK14)) != apply(sF16,X0)
| ~ in(X0,relation_dom(sK15))
| sK2(sK15,sK3(sK14)) = X0 )
| spl19_1
| ~ spl19_7 ),
inference(forward_demodulation,[],[f422,f279]) ).
fof(f460,plain,
( apply(sK14,sK4(sK14)) = apply(relation_composition(sK15,sK14),sK2(sK15,sK4(sK14)))
| ~ function(sK14)
| spl19_1
| ~ spl19_9 ),
inference(resolution,[],[f396,f156]) ).
fof(f465,plain,
( apply(sK14,sK4(sK14)) = apply(relation_composition(sK15,sK14),sK2(sK15,sK4(sK14)))
| spl19_1
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f460,f155]) ).
fof(f466,plain,
( apply(sK14,sK4(sK14)) = apply(sF16,sK2(sK15,sK4(sK14)))
| spl19_1
| ~ spl19_9 ),
inference(forward_demodulation,[],[f465,f172]) ).
fof(f467,plain,
( apply(sK14,sK3(sK14)) = apply(sF16,sK2(sK15,sK4(sK14)))
| spl19_1
| ~ spl19_9 ),
inference(forward_demodulation,[],[f466,f229]) ).
fof(f468,plain,
( apply(sK14,sK3(sK14)) != apply(sK14,sK3(sK14))
| ~ in(sK2(sK15,sK4(sK14)),relation_dom(sK15))
| sK2(sK15,sK4(sK14)) = sK2(sK15,sK3(sK14))
| spl19_1
| ~ spl19_7
| ~ spl19_9 ),
inference(superposition,[],[f424,f467]) ).
fof(f472,plain,
( ~ in(sK2(sK15,sK4(sK14)),relation_dom(sK15))
| sK2(sK15,sK4(sK14)) = sK2(sK15,sK3(sK14))
| spl19_1
| ~ spl19_7
| ~ spl19_9 ),
inference(trivial_inequality_removal,[],[f468]) ).
fof(f475,plain,
( sK2(sK15,sK4(sK14)) = sK2(sK15,sK3(sK14))
| spl19_1
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f472,f363]) ).
fof(f478,plain,
( spl19_10
| spl19_1
| ~ spl19_7
| ~ spl19_9 ),
inference(avatar_split_clause,[],[f475,f362,f334,f180,f366]) ).
fof(f493,plain,
( sK4(sK14) = apply(sK15,sK2(sK15,sK3(sK14)))
| spl19_1
| ~ spl19_10 ),
inference(superposition,[],[f273,f368]) ).
fof(f495,plain,
( sK3(sK14) = sK4(sK14)
| spl19_1
| ~ spl19_10 ),
inference(forward_demodulation,[],[f493,f274]) ).
fof(f496,plain,
( $false
| spl19_1
| ~ spl19_10
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f495,f372]) ).
fof(f497,plain,
( spl19_1
| ~ spl19_10
| spl19_11 ),
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f502,plain,
( sK3(sK14) != sK3(sK14)
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl19_11 ),
inference(superposition,[],[f113,f371]) ).
fof(f504,plain,
( one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl19_11 ),
inference(trivial_inequality_removal,[],[f502]) ).
fof(f505,plain,
( ~ relation(sK14)
| ~ function(sK14)
| spl19_1
| ~ spl19_11 ),
inference(forward_subsumption_resolution,[],[f504,f182]) ).
fof(f506,plain,
( ~ function(sK14)
| spl19_1
| ~ spl19_11 ),
inference(forward_subsumption_resolution,[],[f505,f156]) ).
fof(f507,plain,
( $false
| spl19_1
| ~ spl19_11 ),
inference(forward_subsumption_resolution,[],[f506,f155]) ).
fof(f508,plain,
( spl19_1
| ~ spl19_11 ),
inference(avatar_contradiction_clause,[],[f507]) ).
cnf(s1,plain,
( ~ spl19_1
| ~ spl19_2 ),
inference(sat_conversion,[],[f187]) ).
