%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET713+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:41:43 PM UTC 2026
% Result : Theorem 2.70s 1.28s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 127 ( 12 unt; 12 def)
% Number of atoms : 461 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 542 ( 208 ~; 227 |; 68 &)
% ( 23 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 243 ( 0 sgn 220 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( injective(X0,X1,X2)
& surjective(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X3,X1)
& member(X4,X2) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> one_to_one(inverse_function(X0,X1,X2),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII04) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> one_to_one(inverse_function(X0,X1,X2),X2,X1) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ one_to_one(inverse_function(X0,X1,X2),X2,X1)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2] :
( ~ one_to_one(inverse_function(X0,X1,X2),X2,X1)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f42,plain,
( ~ one_to_one(inverse_function(sK0,sK1,sK2),sK2,sK1)
& maps(sK0,sK1,sK2)
& one_to_one(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f34]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f36]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(nnf_transformation,[],[f38]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) )
& ( ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ( sK4(X0,X1,X2) != sK5(X0,X1,X2)
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& apply(X0,sK5(X0,X1,X2),sK6(X0,X1,X2))
& member(sK4(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X2) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2)),skolemize(X5,sK6(X0,X1,X2))],[f48]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X5] :
( ? [X6] :
( member(X6,X1)
& apply(X0,X6,X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK7(X0,X1,X2)) )
& member(sK7(X0,X1,X2),X2) ) )
& ( ! [X5] :
( ( member(sK8(X0,X1,X5),X1)
& apply(X0,sK8(X0,X1,X5),X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X5))],[f54]) ).
fof(f57,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
~ one_to_one(inverse_function(sK0,sK1,sK2),sK2,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1,X6,X7,X5] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4] :
( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f66,plain,
! [X2,X0,X1] :
( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f69,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f70,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f71,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f73,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| sK4(X0,X1,X2) != sK5(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f81,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f82,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ member(X4,X1)
| ~ apply(X0,X4,sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f86,definition,
! [X0,X1] :
( sQ9_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ9_eqProxy])],[equality_proxy_definition]) ).
fof(f87,plain,
! [X2,X0,X1,X6,X7,X5] :
( sQ9_eqProxy(X6,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f59,f86]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ sQ9_eqProxy(sK4(X0,X1,X2),sK5(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f73,f86]) ).
fof(f96,plain,
( ~ injective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
inference(resolution,[],[f66,f58]) ).
fof(f100,definition,
( spl10_1
<=> surjective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f101,plain,
( ~ surjective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| spl10_1 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,definition,
( spl10_2
<=> injective(inverse_function(sK0,sK1,sK2),sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f104,plain,
( ~ injective(inverse_function(sK0,sK1,sK2),sK2,sK1)
| spl10_2 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f96,f103,f100]) ).
fof(f106,plain,
( member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| spl10_1 ),
inference(resolution,[],[f101,f81]) ).
fof(f107,plain,
! [X0] :
( member(sK3(sK0,sK2,X0),sK2)
| ~ member(X0,sK1) ),
inference(resolution,[],[f61,f57]) ).
fof(f116,plain,
! [X0] :
( apply(sK0,X0,sK3(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(resolution,[],[f60,f57]) ).
fof(f119,plain,
( ! [X0] :
( ~ apply(inverse_function(sK0,sK1,sK2),X0,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(X0,sK2) )
| spl10_1 ),
inference(resolution,[],[f82,f101]) ).
fof(f122,plain,
( ! [X0] :
( ~ apply(sK0,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),X0)
| ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(X0,sK2)
| ~ member(X0,sK2) )
| spl10_1 ),
inference(resolution,[],[f62,f119]) ).
fof(f123,plain,
( ! [X0] :
( ~ apply(sK0,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),X0)
| ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(X0,sK2) )
| spl10_1 ),
inference(duplicate_literal_removal,[],[f122]) ).
fof(f125,definition,
( spl10_3
<=> member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f126,plain,
( ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| spl10_3 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,definition,
( spl10_4
<=> ! [X0] :
( ~ apply(sK0,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),X0)
| ~ member(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f129,plain,
( ! [X0] :
( ~ apply(sK0,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),X0)
| ~ member(X0,sK2) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( ~ spl10_3
| spl10_4
| spl10_1 ),
inference(avatar_split_clause,[],[f123,f100,f128,f125]) ).
fof(f131,plain,
( $false
| spl10_1
| spl10_3 ),
inference(resolution,[],[f126,f106]) ).
fof(f132,plain,
( spl10_1
| spl10_3 ),
inference(avatar_contradiction_clause,[],[f131]) ).
fof(f133,plain,
( ~ member(sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ spl10_4 ),
inference(resolution,[],[f129,f116]) ).
fof(f135,definition,
( spl10_5
<=> member(sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f136,plain,
( ~ member(sK3(sK0,sK2,sK7(inverse_function(sK0,sK1,sK2),sK2,sK1)),sK2)
| spl10_5 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( ~ spl10_3
| ~ spl10_5
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f133,f128,f135,f125]) ).
fof(f138,plain,
( ~ member(sK7(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| spl10_5 ),
inference(resolution,[],[f136,f107]) ).
