%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU018+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 4.43s 1.54s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of formulae : 235 ( 40 unt; 18 def)
% Number of atoms : 867 ( 119 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1135 ( 503 ~; 506 |; 82 &)
% ( 27 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 227 ( 0 sgn 208 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f35,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
& one_to_one(X0) )
=> subset(relation_dom(X0),relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
& one_to_one(X0) )
=> subset(relation_dom(X0),relation_rng(X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,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(ennf_transformation,[],[f5]) ).
fof(f49,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,[],[f48]) ).
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(ennf_transformation,[],[f6]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f56]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f70]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ~ subset(relation_dom(X0),relation_rng(X1))
& relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
& one_to_one(X0)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ~ subset(relation_dom(X0),relation_rng(X1))
& relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
& one_to_one(X0)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f76]) ).
fof(f82,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f83,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f83]) ).
fof(f85,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,[],[f49]) ).
fof(f86,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,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK1(X0,X1) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),relation_dom(X0))
& sK1(X0,X1) = apply(X0,sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK3(X0,X5),relation_dom(X0))
& apply(X0,sK3(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f86]) ).
fof(f88,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,[],[f51]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK4(X0) != sK5(X0)
& in(sK4(X0),relation_dom(X0))
& in(sK5(X0),relation_dom(X0))
& apply(X0,sK4(X0)) = apply(X0,sK5(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,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0))],[f89]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1)) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f69]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1)) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f100]) ).
fof(f103,plain,
( ~ subset(relation_dom(sK15),relation_rng(sK16))
& relation_rng(sK15) = relation_rng(relation_composition(sK16,sK15))
& one_to_one(sK15)
& relation(sK16)
& function(sK16)
& relation(sK15)
& function(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f77]) ).
fof(f108,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f109,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
! [X0,X1,X5] :
( apply(X0,sK3(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f111,plain,
! [X0,X1,X5] :
( in(sK3(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f112,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f116,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,[],[f90]) ).
fof(f121,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f127,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f164,plain,
function(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
relation(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
function(sK16),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
relation(sK16),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
one_to_one(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f169,plain,
relation_rng(sK15) = relation_rng(relation_composition(sK16,sK15)),
inference(cnf_transformation,[],[f103]) ).
fof(f170,plain,
~ subset(relation_dom(sK15),relation_rng(sK16)),
inference(cnf_transformation,[],[f103]) ).
fof(f175,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f112]) ).
fof(f176,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f177,plain,
! [X0,X5] :
( in(sK3(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f111]) ).
fof(f178,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK3(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f179,definition,
sF17 = relation_dom(sK15),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f180,plain,
relation_dom(sK15) = sF17,
inference(reorient_equations,[],[f179]) ).
fof(f181,definition,
sF18 = relation_rng(sK16),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f182,plain,
relation_rng(sK16) = sF18,
inference(reorient_equations,[],[f181]) ).
fof(f183,plain,
~ subset(sF17,sF18),
inference(definition_folding,[],[f170,f182,f180]) ).
fof(f184,definition,
sF19 = relation_rng(sK15),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f185,plain,
relation_rng(sK15) = sF19,
inference(reorient_equations,[],[f184]) ).
fof(f186,definition,
sF20 = relation_composition(sK16,sK15),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f187,plain,
relation_composition(sK16,sK15) = sF20,
inference(reorient_equations,[],[f186]) ).
fof(f188,definition,
sF21 = relation_rng(sF20),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f189,plain,
relation_rng(sF20) = sF21,
inference(reorient_equations,[],[f188]) ).
fof(f190,plain,
sF19 = sF21,
inference(definition_folding,[],[f169,f189,f187,f185]) ).
fof(f191,plain,
sF19 = relation_rng(sF20),
inference(forward_demodulation,[],[f189,f190]) ).
fof(f195,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| in(X0,relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f157,f187]) ).
fof(f196,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| in(X0,relation_dom(sK16))
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f195,f167]) ).
fof(f197,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| in(X0,relation_dom(sK16))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f196,f166]) ).
fof(f198,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| in(X0,relation_dom(sK16))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f197,f165]) ).
fof(f199,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| in(X0,relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[],[f198,f164]) ).
fof(f201,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sK15,apply(sK16,X0)) = apply(sF20,X0)
| ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f159,f187]) ).
fof(f202,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sK15,apply(sK16,X0)) = apply(sF20,X0)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f201,f167]) ).
