%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET742+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 : n017.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 12:41:48 PM UTC 2026
% Result : Theorem 17.46s 3.36s
% Output : Refutation 18.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of formulae : 156 ( 16 unt; 5 def)
% Number of atoms : 688 ( 43 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 911 ( 379 ~; 403 |; 97 &)
% ( 16 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-5 aty)
% Number of variables : 409 ( 0 sgn 375 !; 34 ?)
% 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(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
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(f29,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X5,X3)
& one_to_one(compose_function(X1,X0,X3,X4,X5),X3,X5)
& one_to_one(compose_function(X2,X1,X4,X5,X3),X4,X3) )
=> one_to_one(X0,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII33) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X5,X3)
& one_to_one(compose_function(X1,X0,X3,X4,X5),X3,X5)
& one_to_one(compose_function(X2,X1,X4,X5,X3),X4,X3) )
=> one_to_one(X0,X3,X4) ),
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,X3,X4,X5] :
( ~ one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X5,X3)
& one_to_one(compose_function(X1,X0,X3,X4,X5),X3,X5)
& one_to_one(compose_function(X2,X1,X4,X5,X3),X4,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X5,X3)
& one_to_one(compose_function(X1,X0,X3,X4,X5),X3,X5)
& one_to_one(compose_function(X2,X1,X4,X5,X3),X4,X3) ),
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,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(ennf_transformation,[],[f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
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(sK0,sK3,sK4)
& maps(sK0,sK3,sK4)
& maps(sK1,sK4,sK5)
& maps(sK2,sK5,sK3)
& one_to_one(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK5)
& one_to_one(compose_function(sK2,sK1,sK4,sK5,sK3),sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f34]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK6(X0,X2,X3),X2)
& apply(X0,X3,sK6(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,[sK6]),skolemize(X4,sK6(X0,X2,X3))],[f36]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(nnf_transformation,[],[f38]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X8] :
( member(X8,X3)
& apply(X1,X5,X8)
& apply(X0,X8,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ( member(sK7(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK7(X0,X1,X3,X5,X6))
& apply(X0,sK7(X0,X1,X3,X5,X6),X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X8,sK7(X0,X1,X3,X5,X6))],[f45]) ).
fof(f47,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(f48,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,[],[f47]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ( sK8(X0,X1,X2) != sK9(X0,X1,X2)
& apply(X0,sK8(X0,X1,X2),sK10(X0,X1,X2))
& apply(X0,sK9(X0,X1,X2),sK10(X0,X1,X2))
& member(sK8(X0,X1,X2),X1)
& member(sK9(X0,X1,X2),X1)
& member(sK10(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,[sK8,sK9,sK10]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X4,sK9(X0,X1,X2)),skolemize(X5,sK10(X0,X1,X2))],[f50]) ).
fof(f52,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(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK11(X0,X1,X2)) )
& member(sK11(X0,X1,X2),X2) ) )
& ( ! [X5] :
( ( member(sK12(X0,X1,X5),X1)
& apply(X0,sK12(X0,X1,X5),X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X3,sK11(X0,X1,X2)),skolemize(X6,sK12(X0,X1,X5))],[f53]) ).
fof(f55,plain,
one_to_one(compose_function(sK2,sK1,sK4,sK5,sK3),sK4,sK3),
inference(cnf_transformation,[],[f42]) ).
fof(f56,plain,
one_to_one(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f57,plain,
maps(sK2,sK5,sK3),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
maps(sK1,sK4,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
~ one_to_one(sK0,sK3,sK4),
inference(cnf_transformation,[],[f42]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK6(X0,X2,X3)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK6(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK7(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK7(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f66,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK7(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ apply(X0,X7,X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2)
| X6 = X7 ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X2,X0,X1] :
( member(sK10(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(sK9(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f75,plain,
! [X2,X0,X1] :
( apply(X0,sK9(X0,X1,X2),sK10(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X2,X0,X1] :
( apply(X0,sK8(X0,X1,X2),sK10(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f77,plain,
! [X2,X0,X1] :
( sK8(X0,X1,X2) != sK9(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| apply(X0,sK12(X0,X1,X5),X5) ),
inference(cnf_transformation,[],[f54]) ).
fof(f79,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| member(sK12(X0,X1,X5),X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f80,plain,
! [X2,X0,X1] :
( member(sK11(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK11(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f82,plain,
injective(compose_function(sK2,sK1,sK4,sK5,sK3),sK4,sK3),
inference(resolution,[],[f69,f55]) ).
fof(f83,plain,
injective(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK5),
inference(resolution,[],[f69,f56]) ).
fof(f85,plain,
surjective(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK5),
inference(resolution,[],[f68,f56]) ).
fof(f89,plain,
! [X0] :
( apply(sK1,X0,sK6(sK1,sK5,X0))
| ~ member(X0,sK4) ),
inference(resolution,[],[f62,f58]) ).
