%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET723+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 : n012.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 12:41:44 PM UTC 2026
% Result : Theorem 0.92s 0.97s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 160 ( 24 unt; 10 def)
% Number of atoms : 664 ( 56 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 888 ( 384 ~; 378 |; 87 &)
% ( 19 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 363 ( 0 sgn 335 !; 28 ?)
% 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(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X4,X2)
& member(X5,X3)
& member(X6,X3) )
=> ( ( apply(X0,X4,X5)
& apply(X1,X4,X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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(f29,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X4,X5)
& maps(X1,X3,X4)
& maps(X2,X3,X4)
& injective(X0,X4,X5)
& equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5) )
=> equal_maps(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII14) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X4,X5)
& maps(X1,X3,X4)
& maps(X2,X3,X4)
& injective(X0,X4,X5)
& equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5) )
=> equal_maps(X1,X2,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] :
( 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 ) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ equal_maps(X1,X2,X3,X4)
& maps(X0,X4,X5)
& maps(X1,X3,X4)
& maps(X2,X3,X4)
& injective(X0,X4,X5)
& equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ equal_maps(X1,X2,X3,X4)
& maps(X0,X4,X5)
& maps(X1,X3,X4)
& maps(X2,X3,X4)
& injective(X0,X4,X5)
& equal_maps(compose_function(X0,X1,X3,X4,X5),compose_function(X0,X2,X3,X4,X5),X3,X5) ),
inference(flattening,[],[f34]) ).
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(ennf_transformation,[],[f32]) ).
fof(f37,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,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( X5 = X6
| ~ apply(X0,X4,X5)
| ~ apply(X1,X4,X6)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ member(X6,X3) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( X5 = X6
| ~ apply(X0,X4,X5)
| ~ apply(X1,X4,X6)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ member(X6,X3) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f41,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(flattening,[],[f40]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
( ~ equal_maps(sK1,sK2,sK3,sK4)
& maps(sK0,sK4,sK5)
& maps(sK1,sK3,sK4)
& maps(sK2,sK3,sK4)
& injective(sK0,sK4,sK5)
& equal_maps(compose_function(sK0,sK1,sK3,sK4,sK5),compose_function(sK0,sK2,sK3,sK4,sK5),sK3,sK5) ),
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)],[f35]) ).
fof(f45,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))],[f37]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ apply(X0,X4,X5)
| ~ apply(X1,X4,X6)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ member(X6,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) )
& ( ! [X7,X8,X9] :
( X8 = X9
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( equal_maps(X0,X1,X2,X3)
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
& apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X2)
& member(sK8(X0,X1,X2,X3),X3)
& member(sK9(X0,X1,X2,X3),X3) ) )
& ( ! [X7,X8,X9] :
( X8 = X9
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X4,sK7(X0,X1,X2,X3)),skolemize(X5,sK8(X0,X1,X2,X3)),skolemize(X6,sK9(X0,X1,X2,X3))],[f47]) ).
fof(f49,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,[],[f43]) ).
fof(f50,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,[],[f49]) ).
fof(f51,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(sK10(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK10(X0,X1,X3,X5,X6))
& apply(X0,sK10(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,[sK10]),skolemize(X8,sK10(X0,X1,X3,X5,X6))],[f50]) ).
fof(f55,plain,
equal_maps(compose_function(sK0,sK1,sK3,sK4,sK5),compose_function(sK0,sK2,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f56,plain,
injective(sK0,sK4,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f57,plain,
maps(sK2,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f58,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f59,plain,
maps(sK0,sK4,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f60,plain,
~ equal_maps(sK1,sK2,sK3,sK4),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK6(X0,X2,X3)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK6(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X8,X9,X7] :
( ~ equal_maps(X0,X1,X2,X3)
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3)
| X8 = X9 ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( member(sK9(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2)
| X3 = X4 ),
inference(cnf_transformation,[],[f41]) ).
fof(f75,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,[],[f51]) ).
fof(f93,plain,
! [X0] :
( member(sK6(sK2,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f63,f57]) ).
fof(f94,plain,
! [X0] :
( member(sK6(sK1,sK4,X0),sK4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f63,f58]) ).
fof(f95,plain,
! [X0] :
( member(sK6(sK0,sK5,X0),sK5)
| ~ member(X0,sK4) ),
inference(resolution,[],[f63,f59]) ).
fof(f96,plain,
! [X0] :
( apply(sK2,X0,sK6(sK2,sK4,X0))
| ~ member(X0,sK3) ),
inference(resolution,[],[f62,f57]) ).
fof(f97,plain,
! [X0] :
( apply(sK1,X0,sK6(sK1,sK4,X0))
| ~ member(X0,sK3) ),
inference(resolution,[],[f62,f58]) ).