fof(f203,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sK15,apply(sK16,X0)) = apply(sF20,X0)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f202,f166]) ).
fof(f204,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sK15,apply(sK16,X0)) = apply(sF20,X0)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f203,f165]) ).
fof(f205,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sK15,apply(sK16,X0)) = apply(sF20,X0) ),
inference(forward_subsumption_resolution,[],[f204,f164]) ).
fof(f211,plain,
! [X0] :
( ~ in(X0,sF19)
| apply(sK15,sK3(sK15,X0)) = X0
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f178,f185]) ).
fof(f212,plain,
! [X0] :
( ~ in(X0,sF19)
| apply(sF20,sK3(sF20,X0)) = X0
| ~ relation(sF20)
| ~ function(sF20) ),
inference(superposition,[],[f178,f191]) ).
fof(f214,definition,
( spl22_1
<=> function(sF20) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f215,plain,
( function(sF20)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ function(sF20)
| spl22_1 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f218,definition,
( spl22_2
<=> relation(sF20) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f219,plain,
( relation(sF20)
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ relation(sF20)
| spl22_2 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl22_3
<=> ! [X0] :
( ~ in(X0,sF19)
| apply(sF20,sK3(sF20,X0)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f223,plain,
( ! [X0] :
( ~ in(X0,sF19)
| apply(sF20,sK3(sF20,X0)) = X0 )
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_3 ),
inference(avatar_split_clause,[],[f212,f222,f218,f214]) ).
fof(f225,plain,
! [X0] :
( ~ in(X0,sF19)
| apply(sK15,sK3(sK15,X0)) = X0
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f211,f165]) ).
fof(f227,plain,
! [X0] :
( ~ in(X0,sF19)
| apply(sK15,sK3(sK15,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f225,f164]) ).
fof(f237,plain,
! [X0,X1] :
( ~ in(apply(X0,X1),sF17)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_composition(X0,sK15)))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f158,f180]) ).
fof(f238,plain,
! [X0,X1] :
( ~ in(apply(X0,X1),sF17)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_composition(X0,sK15)))
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f237,f165]) ).
fof(f239,plain,
! [X0,X1] :
( in(X1,relation_dom(relation_composition(X0,sK15)))
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),sF17)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f238,f164]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_composition(X1,X2)))
| ~ relation(relation_composition(X1,X2))
| ~ function(relation_composition(X1,X2))
| in(apply(X1,sK3(relation_composition(X1,X2),X0)),relation_dom(X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(resolution,[],[f177,f156]) ).
fof(f244,plain,
! [X0] :
( ~ in(X0,relation_rng(sF20))
| ~ relation(sF20)
| ~ function(sF20)
| in(sK3(sF20,X0),relation_dom(sK16)) ),
inference(resolution,[],[f177,f199]) ).
fof(f245,plain,
! [X0] :
( ~ in(X0,relation_rng(sF20))
| ~ relation(sF20)
| ~ function(sF20)
| apply(sF20,sK3(sF20,X0)) = apply(sK15,apply(sK16,sK3(sF20,X0))) ),
inference(resolution,[],[f177,f205]) ).
fof(f246,plain,
! [X0] :
( in(sK3(sK15,X0),sF17)
| ~ in(X0,relation_rng(sK15))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f177,f180]) ).
fof(f247,plain,
! [X0] :
( in(sK3(sK15,X0),sF17)
| ~ in(X0,relation_rng(sK15))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f246,f165]) ).
fof(f250,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_composition(X1,X2)))
| ~ function(relation_composition(X1,X2))
| in(apply(X1,sK3(relation_composition(X1,X2),X0)),relation_dom(X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f241,f121]) ).
fof(f251,plain,
! [X0] :
( in(sK3(sK15,X0),sF17)
| ~ in(X0,relation_rng(sK15)) ),
inference(forward_subsumption_resolution,[],[f247,f164]) ).
fof(f254,plain,
! [X2,X0,X1] :
( in(apply(X1,sK3(relation_composition(X1,X2),X0)),relation_dom(X2))
| ~ in(X0,relation_rng(relation_composition(X1,X2)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f250,f127]) ).
fof(f255,plain,
! [X0] :
( in(sK3(sK15,X0),sF17)
| ~ in(X0,sF19) ),
inference(forward_demodulation,[],[f251,f185]) ).