fof(f90,plain,
! [X0] :
( apply(sK2,X0,sK6(sK2,sK3,X0))
| ~ member(X0,sK5) ),
inference(resolution,[],[f57,f62]) ).
fof(f95,plain,
! [X0] :
( apply(compose_function(sK1,sK0,sK3,sK4,sK5),sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0)
| ~ member(X0,sK5) ),
inference(resolution,[],[f78,f85]) ).
fof(f104,plain,
! [X0] :
( ~ member(X0,sK5)
| apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0))
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3)
| ~ member(X0,sK5) ),
inference(resolution,[],[f95,f65]) ).
fof(f105,plain,
! [X0] :
( ~ member(X0,sK5)
| apply(sK1,sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X0)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3)
| ~ member(X0,sK5) ),
inference(resolution,[],[f95,f64]) ).
fof(f106,plain,
! [X0] :
( ~ member(X0,sK5)
| member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),sK4)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3)
| ~ member(X0,sK5) ),
inference(resolution,[],[f95,f66]) ).
fof(f109,plain,
! [X0] :
( member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),sK4)
| ~ member(X0,sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3) ),
inference(duplicate_literal_removal,[],[f106]) ).
fof(f110,plain,
! [X0] :
( apply(sK1,sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X0)
| ~ member(X0,sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3) ),
inference(duplicate_literal_removal,[],[f105]) ).
fof(f111,plain,
! [X0] :
( apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0))
| ~ member(X0,sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK1,X3,X1,X4),X0,X5)
| ~ member(sK6(sK1,sK5,X0),X1)
| ~ apply(X2,sK6(sK1,sK5,X0),X5)
| ~ member(X0,X3)
| ~ member(X5,X4)
| ~ member(X0,sK4) ),
inference(resolution,[],[f67,f89]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(compose_function(X4,X0,X5,X3,X6),sK9(X0,X1,X2),X7)
| ~ member(sK10(X0,X1,X2),X3)
| injective(X0,X1,X2)
| ~ apply(X4,sK10(X0,X1,X2),X7)
| ~ member(sK9(X0,X1,X2),X5)
| ~ member(X7,X6) ),
inference(resolution,[],[f75,f67]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(compose_function(X4,X0,X5,X3,X6),sK8(X0,X1,X2),X7)
| ~ member(sK10(X0,X1,X2),X3)
| injective(X0,X1,X2)
| ~ apply(X4,sK10(X0,X1,X2),X7)
| ~ member(sK8(X0,X1,X2),X5)
| ~ member(X7,X6) ),
inference(resolution,[],[f76,f67]) ).
fof(f128,plain,
! [X0] :
( member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3)
| ~ member(X0,sK5) ),
inference(resolution,[],[f79,f85]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X0,X1)
| ~ member(X0,sK4)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| X0 = X2 ),
inference(resolution,[],[f71,f82]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X2,X1)
| ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X0,X1)
| ~ member(X0,sK3)
| ~ member(X2,sK3)
| ~ member(X1,sK5)
| X0 = X2 ),
inference(resolution,[],[f71,f83]) ).
fof(f176,plain,
! [X0] :
( member(sK6(sK1,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(resolution,[],[f63,f58]) ).
fof(f177,plain,
! [X0] :
( member(sK6(sK2,sK3,X0),sK3)
| ~ member(X0,sK5) ),
inference(resolution,[],[f63,f57]) ).
fof(f197,definition,
( spl13_1
<=> injective(sK0,sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f198,plain,
( ~ injective(sK0,sK3,sK4)
| spl13_1 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( injective(sK0,sK3,sK4)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f213,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(X0,sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3)
| ~ member(X0,X1)
| apply(compose_function(X2,sK1,X3,X1,X4),sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X5)
| ~ apply(X2,X0,X5)
| ~ member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X3)
| ~ member(X5,X4) ),
inference(resolution,[],[f110,f67]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK1,X3,X1,X4),sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X5)
| ~ member(X0,X1)
| ~ member(X0,sK5)
| ~ apply(X2,X0,X5)
| ~ member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),X3)
| ~ member(X5,X4) ),
inference(forward_subsumption_resolution,[],[f213,f128]) ).
fof(f358,plain,
! [X2,X3,X0,X1] :
( ~ member(sK10(sK0,X0,X1),sK4)
| injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),X2)
| ~ member(sK9(sK0,X0,X1),sK3)
| ~ member(X2,sK5)
| ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X3,X2)
| ~ member(X3,sK3)
| ~ member(sK9(sK0,X0,X1),sK3)
| ~ member(X2,sK5)
| sK9(sK0,X0,X1) = X3 ),
inference(resolution,[],[f120,f139]) ).