cnf(s2,plain,
( spl19_2
| spl19_3 ),
inference(sat_conversion,[],[f198]) ).
cnf(s4,plain,
~ spl19_3,
inference(sat_conversion,[],[f245]) ).
cnf(s8,plain,
( spl19_1
| spl19_7 ),
inference(sat_conversion,[],[f347]) ).
cnf(s12,plain,
( spl19_1
| spl19_9 ),
inference(sat_conversion,[],[f390]) ).
cnf(s16,plain,
( spl19_1
| ~ spl19_7
| ~ spl19_9
| spl19_10 ),
inference(sat_conversion,[],[f478]) ).
cnf(s17,plain,
( spl19_1
| ~ spl19_10
| spl19_11 ),
inference(sat_conversion,[],[f497]) ).
cnf(s18,plain,
( spl19_1
| ~ spl19_11 ),
inference(sat_conversion,[],[f508]) ).
cnf(s19,plain,
spl19_2,
inference(rat,[],[s2,s4]) ).
cnf(s20,plain,
~ spl19_1,
inference(rat,[],[s1,s19]) ).
cnf(s21,plain,
~ spl19_11,
inference(rat,[],[s18,s20]) ).
cnf(s22,plain,
~ spl19_10,
inference(rat,[],[s17,s21,s20]) ).
cnf(s23,plain,
spl19_9,
inference(rat,[],[s12,s20]) ).
cnf(s24,plain,
spl19_7,
inference(rat,[],[s8,s20]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s16,s22,s20,s23,s24]) ).
fof(f509,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU015+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:23:00 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.33/1.61 % (2634769)Detected formulas, will run a generic FOF schedule.
% 4.33/1.61 % (2634774)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=2475705435:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.33/1.61 % (2634778)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=138452746:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.33/1.61 % (2634775)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=2625986920:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.33/1.61 % (2634777)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1320583544:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.33/1.61 % (2634776)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=2980320071:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.33/1.61 % (2634779)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2702515927:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.33/1.61 % (2634777)Refutation not found, incomplete strategy
% 4.33/1.61 % (2634777)------------------------------
% 4.33/1.61 % (2634777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634777)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634777)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.61 % (2634777)Time elapsed: 0.003 s
% 4.33/1.61 % (2634777)Peak memory usage: 88 MB
% 4.33/1.61 % (2634777)Instructions burned: 2 (million)
% 4.33/1.61 % (2634780)dis-21_1_sil=8000:lcm=predicate:random_seed=2021074059: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)
% 4.33/1.61 % (2634778)Instruction limit reached!
% 4.33/1.61 % (2634778)------------------------------
% 4.33/1.61 % (2634778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634778)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634778)Termination reason: Instruction limit
% 4.33/1.61 % (2634778)Termination phase: Saturation
% 4.33/1.61 % (2634778)Time elapsed: 0.068 s
% 4.33/1.61 % (2634778)Peak memory usage: 88 MB
% 4.33/1.61 % (2634778)Instructions burned: 119 (million)
% 4.33/1.61 % (2634779)Instruction limit reached!
% 4.33/1.61 % (2634779)------------------------------
% 4.33/1.61 % (2634779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634779)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634779)Termination reason: Instruction limit
% 4.33/1.61 % (2634779)Termination phase: Saturation
% 4.33/1.61 % (2634779)Time elapsed: 0.094 s
% 4.33/1.61 % (2634779)Peak memory usage: 90 MB
% 4.33/1.61 % (2634779)Instructions burned: 140 (million)
% 4.33/1.61 % (2634780)Instruction limit reached!
% 4.33/1.61 % (2634780)------------------------------
% 4.33/1.61 % (2634780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634780)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634780)Termination reason: Instruction limit
% 4.33/1.61 % (2634780)Termination phase: Saturation
% 4.33/1.61 % (2634780)Time elapsed: 0.076 s
% 4.33/1.61 % (2634780)Peak memory usage: 90 MB
% 4.33/1.61 % (2634780)Instructions burned: 129 (million)
% 4.33/1.61 % (2634788)lrs+10_1_sil=8000:sp=occurrence:random_seed=1520436214:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.33/1.61 % (2634777)------------------------------
% 4.33/1.61 % (2634777)------------------------------
% 4.33/1.61 % (2634790)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1057937727:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.33/1.61 % (2634789)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2765210652:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.33/1.61 % (2634789)Instruction limit reached!