fof(f258,plain,
! [X0] :
( in(apply(sK15,X0),sF19)
| ~ in(X0,relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f176,f185]) ).
fof(f261,plain,
! [X0] :
( in(apply(sK15,X0),sF19)
| ~ in(X0,relation_dom(sK15))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f258,f165]) ).
fof(f263,plain,
! [X0] :
( in(apply(sK15,X0),sF19)
| ~ in(X0,relation_dom(sK15)) ),
inference(forward_subsumption_resolution,[],[f261,f164]) ).
fof(f265,plain,
! [X0] :
( in(apply(sK15,X0),sF19)
| ~ in(X0,sF17) ),
inference(forward_demodulation,[],[f263,f180]) ).
fof(f269,plain,
( function(sF20)
| ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f127,f187]) ).
fof(f270,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f269,f216]) ).
fof(f271,plain,
( ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f270,f167]) ).
fof(f272,plain,
( ~ relation(sK15)
| ~ function(sK15)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f271,f166]) ).
fof(f273,plain,
( ~ function(sK15)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f272,f165]) ).
fof(f274,plain,
( $false
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f273,f164]) ).
fof(f275,plain,
spl22_1,
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f276,plain,
( relation(sF20)
| ~ relation(sK16)
| ~ relation(sK15) ),
inference(superposition,[],[f121,f187]) ).
fof(f277,plain,
( ~ relation(sK16)
| ~ relation(sK15)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f276,f220]) ).
fof(f278,plain,
( ~ relation(sK15)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f277,f167]) ).
fof(f279,plain,
( $false
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f278,f165]) ).
fof(f280,plain,
spl22_2,
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f281,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sF20))
| ~ function(sF20)
| apply(sF20,sK3(sF20,X0)) = apply(sK15,apply(sK16,sK3(sF20,X0))) )
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f245,f219]) ).
fof(f282,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sF20))
| ~ function(sF20)
| in(sK3(sF20,X0),relation_dom(sK16)) )
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f244,f219]) ).
fof(f284,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sF20))
| apply(sF20,sK3(sF20,X0)) = apply(sK15,apply(sK16,sK3(sF20,X0))) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f281,f215]) ).
fof(f285,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sF20))
| in(sK3(sF20,X0),relation_dom(sK16)) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f282,f215]) ).
fof(f287,plain,
( ! [X0] :
( ~ in(X0,sF19)
| apply(sF20,sK3(sF20,X0)) = apply(sK15,apply(sK16,sK3(sF20,X0))) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_demodulation,[],[f284,f191]) ).
fof(f288,plain,
( ! [X0] :
( in(sK3(sF20,X0),relation_dom(sK16))
| ~ in(X0,sF19) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_demodulation,[],[f285,f191]) ).
fof(f290,plain,
( ! [X0] :
( ~ in(X0,sF17)
| apply(sK15,X0) = apply(sF20,sK3(sF20,apply(sK15,X0))) )
| ~ spl22_3 ),
inference(resolution,[],[f223,f265]) ).
fof(f301,plain,
! [X0] :
( in(X0,relation_dom(sF20))
| ~ in(X0,relation_dom(sK16))
| ~ in(apply(sK16,X0),sF17)
| ~ relation(sK16)
| ~ function(sK16) ),
inference(superposition,[],[f239,f187]) ).
fof(f305,plain,
! [X0] :
( in(X0,relation_dom(sF20))
| ~ in(X0,relation_dom(sK16))
| ~ in(apply(sK16,X0),sF17)
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f301,f167]) ).
fof(f308,plain,
! [X0] :
( ~ in(apply(sK16,X0),sF17)
| ~ in(X0,relation_dom(sK16))
| in(X0,relation_dom(sF20)) ),
inference(forward_subsumption_resolution,[],[f305,f166]) ).
fof(f314,plain,
( ! [X0] :
( subset(sF17,X0)
| apply(sK15,sK0(sF17,X0)) = apply(sF20,sK3(sF20,apply(sK15,sK0(sF17,X0)))) )
| ~ spl22_3 ),
inference(resolution,[],[f290,f108]) ).
fof(f455,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),relation_dom(sK15))
| ~ in(X0,relation_rng(sF20))
| ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f254,f187]) ).
fof(f459,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),relation_dom(sK15))
| ~ in(X0,relation_rng(sF20))
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f455,f167]) ).