fof(f362,plain,
! [X2,X3,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X3,X2)
| injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),X2)
| ~ member(sK9(sK0,X0,X1),sK3)
| ~ member(X2,sK5)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(X3,sK3)
| sK9(sK0,X0,X1) = X3 ),
inference(duplicate_literal_removal,[],[f358]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK10(sK0,X0,X1),sK4)
| injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),X2)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(X2,sK5)
| injective(sK0,X3,X4)
| ~ apply(sK1,sK10(sK0,X3,X4),X2)
| ~ member(sK9(sK0,X3,X4),sK3)
| ~ member(X2,sK5)
| ~ member(sK10(sK0,X3,X4),sK4)
| ~ member(sK8(sK0,X0,X1),sK3)
| sK8(sK0,X0,X1) = sK9(sK0,X3,X4) ),
inference(resolution,[],[f125,f362]) ).
fof(f442,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK1,sK10(sK0,X3,X4),X2)
| injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),X2)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(X2,sK5)
| injective(sK0,X3,X4)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X3,X4),sK3)
| ~ member(sK10(sK0,X3,X4),sK4)
| sK8(sK0,X0,X1) = sK9(sK0,X3,X4) ),
inference(duplicate_literal_removal,[],[f432]) ).
fof(f467,plain,
! [X2,X3,X0,X1] :
( injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),sK6(sK1,sK5,sK10(sK0,X2,X3)))
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK6(sK1,sK5,sK10(sK0,X2,X3)),sK5)
| injective(sK0,X2,X3)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X2,X3),sK3)
| ~ member(sK10(sK0,X2,X3),sK4)
| sK8(sK0,X0,X1) = sK9(sK0,X2,X3)
| ~ member(sK10(sK0,X2,X3),sK4) ),
inference(resolution,[],[f442,f89]) ).
fof(f468,plain,
! [X2,X3,X0,X1] :
( injective(sK0,X0,X1)
| ~ apply(sK1,sK10(sK0,X0,X1),sK6(sK1,sK5,sK10(sK0,X2,X3)))
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK6(sK1,sK5,sK10(sK0,X2,X3)),sK5)
| injective(sK0,X2,X3)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X2,X3),sK3)
| ~ member(sK10(sK0,X2,X3),sK4)
| sK8(sK0,X0,X1) = sK9(sK0,X2,X3) ),
inference(duplicate_literal_removal,[],[f467]) ).
fof(f469,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK1,sK10(sK0,X0,X1),sK6(sK1,sK5,sK10(sK0,X2,X3)))
| injective(sK0,X0,X1)
| ~ member(sK8(sK0,X0,X1),sK3)
| injective(sK0,X2,X3)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X2,X3),sK3)
| ~ member(sK10(sK0,X2,X3),sK4)
| sK8(sK0,X0,X1) = sK9(sK0,X2,X3) ),
inference(forward_subsumption_resolution,[],[f468,f176]) ).
fof(f512,plain,
! [X0,X1] :
( injective(sK0,X0,X1)
| ~ member(sK8(sK0,X0,X1),sK3)
| injective(sK0,X0,X1)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X0,X1),sK3)
| ~ member(sK10(sK0,X0,X1),sK4)
| sK9(sK0,X0,X1) = sK8(sK0,X0,X1)
| ~ member(sK10(sK0,X0,X1),sK4) ),
inference(resolution,[],[f469,f89]) ).
fof(f513,plain,
! [X0,X1] :
( injective(sK0,X0,X1)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK9(sK0,X0,X1),sK3)
| sK9(sK0,X0,X1) = sK8(sK0,X0,X1) ),
inference(duplicate_literal_removal,[],[f512]) ).
fof(f514,plain,
! [X0,X1] :
( ~ member(sK10(sK0,X0,X1),sK4)
| ~ member(sK8(sK0,X0,X1),sK3)
| injective(sK0,X0,X1)
| ~ member(sK9(sK0,X0,X1),sK3) ),
inference(forward_subsumption_resolution,[],[f513,f77]) ).
fof(f515,plain,
! [X0] :
( ~ member(sK8(sK0,X0,sK4),sK3)
| injective(sK0,X0,sK4)
| ~ member(sK9(sK0,X0,sK4),sK3)
| injective(sK0,X0,sK4) ),
inference(resolution,[],[f514,f72]) ).
fof(f516,plain,
! [X0] :
( ~ member(sK9(sK0,X0,sK4),sK3)
| injective(sK0,X0,sK4)
| ~ member(sK8(sK0,X0,sK4),sK3) ),
inference(duplicate_literal_removal,[],[f515]) ).
fof(f517,plain,
( injective(sK0,sK3,sK4)
| ~ member(sK8(sK0,sK3,sK4),sK3)
| injective(sK0,sK3,sK4) ),
inference(resolution,[],[f516,f73]) ).
fof(f518,plain,
( injective(sK0,sK3,sK4)
| ~ member(sK8(sK0,sK3,sK4),sK3) ),
inference(duplicate_literal_removal,[],[f517]) ).