fof(f139,plain,
( ~ spl10_3
| spl10_5 ),
inference(avatar_split_clause,[],[f138,f135,f125]) ).
fof(f141,plain,
( apply(inverse_function(sK0,sK1,sK2),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))
| spl10_2 ),
inference(resolution,[],[f104,f72]) ).
fof(f142,plain,
( apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK6(inverse_function(sK0,sK1,sK2),sK2,sK1))
| spl10_2 ),
inference(resolution,[],[f104,f71]) ).
fof(f143,plain,
( member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_2 ),
inference(resolution,[],[f104,f70]) ).
fof(f144,plain,
( member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_2 ),
inference(resolution,[],[f104,f69]) ).
fof(f145,plain,
( member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| spl10_2 ),
inference(resolution,[],[f104,f68]) ).
fof(f148,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_2 ),
inference(resolution,[],[f63,f141]) ).
fof(f149,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_2 ),
inference(resolution,[],[f63,f142]) ).
fof(f152,definition,
( spl10_6
<=> member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f153,plain,
( ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_6 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl10_7
<=> member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f156,plain,
( ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| spl10_7 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl10_8
<=> apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f159,plain,
( apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( ~ spl10_6
| ~ spl10_7
| spl10_8
| spl10_2 ),
inference(avatar_split_clause,[],[f149,f103,f158,f155,f152]) ).
fof(f162,definition,
( spl10_9
<=> member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f163,plain,
( ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| spl10_9 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,definition,
( spl10_10
<=> apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f167,plain,
( ~ spl10_9
| ~ spl10_7
| spl10_10
| spl10_2 ),
inference(avatar_split_clause,[],[f148,f103,f165,f155,f162]) ).
fof(f169,plain,
( $false
| spl10_2
| spl10_7 ),
inference(resolution,[],[f156,f145]) ).
fof(f170,plain,
( spl10_2
| spl10_7 ),
inference(avatar_contradiction_clause,[],[f169]) ).
fof(f171,plain,
( $false
| spl10_2
| spl10_6 ),
inference(resolution,[],[f153,f144]) ).
fof(f172,plain,
( spl10_2
| spl10_6 ),
inference(avatar_contradiction_clause,[],[f171]) ).
fof(f173,plain,
( $false
| spl10_2
| spl10_9 ),
inference(resolution,[],[f163,f143]) ).
fof(f174,plain,
( spl10_2
| spl10_9 ),
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ maps(X0,X5,X6)
| ~ apply(X0,X1,sK5(X2,X3,X4))
| ~ member(X1,X5)
| ~ member(sK4(X2,X3,X4),X6)
| ~ member(sK5(X2,X3,X4),X6)
| ~ apply(X0,X1,sK4(X2,X3,X4))
| injective(X2,X3,X4) ),
inference(resolution,[],[f87,f88]) ).
fof(f188,plain,
! [X2,X3,X0,X1] :
( injective(X1,X2,X3)
| ~ member(X0,sK1)
| ~ member(sK4(X1,X2,X3),sK2)
| ~ member(sK5(X1,X2,X3),sK2)
| ~ apply(sK0,X0,sK4(X1,X2,X3))
| ~ apply(sK0,X0,sK5(X1,X2,X3)) ),
inference(resolution,[],[f175,f57]) ).
fof(f189,plain,
( ! [X0] :
( ~ member(X0,sK1)
| ~ member(sK4(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ member(sK5(inverse_function(sK0,sK1,sK2),sK2,sK1),sK2)
| ~ apply(sK0,X0,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ apply(sK0,X0,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1)) )
| spl10_2 ),
inference(resolution,[],[f188,f104]) ).
fof(f191,definition,
( spl10_11
<=> ! [X0] :
( ~ member(X0,sK1)
| ~ apply(sK0,X0,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ apply(sK0,X0,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f192,plain,
( ! [X0] :
( ~ apply(sK0,X0,sK5(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK4(inverse_function(sK0,sK1,sK2),sK2,sK1)) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( ~ spl10_6
| ~ spl10_9
| spl10_11
| spl10_2 ),
inference(avatar_split_clause,[],[f189,f103,f191,f162,f152]) ).
fof(f195,plain,
( ~ member(sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK1)
| ~ apply(sK0,sK6(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(sK0,sK1,sK2),sK2,sK1))
| ~ spl10_8
| ~ spl10_11 ),
inference(resolution,[],[f192,f159]) ).
fof(f199,plain,
( ~ spl10_10
| ~ spl10_7
| ~ spl10_8
| ~ spl10_11 ),
inference(avatar_split_clause,[],[f195,f191,f158,f155,f165]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f105]) ).
cnf(s2,plain,
( spl10_1
| ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
( ~ spl10_3
| ~ spl10_4
| ~ spl10_5 ),
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
( ~ spl10_3
| spl10_5 ),
inference(sat_conversion,[],[f139]) ).
cnf(s6,plain,
( spl10_2
| ~ spl10_6
| ~ spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f160]) ).