fof(f467,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),relation_dom(sK15))
| ~ in(X0,relation_rng(sF20))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f459,f166]) ).
fof(f473,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),relation_dom(sK15))
| ~ in(X0,relation_rng(sF20))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f467,f165]) ).
fof(f474,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),relation_dom(sK15))
| ~ in(X0,relation_rng(sF20)) ),
inference(forward_subsumption_resolution,[],[f473,f164]) ).
fof(f475,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),sF17)
| ~ in(X0,relation_rng(sF20)) ),
inference(forward_demodulation,[],[f474,f180]) ).
fof(f476,plain,
! [X0] :
( in(apply(sK16,sK3(sF20,X0)),sF17)
| ~ in(X0,sF19) ),
inference(forward_demodulation,[],[f475,f191]) ).
fof(f477,plain,
! [X0] :
( ~ in(X0,sF19)
| ~ in(sK3(sF20,X0),relation_dom(sK16))
| in(sK3(sF20,X0),relation_dom(sF20)) ),
inference(resolution,[],[f476,f308]) ).
fof(f483,plain,
( ! [X0] :
( in(sK3(sF20,X0),relation_dom(sF20))
| ~ in(X0,sF19) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f477,f288]) ).
fof(f516,plain,
( apply(sK15,sK0(sF17,sF18)) = apply(sF20,sK3(sF20,apply(sK15,sK0(sF17,sF18))))
| ~ spl22_3 ),
inference(resolution,[],[f314,f183]) ).
fof(f532,definition,
( spl22_14
<=> in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sF20)) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
fof(f533,plain,
( in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sF20))
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f534,plain,
( ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sF20))
| spl22_14 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f536,definition,
( spl22_15
<=> in(apply(sK15,sK0(sF17,sF18)),sF19) ),
introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition]) ).
fof(f537,plain,
( ~ in(apply(sK15,sK0(sF17,sF18)),sF19)
| spl22_15 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f538,plain,
( in(apply(sK15,sK0(sF17,sF18)),sF19)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f575,plain,
( ~ in(apply(sK15,sK0(sF17,sF18)),sF19)
| ~ spl22_1
| ~ spl22_2
| spl22_14 ),
inference(resolution,[],[f534,f483]) ).
fof(f578,plain,
( ~ spl22_15
| ~ spl22_1
| ~ spl22_2
| spl22_14 ),
inference(avatar_split_clause,[],[f575,f532,f218,f214,f536]) ).
fof(f581,plain,
( ~ in(sK0(sF17,sF18),sF17)
| spl22_15 ),
inference(resolution,[],[f537,f265]) ).
fof(f582,plain,
( subset(sF17,sF18)
| spl22_15 ),
inference(resolution,[],[f581,f108]) ).
fof(f583,plain,
( $false
| spl22_15 ),
inference(forward_subsumption_resolution,[],[f582,f183]) ).
fof(f584,plain,
spl22_15,
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f585,plain,
( apply(sF20,sK3(sF20,apply(sK15,sK0(sF17,sF18)))) = apply(sK15,apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))))
| ~ spl22_1
| ~ spl22_2
| ~ spl22_15 ),
inference(resolution,[],[f538,f287]) ).
fof(f587,plain,
( apply(sK15,sK0(sF17,sF18)) = apply(sK15,sK3(sK15,apply(sK15,sK0(sF17,sF18))))
| ~ spl22_15 ),
inference(resolution,[],[f538,f227]) ).
fof(f590,plain,
( apply(sK15,sK0(sF17,sF18)) = apply(sK15,apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))))
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15 ),
inference(forward_demodulation,[],[f585,f516]) ).
fof(f596,plain,
( ! [X0] :
( apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| ~ in(X0,relation_dom(sK15))
| ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),relation_dom(sK15))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15) )
| ~ spl22_15 ),
inference(superposition,[],[f116,f587]) ).
fof(f599,plain,
( ! [X0] :
( apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| ~ in(X0,relation_dom(sK15))
| ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),relation_dom(sK15))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0
| ~ relation(sK15)
| ~ function(sK15) )
| ~ spl22_15 ),
inference(forward_subsumption_resolution,[],[f596,f168]) ).
fof(f604,plain,
( ! [X0] :
( apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| ~ in(X0,relation_dom(sK15))
| ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),relation_dom(sK15))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0
| ~ function(sK15) )
| ~ spl22_15 ),
inference(forward_subsumption_resolution,[],[f599,f165]) ).