fof(f604,plain,
! [X2,X0,X1] :
( ~ member(X0,sK5)
| ~ member(X0,sK5)
| ~ apply(sK2,X0,X1)
| ~ member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),sK4)
| ~ member(X1,sK3)
| ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ member(X2,sK4)
| ~ member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),sK4)
| ~ member(X1,sK3)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2 ),
inference(resolution,[],[f219,f138]) ).
fof(f608,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0),sK4)
| ~ apply(sK2,X0,X1)
| ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2 ),
inference(duplicate_literal_removal,[],[f604]) ).
fof(f617,plain,
! [X2,X0,X1] :
( ~ apply(sK2,X0,X1)
| ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2
| ~ member(X0,sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3) ),
inference(resolution,[],[f608,f109]) ).
fof(f618,plain,
! [X2,X0,X1] :
( ~ apply(sK2,X0,X1)
| ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),sK3) ),
inference(duplicate_literal_removal,[],[f617]) ).
fof(f619,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK2,sK1,sK4,sK5,sK3),X2,X1)
| ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2 ),
inference(forward_subsumption_resolution,[],[f618,f128]) ).
fof(f621,plain,
! [X2,X0,X1] :
( ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2
| ~ member(sK6(sK1,sK5,X2),sK5)
| ~ apply(sK2,sK6(sK1,sK5,X2),X1)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X2,sK4) ),
inference(resolution,[],[f619,f113]) ).
fof(f630,plain,
! [X2,X0,X1] :
( ~ member(X0,sK5)
| ~ member(X1,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2
| ~ member(sK6(sK1,sK5,X2),sK5)
| ~ apply(sK2,sK6(sK1,sK5,X2),X1) ),
inference(duplicate_literal_removal,[],[f621]) ).
fof(f632,plain,
! [X2,X0,X1] :
( ~ apply(sK2,sK6(sK1,sK5,X2),X1)
| ~ member(X1,sK3)
| ~ apply(sK2,X0,X1)
| ~ member(X2,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X0),X0) = X2
| ~ member(X0,sK5) ),
inference(forward_subsumption_resolution,[],[f630,f176]) ).
fof(f654,plain,
! [X0,X1] :
( ~ member(sK6(sK2,sK3,sK6(sK1,sK5,X0)),sK3)
| ~ apply(sK2,X1,sK6(sK2,sK3,sK6(sK1,sK5,X0)))
| ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X1),X1) = X0
| ~ member(X1,sK5)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(resolution,[],[f632,f90]) ).
fof(f655,plain,
! [X0,X1] :
( ~ apply(sK2,X1,sK6(sK2,sK3,sK6(sK1,sK5,X0)))
| ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X1),X1) = X0
| ~ member(X1,sK5)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(forward_subsumption_resolution,[],[f654,f177]) ).
fof(f656,plain,
! [X0,X1] :
( ~ apply(sK2,X1,sK6(sK2,sK3,sK6(sK1,sK5,X0)))
| ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,X1),X1) = X0
| ~ member(X1,sK5) ),
inference(forward_subsumption_resolution,[],[f655,f176]) ).
fof(f657,plain,
! [X0] :
( ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,X0)),sK6(sK1,sK5,X0)) = X0
| ~ member(sK6(sK1,sK5,X0),sK5)
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(resolution,[],[f656,f90]) ).
fof(f660,plain,
! [X0] :
( ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,X0)),sK6(sK1,sK5,X0)) = X0
| ~ member(sK6(sK1,sK5,X0),sK5) ),
inference(duplicate_literal_removal,[],[f657]) ).
fof(f663,plain,
! [X0] :
( ~ member(X0,sK4)
| sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,X0)),sK6(sK1,sK5,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f660,f176]) ).
fof(f1672,definition,
( spl13_34
<=> member(sK6(sK1,sK5,sK11(sK0,sK3,sK4)),sK5) ),
introduced(definition,[new_symbols(definition,[spl13_34])],[avatar_definition]) ).
fof(f1673,plain,
( member(sK6(sK1,sK5,sK11(sK0,sK3,sK4)),sK5)
| ~ spl13_34 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1674,plain,
( ~ member(sK6(sK1,sK5,sK11(sK0,sK3,sK4)),sK5)
| spl13_34 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1676,definition,
( spl13_35
<=> member(sK11(sK0,sK3,sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl13_35])],[avatar_definition]) ).
fof(f1677,plain,
( ~ member(sK11(sK0,sK3,sK4),sK4)
| spl13_35 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f1678,plain,
( member(sK11(sK0,sK3,sK4),sK4)
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f1693,plain,
( ~ member(sK11(sK0,sK3,sK4),sK4)
| spl13_34 ),
inference(resolution,[],[f1674,f176]) ).
fof(f1694,plain,
( ~ spl13_35
| spl13_34 ),
inference(avatar_split_clause,[],[f1693,f1672,f1676]) ).
fof(f1695,plain,
( surjective(sK0,sK3,sK4)
| spl13_35 ),
inference(resolution,[],[f1677,f80]) ).