cnf(s7,plain,
( spl10_2
| ~ spl10_7
| ~ spl10_9
| spl10_10 ),
inference(sat_conversion,[],[f167]) ).
cnf(s8,plain,
( spl10_2
| spl10_7 ),
inference(sat_conversion,[],[f170]) ).
cnf(s9,plain,
( spl10_2
| spl10_6 ),
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
( spl10_2
| spl10_9 ),
inference(sat_conversion,[],[f174]) ).
cnf(s11,plain,
( spl10_2
| ~ spl10_6
| ~ spl10_9
| spl10_11 ),
inference(sat_conversion,[],[f193]) ).
cnf(s12,plain,
( ~ spl10_7
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11 ),
inference(sat_conversion,[],[f199]) ).
cnf(s14,plain,
spl10_1,
inference(rat,[],[s2,s4,s5,s3]) ).
cnf(s15,plain,
~ spl10_2,
inference(rat,[],[s1,s14]) ).
cnf(s16,plain,
spl10_9,
inference(rat,[],[s10,s15]) ).
cnf(s17,plain,
spl10_6,
inference(rat,[],[s9,s15]) ).
cnf(s18,plain,
spl10_7,
inference(rat,[],[s8,s15]) ).
cnf(s19,plain,
spl10_11,
inference(rat,[],[s11,s16,s15,s17]) ).
cnf(s20,plain,
spl10_8,
inference(rat,[],[s6,s15,s18,s17]) ).
cnf(s21,plain,
spl10_10,
inference(rat,[],[s7,s15,s16,s18]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s12,s19,s18,s21,s20]) ).
fof(f207,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET713+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:37:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.70/1.28 % (2941568)Detected formulas, will run a generic FOF schedule.
% 2.70/1.28 % (2941575)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=2173656290:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.28 % (2941573)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=2647615582:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.28 % (2941578)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4141591129:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.28 % (2941577)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3794840687:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.28 % (2941579)dis-21_1_sil=8000:lcm=predicate:random_seed=1956682314: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)
% 2.70/1.28 % (2941574)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=3799179841:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.28 % (2941576)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4046451875:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.28 % (2941576)Refutation not found, incomplete strategy
% 2.70/1.28 % (2941576)------------------------------
% 2.70/1.28 % (2941576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2941576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2941576)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2941576)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (2941576)Time elapsed: 0.001 s
% 2.70/1.28 % (2941576)Peak memory usage: 88 MB
% 2.70/1.28 % (2941579)First to succeed.
% 2.70/1.28 % (2941579)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2941568"
% 2.70/1.28 % (2941577)Instruction limit reached!
% 2.70/1.28 % (2941577)------------------------------
% 2.70/1.28 % (2941577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2941577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2941577)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2941577)Termination reason: Instruction limit
% 2.70/1.28 % (2941577)Termination phase: Saturation
% 2.70/1.28 % (2941577)Time elapsed: 0.066 s
% 2.70/1.28 % (2941577)Peak memory usage: 88 MB
% 2.70/1.28 % (2941577)Instructions burned: 119 (million)
% 2.70/1.28 % (2941578)Instruction limit reached!
% 2.70/1.28 % (2941578)------------------------------
% 2.70/1.28 % (2941578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2941578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2941578)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2941578)Termination reason: Instruction limit
% 2.70/1.28 % (2941578)Termination phase: Saturation
% 2.70/1.28 % (2941578)Time elapsed: 0.095 s
% 2.70/1.28 % (2941578)Peak memory usage: 89 MB
% 2.70/1.28 % (2941578)Instructions burned: 139 (million)
% 2.70/1.28 % (2941587)lrs+10_1_sil=8000:sp=occurrence:random_seed=3679955915:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.70/1.28 % (2941576)------------------------------
% 2.70/1.28 % (2941576)------------------------------
% 2.70/1.28 % (2941588)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1031657439:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.70/1.28 % (2941588)Refutation not found, incomplete strategy
% 2.70/1.28 % (2941588)------------------------------
% 2.70/1.28 % (2941588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2941588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2941588)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2941588)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (2941588)Time elapsed: 0.002 s
% 2.70/1.28 % (2941588)Peak memory usage: 88 MB
% 2.70/1.28 % (2941588)Instructions burned: 1 (million)
% 2.70/1.28 % (2941579)Refutation found. Thanks to Tanya!
% 2.70/1.28 % SZS status Theorem for theBenchmark
% 2.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.37 % (2941579)------------------------------
% 3.53/1.37 % (2941579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.37 % (2941579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.37 % (2941579)CaDiCaL version: 2.1.3
% 3.53/1.37 % (2941579)Termination reason: Refutation
% 3.53/1.37 % (2941579)Time elapsed: 0.007 s
% 3.53/1.37 % (2941579)Peak memory usage: 89 MB
% 3.53/1.37 % (2941579)Instructions burned: 8 (million)
% 3.53/1.37 % (2941579)------------------------------
% 3.53/1.37 % (2941579)------------------------------
% 3.53/1.37 % (2941568)Success in time 0.434 s
% 3.53/1.37 % Vampire exiting
%------------------------------------------------------------------------------