fof(f609,plain,
( ! [X0] :
( apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| ~ in(X0,relation_dom(sK15))
| ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),relation_dom(sK15))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0 )
| ~ spl22_15 ),
inference(forward_subsumption_resolution,[],[f604,f164]) ).
fof(f614,plain,
( ! [X0] :
( ~ in(X0,sF17)
| apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),relation_dom(sK15))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0 )
| ~ spl22_15 ),
inference(forward_demodulation,[],[f609,f180]) ).
fof(f619,definition,
( spl22_23
<=> in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),sF17) ),
introduced(definition,[new_symbols(definition,[spl22_23])],[avatar_definition]) ).
fof(f621,plain,
( ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),sF17)
| spl22_23 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f625,plain,
( ! [X0] :
( ~ in(sK3(sK15,apply(sK15,sK0(sF17,sF18))),sF17)
| ~ in(X0,sF17)
| apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0 )
| ~ spl22_15 ),
inference(forward_demodulation,[],[f614,f180]) ).
fof(f631,definition,
( spl22_25
<=> ! [X0] :
( ~ in(X0,sF17)
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0
| apply(sK15,X0) != apply(sK15,sK0(sF17,sF18)) ) ),
introduced(definition,[new_symbols(definition,[spl22_25])],[avatar_definition]) ).
fof(f632,plain,
( ! [X0] :
( apply(sK15,X0) != apply(sK15,sK0(sF17,sF18))
| sK3(sK15,apply(sK15,sK0(sF17,sF18))) = X0
| ~ in(X0,sF17) )
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f634,plain,
( spl22_25
| ~ spl22_23
| ~ spl22_15 ),
inference(avatar_split_clause,[],[f625,f536,f619,f631]) ).
fof(f635,plain,
( ~ in(apply(sK15,sK0(sF17,sF18)),sF19)
| spl22_23 ),
inference(resolution,[],[f621,f255]) ).
fof(f636,plain,
( $false
| ~ spl22_15
| spl22_23 ),
inference(forward_subsumption_resolution,[],[f635,f538]) ).
fof(f637,plain,
( ~ spl22_15
| spl22_23 ),
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f638,plain,
( sK0(sF17,sF18) = sK3(sK15,apply(sK15,sK0(sF17,sF18)))
| ~ in(sK0(sF17,sF18),sF17)
| ~ spl22_25 ),
inference(equality_resolution,[],[f632]) ).
fof(f640,definition,
( spl22_26
<=> in(sK0(sF17,sF18),sF17) ),
introduced(definition,[new_symbols(definition,[spl22_26])],[avatar_definition]) ).
fof(f642,plain,
( ~ in(sK0(sF17,sF18),sF17)
| spl22_26 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f644,definition,
( spl22_27
<=> sK0(sF17,sF18) = sK3(sK15,apply(sK15,sK0(sF17,sF18))) ),
introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition]) ).
fof(f646,plain,
( sK0(sF17,sF18) = sK3(sK15,apply(sK15,sK0(sF17,sF18)))
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f647,plain,
( ~ spl22_26
| spl22_27
| ~ spl22_25 ),
inference(avatar_split_clause,[],[f638,f631,f644,f640]) ).
fof(f648,plain,
( subset(sF17,sF18)
| spl22_26 ),
inference(resolution,[],[f642,f108]) ).
fof(f649,plain,
( $false
| spl22_26 ),
inference(forward_subsumption_resolution,[],[f648,f183]) ).
fof(f650,plain,
spl22_26,
inference(avatar_contradiction_clause,[],[f649]) ).
fof(f665,plain,
( apply(sK15,sK0(sF17,sF18)) != apply(sK15,sK0(sF17,sF18))
| apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))) = sK3(sK15,apply(sK15,sK0(sF17,sF18)))
| ~ in(apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))),sF17)
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15
| ~ spl22_25 ),
inference(superposition,[],[f632,f590]) ).
fof(f673,plain,
( apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))) = sK3(sK15,apply(sK15,sK0(sF17,sF18)))
| ~ in(apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))),sF17)
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15
| ~ spl22_25 ),
inference(trivial_inequality_removal,[],[f665]) ).