fof(f1698,plain,
( ~ injective(sK0,sK3,sK4)
| one_to_one(sK0,sK3,sK4)
| spl13_35 ),
inference(resolution,[],[f1695,f70]) ).
fof(f1699,plain,
( one_to_one(sK0,sK3,sK4)
| ~ spl13_1
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f1698,f199]) ).
fof(f1700,plain,
( $false
| ~ spl13_1
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f1699,f60]) ).
fof(f1701,plain,
( ~ spl13_1
| spl13_35 ),
inference(avatar_contradiction_clause,[],[f1700]) ).
fof(f1705,plain,
( ~ member(sK8(sK0,sK3,sK4),sK3)
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f518,f198]) ).
fof(f1922,plain,
( injective(sK0,sK3,sK4)
| spl13_1 ),
inference(resolution,[],[f1705,f74]) ).
fof(f1923,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f1922,f198]) ).
fof(f1924,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f1923]) ).
fof(f1999,plain,
( sK11(sK0,sK3,sK4) = sK7(sK1,sK0,sK4,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK6(sK1,sK5,sK11(sK0,sK3,sK4)))
| ~ spl13_35 ),
inference(resolution,[],[f1678,f663]) ).
fof(f2391,plain,
( apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK11(sK0,sK3,sK4))
| ~ member(sK6(sK1,sK5,sK11(sK0,sK3,sK4)),sK5)
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3)
| ~ spl13_35 ),
inference(superposition,[],[f111,f1999]) ).
fof(f2400,plain,
( apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK11(sK0,sK3,sK4))
| ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3)
| ~ spl13_34
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f2391,f1673]) ).
fof(f2402,definition,
( spl13_123
<=> member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3) ),
introduced(definition,[new_symbols(definition,[spl13_123])],[avatar_definition]) ).
fof(f2403,plain,
( member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3)
| ~ spl13_123 ),
inference(avatar_component_clause,[],[f2402]) ).
fof(f2404,plain,
( ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3)
| spl13_123 ),
inference(avatar_component_clause,[],[f2402]) ).
fof(f2406,definition,
( spl13_124
<=> apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK11(sK0,sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl13_124])],[avatar_definition]) ).
fof(f2408,plain,
( apply(sK0,sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK11(sK0,sK3,sK4))
| ~ spl13_124 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f2409,plain,
( ~ spl13_123
| spl13_124
| ~ spl13_34
| ~ spl13_35 ),
inference(avatar_split_clause,[],[f2400,f1676,f1672,f2406,f2402]) ).
fof(f2410,plain,
( ~ member(sK6(sK1,sK5,sK11(sK0,sK3,sK4)),sK5)
| spl13_123 ),
inference(resolution,[],[f2404,f128]) ).
fof(f2411,plain,
( $false
| ~ spl13_34
| spl13_123 ),
inference(forward_subsumption_resolution,[],[f2410,f1673]) ).
fof(f2412,plain,
( ~ spl13_34
| spl13_123 ),
inference(avatar_contradiction_clause,[],[f2411]) ).
fof(f2415,plain,
( ~ member(sK12(compose_function(sK1,sK0,sK3,sK4,sK5),sK3,sK6(sK1,sK5,sK11(sK0,sK3,sK4))),sK3)
| surjective(sK0,sK3,sK4)
| ~ spl13_124 ),
inference(resolution,[],[f2408,f81]) ).
fof(f2420,plain,
( surjective(sK0,sK3,sK4)
| ~ spl13_123
| ~ spl13_124 ),
inference(forward_subsumption_resolution,[],[f2415,f2403]) ).
fof(f2482,plain,
( ~ injective(sK0,sK3,sK4)
| one_to_one(sK0,sK3,sK4)
| ~ spl13_123
| ~ spl13_124 ),
inference(resolution,[],[f2420,f70]) ).
fof(f2483,plain,
( one_to_one(sK0,sK3,sK4)
| ~ spl13_1
| ~ spl13_123
| ~ spl13_124 ),
inference(forward_subsumption_resolution,[],[f2482,f199]) ).
fof(f2484,plain,
( $false
| ~ spl13_1
| ~ spl13_123
| ~ spl13_124 ),
inference(forward_subsumption_resolution,[],[f2483,f60]) ).
fof(f2485,plain,
( ~ spl13_1
| ~ spl13_123
| ~ spl13_124 ),
inference(avatar_contradiction_clause,[],[f2484]) ).
cnf(s35,plain,
( spl13_34
| ~ spl13_35 ),
inference(sat_conversion,[],[f1694]) ).
cnf(s36,plain,
( ~ spl13_1
| spl13_35 ),
inference(sat_conversion,[],[f1701]) ).
cnf(s60,plain,
spl13_1,
inference(sat_conversion,[],[f1924]) ).
cnf(s121,plain,
( ~ spl13_34
| ~ spl13_35
| ~ spl13_123
| spl13_124 ),
inference(sat_conversion,[],[f2409]) ).