% 4.33/1.61 % (2634789)------------------------------
% 4.33/1.61 % (2634789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634789)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634789)Termination reason: Instruction limit
% 4.33/1.61 % (2634789)Termination phase: Saturation
% 4.33/1.61 % (2634789)Time elapsed: 0.076 s
% 4.33/1.61 % (2634789)Peak memory usage: 89 MB
% 4.33/1.61 % (2634789)Instructions burned: 158 (million)
% 4.33/1.61 % (2634788)Instruction limit reached!
% 4.33/1.61 % (2634788)------------------------------
% 4.33/1.61 % (2634788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634788)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634788)Termination reason: Instruction limit
% 4.33/1.61 % (2634788)Termination phase: Saturation
% 4.33/1.61 % (2634788)Time elapsed: 0.162 s
% 4.33/1.61 % (2634788)Peak memory usage: 91 MB
% 4.33/1.61 % (2634788)Instructions burned: 285 (million)
% 4.33/1.61 % (2634774)First to succeed.
% 4.33/1.61 % (2634774)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2634769"
% 4.33/1.61 % (2634794)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=226790131:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.33/1.61 % (2634790)Instruction limit reached!
% 4.33/1.61 % (2634790)------------------------------
% 4.33/1.61 % (2634790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634790)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634790)Termination reason: Instruction limit
% 4.33/1.61 % (2634790)Termination phase: Saturation
% 4.33/1.61 % (2634790)Time elapsed: 0.190 s
% 4.33/1.61 % (2634790)Peak memory usage: 91 MB
% 4.33/1.61 % (2634790)Instructions burned: 326 (million)
% 4.33/1.61 % (2634795)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=344880760:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.33/1.61 % (2634795)Refutation not found, incomplete strategy
% 4.33/1.61 % (2634795)------------------------------
% 4.33/1.61 % (2634795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634795)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634795)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.61 % (2634795)Time elapsed: 0.005 s
% 4.33/1.61 % (2634795)Peak memory usage: 88 MB
% 4.33/1.61 % (2634795)Instructions burned: 5 (million)
% 4.33/1.61 % (2634794)Instruction limit reached!
% 4.33/1.61 % (2634794)------------------------------
% 4.33/1.61 % (2634794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.61 % (2634794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.61 % (2634794)CaDiCaL version: 2.1.3
% 4.33/1.61 % (2634794)Termination reason: Instruction limit
% 4.33/1.61 % (2634794)Termination phase: Saturation
% 4.33/1.61 % (2634794)Time elapsed: 0.132 s
% 4.33/1.61 % (2634794)Peak memory usage: 93 MB
% 4.33/1.61 % (2634794)Instructions burned: 249 (million)
% 4.33/1.61 % (2634796)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=146286319:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.33/1.61 % (2634774)Refutation found. Thanks to Tanya!
% 4.33/1.61 % SZS status Theorem for theBenchmark
% 4.33/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.80 % (2634774)------------------------------
% 0.15/1.80 % (2634774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.80 % (2634774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.80 % (2634774)CaDiCaL version: 2.1.3
% 0.15/1.80 % (2634774)Termination reason: Refutation
% 0.15/1.80 % (2634774)Time elapsed: 0.431 s
% 0.15/1.80 % (2634774)Peak memory usage: 130 MB
% 0.15/1.80 % (2634774)Instructions burned: 984 (million)
% 0.15/1.80 % (2634774)------------------------------
% 0.15/1.80 % (2634774)------------------------------
% 0.15/1.80 % (2634769)Success in time 0.751 s
% 0.15/1.80 % Vampire exiting
%------------------------------------------------------------------------------