fof(f679,plain,
( sK0(sF17,sF18) = apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18))))
| ~ in(apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))),sF17)
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15
| ~ spl22_25
| ~ spl22_27 ),
inference(forward_demodulation,[],[f673,f646]) ).
fof(f686,definition,
( spl22_28
<=> in(apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))),sF17) ),
introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition]) ).
fof(f688,plain,
( ~ in(apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))),sF17)
| spl22_28 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f690,definition,
( spl22_29
<=> sK0(sF17,sF18) = apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18)))) ),
introduced(definition,[new_symbols(definition,[spl22_29])],[avatar_definition]) ).
fof(f692,plain,
( sK0(sF17,sF18) = apply(sK16,sK3(sF20,apply(sK15,sK0(sF17,sF18))))
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f693,plain,
( ~ spl22_28
| spl22_29
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15
| ~ spl22_25
| ~ spl22_27 ),
inference(avatar_split_clause,[],[f679,f644,f631,f536,f222,f218,f214,f690,f686]) ).
fof(f713,plain,
( ~ in(apply(sK15,sK0(sF17,sF18)),sF19)
| spl22_28 ),
inference(resolution,[],[f688,f476]) ).
fof(f717,plain,
( $false
| ~ spl22_15
| spl22_28 ),
inference(forward_subsumption_resolution,[],[f713,f538]) ).
fof(f718,plain,
( ~ spl22_15
| spl22_28 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f732,plain,
( in(sK0(sF17,sF18),relation_rng(sK16))
| ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl22_29 ),
inference(superposition,[],[f176,f692]) ).
fof(f739,plain,
( in(sK0(sF17,sF18),relation_rng(sK16))
| ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| ~ function(sK16)
| ~ spl22_29 ),
inference(forward_subsumption_resolution,[],[f732,f167]) ).
fof(f743,definition,
( spl22_32
<=> in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl22_32])],[avatar_definition]) ).
fof(f745,plain,
( ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| spl22_32 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f747,definition,
( spl22_33
<=> in(sK0(sF17,sF18),sF18) ),
introduced(definition,[new_symbols(definition,[spl22_33])],[avatar_definition]) ).
fof(f749,plain,
( in(sK0(sF17,sF18),sF18)
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f754,plain,
( in(sK0(sF17,sF18),relation_rng(sK16))
| ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| ~ spl22_29 ),
inference(forward_subsumption_resolution,[],[f739,f166]) ).
fof(f770,plain,
( in(sK0(sF17,sF18),sF18)
| ~ in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| ~ spl22_29 ),
inference(forward_demodulation,[],[f754,f182]) ).
fof(f773,plain,
( ~ spl22_32
| spl22_33
| ~ spl22_29 ),
inference(avatar_split_clause,[],[f770,f690,f747,f743]) ).
fof(f787,plain,
( in(sK3(sF20,apply(sK15,sK0(sF17,sF18))),relation_dom(sK16))
| ~ spl22_14 ),
inference(resolution,[],[f533,f199]) ).
fof(f792,plain,
( $false
| ~ spl22_14
| spl22_32 ),
inference(forward_subsumption_resolution,[],[f787,f745]) ).
fof(f793,plain,
( ~ spl22_14
| spl22_32 ),
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f799,plain,
( subset(sF17,sF18)
| ~ spl22_33 ),
inference(resolution,[],[f749,f109]) ).
fof(f803,plain,
( $false
| ~ spl22_33 ),
inference(forward_subsumption_resolution,[],[f799,f183]) ).
fof(f804,plain,
~ spl22_33,
inference(avatar_contradiction_clause,[],[f803]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_3 ),
inference(sat_conversion,[],[f224]) ).
cnf(s2,plain,
spl22_1,
inference(sat_conversion,[],[f275]) ).
cnf(s3,plain,
spl22_2,
inference(sat_conversion,[],[f280]) ).
cnf(s21,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_14
| ~ spl22_15 ),
inference(sat_conversion,[],[f578]) ).
cnf(s23,plain,
spl22_15,
inference(sat_conversion,[],[f584]) ).
cnf(s27,plain,
( ~ spl22_15
| ~ spl22_23
| spl22_25 ),
inference(sat_conversion,[],[f634]) ).
cnf(s28,plain,
( ~ spl22_15
| spl22_23 ),
inference(sat_conversion,[],[f637]) ).