cnf(s122,plain,
( ~ spl13_34
| spl13_123 ),
inference(sat_conversion,[],[f2412]) ).
cnf(s124,plain,
( ~ spl13_1
| ~ spl13_123
| ~ spl13_124 ),
inference(sat_conversion,[],[f2485]) ).
cnf(s125,plain,
spl13_35,
inference(rat,[],[s36,s60]) ).
cnf(s127,plain,
spl13_34,
inference(rat,[],[s35,s125]) ).
cnf(s128,plain,
spl13_123,
inference(rat,[],[s122,s127]) ).
cnf(s130,plain,
~ spl13_124,
inference(rat,[],[s124,s60,s128]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s121,s127,s125,s130,s128]) ).
fof(f2486,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET742+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 02:36:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 11.47/2.56 % (3160752)Detected formulas, will run a generic FOF schedule.
% 11.47/2.56 % (3160761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=82501379:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.47/2.56 % (3160761)Instruction limit reached!
% 11.47/2.56 % (3160761)------------------------------
% 11.47/2.56 % (3160761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.47/2.56 % (3160761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.47/2.56 % (3160761)CaDiCaL version: 2.1.3
% 11.47/2.56 % (3160761)Termination reason: Instruction limit
% 11.47/2.56 % (3160761)Termination phase: Saturation
% 11.47/2.56 % (3160761)Time elapsed: 0.033 s
% 11.47/2.56 % (3160761)Peak memory usage: 88 MB
% 11.47/2.56 % (3160761)Instructions burned: 121 (million)
% 11.47/2.56 % (3160759)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=3357892356:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.47/2.56 % (3160758)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=1862034679:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.47/2.56 % (3160757)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=547215326:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.47/2.56 % (3160760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1925153241:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.47/2.56 % (3160763)dis-21_1_sil=8000:lcm=predicate:random_seed=639128513: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)
% 11.47/2.56 % (3160762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=70769251:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.47/2.56 % (3160760)Refutation not found, incomplete strategy
% 11.47/2.56 % (3160760)------------------------------
% 11.47/2.56 % (3160760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.47/2.56 % (3160760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.47/2.56 % (3160760)CaDiCaL version: 2.1.3
% 11.47/2.56 % (3160760)Termination reason: Refutation not found, incomplete strategy
% 11.47/2.56 % (3160760)Time elapsed: 0.004 s
% 11.47/2.56 % (3160760)Peak memory usage: 88 MB
% 11.47/2.56 % (3160760)Instructions burned: 3 (million)
% 11.47/2.56 % (3160763)Instruction limit reached!
% 11.47/2.56 % (3160763)------------------------------
% 11.47/2.56 % (3160763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.47/2.56 % (3160763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.47/2.56 % (3160763)CaDiCaL version: 2.1.3
% 11.47/2.56 % (3160763)Termination reason: Instruction limit
% 11.47/2.56 % (3160763)Termination phase: Saturation
% 11.47/2.56 % (3160763)Time elapsed: 0.060 s
% 11.47/2.56 % (3160763)Peak memory usage: 89 MB
% 11.47/2.56 % (3160763)Instructions burned: 129 (million)
% 11.47/2.56 % (3160762)Instruction limit reached!
% 11.47/2.56 % (3160762)------------------------------
% 11.47/2.56 % (3160762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.47/2.56 % (3160762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.47/2.56 % (3160762)CaDiCaL version: 2.1.3
% 11.47/2.56 % (3160762)Termination reason: Instruction limit
% 11.47/2.56 % (3160762)Termination phase: Saturation
% 11.47/2.56 % (3160762)Time elapsed: 0.094 s
% 11.47/2.56 % (3160762)Peak memory usage: 89 MB
% 11.47/2.56 % (3160762)Instructions burned: 140 (million)
% 11.47/2.56 % (3160765)lrs+10_1_sil=8000:sp=occurrence:random_seed=255924136:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.47/2.56 % (3160765)Instruction limit reached!
% 11.47/2.56 % (3160765)------------------------------
% 11.47/2.56 % (3160765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.47/2.56 % (3160765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.47/2.56 % (3160765)CaDiCaL version: 2.1.3
% 11.47/2.56 % (3160765)Termination reason: Instruction limit
% 11.47/2.56 % (3160765)Termination phase: Saturation
% 11.47/2.56 % (3160765)Time elapsed: 0.087 s
% 11.47/2.56 % (3160765)Peak memory usage: 92 MB
% 11.47/2.56 % (3160765)Instructions burned: 288 (million)
% 11.47/2.56 % (3160772)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3963530431:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 17.46/3.36 % (3160772)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160772)------------------------------
% 17.46/3.36 % (3160772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160772)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160772)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160772)Time elapsed: 0.003 s
% 17.46/3.36 % (3160772)Peak memory usage: 88 MB
% 17.46/3.36 % (3160772)Instructions burned: 2 (million)
% 17.46/3.36 % (3160760)------------------------------
% 17.46/3.36 % (3160760)------------------------------
% 17.46/3.36 % (3160773)lrs+1011_1_sil=32000:sp=occurrence:random_seed=613697004:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 17.46/3.36 % (3160775)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=903522086:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 17.46/3.36 % (3160775)Instruction limit reached!