cnf(s29,plain,
( ~ spl22_25
| ~ spl22_26
| spl22_27 ),
inference(sat_conversion,[],[f647]) ).
cnf(s30,plain,
spl22_26,
inference(sat_conversion,[],[f650]) ).
cnf(s31,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_15
| ~ spl22_25
| ~ spl22_27
| ~ spl22_28
| spl22_29 ),
inference(sat_conversion,[],[f693]) ).
cnf(s36,plain,
( ~ spl22_15
| spl22_28 ),
inference(sat_conversion,[],[f718]) ).
cnf(s41,plain,
( ~ spl22_29
| ~ spl22_32
| spl22_33 ),
inference(sat_conversion,[],[f773]) ).
cnf(s43,plain,
( ~ spl22_14
| spl22_32 ),
inference(sat_conversion,[],[f793]) ).
cnf(s44,plain,
~ spl22_33,
inference(sat_conversion,[],[f804]) ).
cnf(s45,plain,
( ~ spl22_29
| ~ spl22_32 ),
inference(rat,[],[s41,s44]) ).
cnf(s47,plain,
( ~ spl22_25
| spl22_27 ),
inference(rat,[],[s29,s30]) ).
cnf(s48,plain,
spl22_28,
inference(rat,[],[s36,s23]) ).
cnf(s49,plain,
spl22_23,
inference(rat,[],[s28,s23]) ).
cnf(s51,plain,
spl22_25,
inference(rat,[],[s27,s23,s49]) ).
cnf(s53,plain,
spl22_27,
inference(rat,[],[s47,s51]) ).
cnf(s54,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_14 ),
inference(rat,[],[s21,s23]) ).
cnf(s55,plain,
spl22_14,
inference(rat,[],[s54,s3,s2]) ).
cnf(s56,plain,
spl22_32,
inference(rat,[],[s43,s55]) ).
cnf(s57,plain,
~ spl22_29,
inference(rat,[],[s45,s56]) ).
cnf(s58,plain,
~ spl22_3,
inference(rat,[],[s31,s2,s48,s53,s51,s23,s3,s57]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s1,s58,s3,s2]) ).
fof(f805,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU018+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 03:25:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.43/1.54 % (4120754)Detected formulas, will run a generic FOF schedule.
% 4.43/1.54 % (4120759)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=3521829399:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.43/1.54 % (4120760)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=4063662800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.43/1.54 % (4120764)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3351246861:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.43/1.54 % (4120761)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=1465239290:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.43/1.54 % (4120763)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3069898361:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.43/1.54 % (4120765)dis-21_1_sil=8000:lcm=predicate:random_seed=3801810132: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)
% 4.43/1.54 % (4120762)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2005203644:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.43/1.54 % (4120762)Refutation not found, incomplete strategy
% 4.43/1.54 % (4120762)------------------------------
% 4.43/1.54 % (4120762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120762)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120762)Termination reason: Refutation not found, incomplete strategy
% 4.43/1.54 % (4120762)Time elapsed: 0.004 s
% 4.43/1.54 % (4120762)Peak memory usage: 88 MB
% 4.43/1.54 % (4120762)Instructions burned: 4 (million)
% 4.43/1.54 % (4120763)Instruction limit reached!
% 4.43/1.54 % (4120763)------------------------------
% 4.43/1.54 % (4120763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120763)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120763)Termination reason: Instruction limit
% 4.43/1.54 % (4120763)Termination phase: Saturation
% 4.43/1.54 % (4120763)Time elapsed: 0.069 s
% 4.43/1.54 % (4120763)Peak memory usage: 88 MB
% 4.43/1.54 % (4120763)Instructions burned: 120 (million)
% 4.43/1.54 % (4120765)Instruction limit reached!
% 4.43/1.54 % (4120765)------------------------------
% 4.43/1.54 % (4120765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120765)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120765)Termination reason: Instruction limit
% 4.43/1.54 % (4120765)Termination phase: Saturation
% 4.43/1.54 % (4120765)Time elapsed: 0.077 s
% 4.43/1.54 % (4120765)Peak memory usage: 89 MB
% 4.43/1.54 % (4120765)Instructions burned: 131 (million)
% 4.43/1.54 % (4120764)Instruction limit reached!
% 4.43/1.54 % (4120764)------------------------------
% 4.43/1.54 % (4120764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120764)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120764)Termination reason: Instruction limit
% 4.43/1.54 % (4120764)Termination phase: Saturation
% 4.43/1.54 % (4120764)Time elapsed: 0.091 s
% 4.43/1.54 % (4120764)Peak memory usage: 89 MB
% 4.43/1.54 % (4120764)Instructions burned: 139 (million)
% 4.43/1.54 % (4120773)lrs+10_1_sil=8000:sp=occurrence:random_seed=2542005327:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.43/1.54 % (4120774)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2636628826:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.43/1.54 % (4120775)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4170122696:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.43/1.54 % (4120762)------------------------------
% 4.43/1.54 % (4120762)------------------------------
% 4.43/1.54 % (4120774)Instruction limit reached!
% 4.43/1.54 % (4120774)------------------------------
% 4.43/1.54 % (4120774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120774)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120774)Termination reason: Instruction limit
% 4.43/1.54 % (4120774)Termination phase: Saturation
% 4.43/1.54 % (4120774)Time elapsed: 0.077 s
% 4.43/1.54 % (4120774)Peak memory usage: 90 MB
% 4.43/1.54 % (4120774)Instructions burned: 157 (million)
% 4.43/1.54 % (4120773)Instruction limit reached!
% 4.43/1.54 % (4120773)------------------------------
% 4.43/1.54 % (4120773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120773)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120773)Termination reason: Instruction limit
% 4.43/1.54 % (4120773)Termination phase: Saturation
% 4.43/1.54 % (4120773)Time elapsed: 0.158 s
% 4.43/1.54 % (4120773)Peak memory usage: 91 MB
% 4.43/1.54 % (4120773)Instructions burned: 287 (million)
% 4.43/1.54 % (4120759)First to succeed.
% 4.43/1.54 % (4120779)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=3003060722:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.43/1.54 % (4120759)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4120754"
% 4.43/1.54 % (4120780)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3569671954:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.43/1.54 % (4120775)Instruction limit reached!
% 4.43/1.54 % (4120775)------------------------------
% 4.43/1.54 % (4120775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120775)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120775)Termination reason: Instruction limit
% 4.43/1.54 % (4120775)Termination phase: Saturation
% 4.43/1.54 % (4120775)Time elapsed: 0.201 s
% 4.43/1.54 % (4120775)Peak memory usage: 92 MB
% 4.43/1.54 % (4120775)Instructions burned: 325 (million)
% 4.43/1.54 % (4120780)Refutation not found, incomplete strategy
% 4.43/1.54 % (4120780)------------------------------
% 4.43/1.54 % (4120780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120780)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120780)Termination reason: Refutation not found, incomplete strategy
% 4.43/1.54 % (4120780)Time elapsed: 0.010 s
% 4.43/1.54 % (4120780)Peak memory usage: 88 MB
% 4.43/1.54 % (4120780)Instructions burned: 14 (million)
% 4.43/1.54 % (4120782)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=592365555:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.43/1.54 % (4120779)Instruction limit reached!
% 4.43/1.54 % (4120779)------------------------------
% 4.43/1.54 % (4120779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.54 % (4120779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.54 % (4120779)CaDiCaL version: 2.1.3
% 4.43/1.54 % (4120779)Termination reason: Instruction limit
% 4.43/1.54 % (4120779)Termination phase: Saturation
% 4.43/1.54 % (4120779)Time elapsed: 0.134 s
% 4.43/1.54 % (4120779)Peak memory usage: 93 MB
% 4.43/1.54 % (4120779)Instructions burned: 249 (million)
% 4.43/1.54 % (4120759)Refutation found. Thanks to Tanya!
% 4.43/1.54 % SZS status Theorem for theBenchmark
% 4.43/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.53/1.73 % (4120759)------------------------------
% 5.53/1.73 % (4120759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.73 % (4120759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.73 % (4120759)CaDiCaL version: 2.1.3
% 5.53/1.73 % (4120759)Termination reason: Refutation
% 5.53/1.73 % (4120759)Time elapsed: 0.414 s
% 5.53/1.73 % (4120759)Peak memory usage: 130 MB
% 5.53/1.73 % (4120759)Instructions burned: 1034 (million)
% 5.53/1.73 % (4120759)------------------------------
% 5.53/1.73 % (4120759)------------------------------
% 5.53/1.73 % (4120754)Success in time 0.704 s
% 5.53/1.73 % Vampire exiting
%------------------------------------------------------------------------------