% 17.46/3.36 % (3160775)------------------------------
% 17.46/3.36 % (3160775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160775)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160775)Termination reason: Instruction limit
% 17.46/3.36 % (3160775)Termination phase: Saturation
% 17.46/3.36 % (3160775)Time elapsed: 0.070 s
% 17.46/3.36 % (3160775)Peak memory usage: 92 MB
% 17.46/3.36 % (3160775)Instructions burned: 250 (million)
% 17.46/3.36 % (3160773)Instruction limit reached!
% 17.46/3.36 % (3160773)------------------------------
% 17.46/3.36 % (3160773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160773)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160773)Termination reason: Instruction limit
% 17.46/3.36 % (3160773)Termination phase: Saturation
% 17.46/3.36 % (3160773)Time elapsed: 0.169 s
% 17.46/3.36 % (3160773)Peak memory usage: 91 MB
% 17.46/3.36 % (3160773)Instructions burned: 329 (million)
% 17.46/3.36 % (3160778)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=996355408:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 17.46/3.36 % (3160772)------------------------------
% 17.46/3.36 % (3160772)------------------------------
% 17.46/3.36 % (3160780)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2402774894:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 17.46/3.36 % (3160782)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3023534319:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 17.46/3.36 % (3160782)Instruction limit reached!
% 17.46/3.36 % (3160782)------------------------------
% 17.46/3.36 % (3160782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160782)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160782)Termination reason: Instruction limit
% 17.46/3.36 % (3160782)Termination phase: Saturation
% 17.46/3.36 % (3160782)Time elapsed: 0.040 s
% 17.46/3.36 % (3160782)Peak memory usage: 89 MB
% 17.46/3.36 % (3160782)Instructions burned: 113 (million)
% 17.46/3.36 % (3160778)Instruction limit reached!
% 17.46/3.36 % (3160778)------------------------------
% 17.46/3.36 % (3160778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160778)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160778)Termination reason: Instruction limit
% 17.46/3.36 % (3160778)Termination phase: Saturation
% 17.46/3.36 % (3160778)Time elapsed: 0.172 s
% 17.46/3.36 % (3160778)Peak memory usage: 89 MB
% 17.46/3.36 % (3160778)Instructions burned: 295 (million)
% 17.46/3.36 % (3160783)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1724446716:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 17.46/3.36 % (3160783)Instruction limit reached!
% 17.46/3.36 % (3160783)------------------------------
% 17.46/3.36 % (3160783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160783)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160783)Termination reason: Instruction limit
% 17.46/3.36 % (3160783)Termination phase: Saturation
% 17.46/3.36 % (3160783)Time elapsed: 0.070 s
% 17.46/3.36 % (3160783)Peak memory usage: 89 MB
% 17.46/3.36 % (3160783)Instructions burned: 128 (million)
% 17.46/3.36 % (3160786)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1169360885:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 17.46/3.36 % (3160787)lrs+10_1_sil=8000:sp=occurrence:random_seed=2971039835:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 17.46/3.36 % (3160786)Instruction limit reached!
% 17.46/3.36 % (3160786)------------------------------
% 17.46/3.36 % (3160786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160786)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160786)Termination reason: Instruction limit
% 17.46/3.36 % (3160786)Termination phase: Saturation
% 17.46/3.36 % (3160786)Time elapsed: 0.071 s
% 17.46/3.36 % (3160786)Peak memory usage: 89 MB
% 17.46/3.36 % (3160786)Instructions burned: 114 (million)
% 17.46/3.36 % (3160789)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3134818348:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 17.46/3.36 % (3160789)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160789)------------------------------
% 17.46/3.36 % (3160789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160789)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160789)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160789)Time elapsed: 0.002 s
% 17.46/3.36 % (3160789)Peak memory usage: 88 MB
% 17.46/3.36 % (3160789)Instructions burned: 1 (million)
% 17.46/3.36 % (3160792)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2724072201:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 17.46/3.36 % (3160789)------------------------------
% 17.46/3.36 % (3160789)------------------------------
% 17.46/3.36 % (3160787)Instruction limit reached!
% 17.46/3.36 % (3160787)------------------------------
% 17.46/3.36 % (3160787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160787)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160787)Termination reason: Instruction limit
% 17.46/3.36 % (3160787)Termination phase: Saturation
% 17.46/3.36 % (3160787)Time elapsed: 0.502 s
% 17.46/3.36 % (3160787)Peak memory usage: 98 MB
% 17.46/3.36 % (3160787)Instructions burned: 908 (million)
% 17.46/3.36 % (3160795)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1667745442:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 17.46/3.36 % (3160795)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160795)------------------------------
% 17.46/3.36 % (3160795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160795)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160795)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160795)Time elapsed: 0.002 s
% 17.46/3.36 % (3160795)Peak memory usage: 88 MB
% 17.46/3.36 % (3160795)Instructions burned: 1 (million)
% 17.46/3.36 % (3160796)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3700977365:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 17.46/3.36 % (3160780)Instruction limit reached!
% 17.46/3.36 % (3160780)------------------------------
% 17.46/3.36 % (3160780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160780)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160780)Termination reason: Instruction limit
% 17.46/3.36 % (3160780)Termination phase: Saturation
% 17.46/3.36 % (3160780)Time elapsed: 0.889 s
% 17.46/3.36 % (3160780)Peak memory usage: 140 MB
% 17.46/3.36 % (3160780)Instructions burned: 2352 (million)
% 17.46/3.36 % (3160795)------------------------------
% 17.46/3.36 % (3160795)------------------------------
% 17.46/3.36 % (3160799)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1968409302:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 17.46/3.36 % (3160796)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160796)------------------------------
% 17.46/3.36 % (3160796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160796)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160796)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160796)Time elapsed: 0.146 s
% 17.46/3.36 % (3160796)Peak memory usage: 92 MB
% 17.46/3.36 % (3160796)Instructions burned: 240 (million)
% 17.46/3.36 % (3160800)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=3151753397:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 17.46/3.36 % (3160800)Instruction limit reached!
% 17.46/3.36 % (3160800)------------------------------
% 17.46/3.36 % (3160800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160800)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160800)Termination reason: Instruction limit
% 17.46/3.36 % (3160800)Termination phase: Saturation
% 17.46/3.36 % (3160800)Time elapsed: 0.091 s
% 17.46/3.36 % (3160800)Peak memory usage: 90 MB
% 17.46/3.36 % (3160800)Instructions burned: 125 (million)
% 17.46/3.36 % (3160796)------------------------------
% 17.46/3.36 % (3160796)------------------------------
% 17.46/3.36 % (3160804)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2905400907:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/141Mi)
% 17.46/3.36 % (3160803)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=4030158006:i=134:gtgl=5:slsql=off:gtg=exists_sym_2980 on theBenchmark for (2980ds/134Mi)
% 17.46/3.36 % (3160804)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160804)------------------------------
% 17.46/3.36 % (3160804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160804)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160804)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160804)Time elapsed: 0.002 s
% 17.46/3.36 % (3160804)Peak memory usage: 88 MB
% 17.46/3.36 % (3160804)Instructions burned: 2 (million)
% 17.46/3.36 % (3160803)Instruction limit reached!
% 17.46/3.36 % (3160803)------------------------------
% 17.46/3.36 % (3160803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160803)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160803)Termination reason: Instruction limit
% 17.46/3.36 % (3160803)Termination phase: Saturation
% 17.46/3.36 % (3160803)Time elapsed: 0.071 s
% 17.46/3.36 % (3160803)Peak memory usage: 89 MB
% 17.46/3.36 % (3160803)Instructions burned: 135 (million)
% 17.46/3.36 % (3160799)First to succeed.
% 17.46/3.36 % (3160799)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3160752"
% 17.46/3.36 % (3160804)------------------------------
% 17.46/3.36 % (3160804)------------------------------
% 17.46/3.36 % (3160807)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2353345402:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2978 on theBenchmark for (2978ds/431Mi)
% 17.46/3.36 % (3160807)Refutation not found, incomplete strategy
% 17.46/3.36 % (3160807)------------------------------
% 17.46/3.36 % (3160807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.36 % (3160807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.36 % (3160807)CaDiCaL version: 2.1.3
% 17.46/3.36 % (3160807)Termination reason: Refutation not found, incomplete strategy
% 17.46/3.36 % (3160807)Time elapsed: 0.002 s
% 17.46/3.36 % (3160807)Peak memory usage: 88 MB
% 17.46/3.36 % (3160807)Instructions burned: 1 (million)
% 17.46/3.36 % (3160799)Refutation found. Thanks to Tanya!
% 17.46/3.36 % SZS status Theorem for theBenchmark
% 17.46/3.36 % SZS output start Proof for theBenchmark
% See solution above
% 18.22/3.45 % (3160799)------------------------------
% 18.22/3.45 % (3160799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.22/3.45 % (3160799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.22/3.45 % (3160799)CaDiCaL version: 2.1.3
% 18.22/3.45 % (3160799)Termination reason: Refutation
% 18.22/3.45 % (3160799)Time elapsed: 0.623 s
% 18.22/3.45 % (3160799)Peak memory usage: 135 MB
% 18.22/3.45 % (3160799)Instructions burned: 1623 (million)
% 18.22/3.45 % (3160799)------------------------------
% 18.22/3.45 % (3160799)------------------------------
% 18.22/3.45 % (3160752)Success in time 2.515 s
% 18.22/3.45 % Vampire exiting
%------------------------------------------------------------------------------