fof(f98,plain,
! [X0] :
( apply(sK0,X0,sK6(sK0,sK5,X0))
| ~ member(X0,sK4) ),
inference(resolution,[],[f62,f59]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(X0,sK7(X1,X0,X2,X3),X4)
| sK9(X1,X0,X2,X3) = X4
| ~ member(sK7(X1,X0,X2,X3),X5)
| ~ member(X4,X6)
| ~ member(sK9(X1,X0,X2,X3),X6)
| ~ maps(X0,X5,X6)
| equal_maps(X1,X0,X2,X3) ),
inference(resolution,[],[f61,f68]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(X0,sK7(X0,X1,X2,X3),X4)
| sK8(X0,X1,X2,X3) = X4
| ~ member(sK7(X0,X1,X2,X3),X5)
| ~ member(X4,X6)
| ~ member(sK8(X0,X1,X2,X3),X6)
| ~ maps(X0,X5,X6)
| equal_maps(X0,X1,X2,X3) ),
inference(resolution,[],[f61,f69]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ apply(sK0,X2,X1)
| ~ apply(sK0,X0,X1)
| ~ member(X0,sK4)
| ~ member(X2,sK4)
| ~ member(X1,sK5)
| X0 = X2 ),
inference(resolution,[],[f71,f56]) ).
fof(f109,plain,
! [X0,X1] :
( ~ apply(sK0,X0,sK6(sK0,sK5,X1))
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| ~ member(sK6(sK0,sK5,X1),sK5)
| X0 = X1
| ~ member(X1,sK4) ),
inference(resolution,[],[f106,f98]) ).
fof(f110,plain,
! [X0,X1] :
( ~ apply(sK0,X0,sK6(sK0,sK5,X1))
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| ~ member(sK6(sK0,sK5,X1),sK5)
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ apply(sK0,X0,sK6(sK0,sK5,X1))
| ~ member(X0,sK4)
| ~ member(X1,sK4)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f110,f95]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK0,sK2,sK3,sK4,sK5),X0,X2)
| ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2 ),
inference(resolution,[],[f64,f55]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK2,X3,X1,X4),X0,X5)
| ~ member(sK6(sK2,sK4,X0),X1)
| ~ apply(X2,sK6(sK2,sK4,X0),X5)
| ~ member(X0,X3)
| ~ member(X5,X4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f75,f96]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK1,X3,X1,X4),X0,X5)
| ~ member(sK6(sK1,sK4,X0),X1)
| ~ apply(X2,sK6(sK1,sK4,X0),X5)
| ~ member(X0,X3)
| ~ member(X5,X4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f75,f97]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK2,sK4,X0),sK4)
| ~ apply(sK0,sK6(sK2,sK4,X0),X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X2)
| ~ member(X0,sK3)
| ~ member(X2,sK5)
| ~ member(X1,sK5)
| X1 = X2 ),
inference(resolution,[],[f130,f123]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK2,sK4,X0),sK4)
| ~ apply(sK0,sK6(sK2,sK4,X0),X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X2)
| ~ member(X2,sK5)
| X1 = X2 ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK0,sK1,sK3,sK4,sK5),X0,X2)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ apply(sK0,sK6(sK2,sK4,X0),X1)
| ~ member(X2,sK5)
| X1 = X2 ),
inference(forward_subsumption_resolution,[],[f162,f93]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK1,sK4,X0),sK4)
| ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| ~ member(X0,sK3)
| ~ member(X2,sK5)
| ~ apply(sK0,sK6(sK2,sK4,X0),X2)
| ~ member(X1,sK5)
| X1 = X2 ),
inference(resolution,[],[f131,f166]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK1,sK4,X0),sK4)
| ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| ~ apply(sK0,sK6(sK2,sK4,X0),X2)
| X1 = X2 ),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ apply(sK0,sK6(sK2,sK4,X0),X2)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| X1 = X2 ),
inference(forward_subsumption_resolution,[],[f184,f94]) ).
fof(f191,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(sK2,sK4,sK7(X0,sK2,X1,X2)),X4)
| ~ member(sK7(X0,sK2,X1,X2),X3)
| sK9(X0,sK2,X1,X2) = sK6(sK2,sK4,sK7(X0,sK2,X1,X2))
| ~ member(sK9(X0,sK2,X1,X2),X4)
| ~ maps(sK2,X3,X4)
| equal_maps(X0,sK2,X1,X2)
| ~ member(sK7(X0,sK2,X1,X2),sK3) ),
inference(resolution,[],[f101,f96]) ).
fof(f199,plain,
! [X0,X1] :
( ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(sK6(sK0,sK5,sK6(sK2,sK4,X0)),sK5)
| ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = X1
| ~ member(sK6(sK2,sK4,X0),sK4) ),
inference(resolution,[],[f188,f98]) ).
fof(f200,plain,
! [X0,X1] :
( ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = X1
| ~ member(sK6(sK2,sK4,X0),sK4) ),
inference(forward_subsumption_resolution,[],[f199,f95]) ).
fof(f201,plain,
! [X0,X1] :
( ~ apply(sK0,sK6(sK1,sK4,X0),X1)
| ~ member(X1,sK5)
| ~ member(X0,sK3)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = X1 ),
inference(forward_subsumption_resolution,[],[f200,f93]) ).
fof(f205,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(sK1,sK4,sK7(sK1,X0,X1,X2)),X4)
| ~ member(sK7(sK1,X0,X1,X2),X3)
| sK8(sK1,X0,X1,X2) = sK6(sK1,sK4,sK7(sK1,X0,X1,X2))
| ~ member(sK8(sK1,X0,X1,X2),X4)
| ~ maps(sK1,X3,X4)
| equal_maps(sK1,X0,X1,X2)
| ~ member(sK7(sK1,X0,X1,X2),sK3) ),
inference(resolution,[],[f102,f97]) ).
fof(f211,plain,
! [X0] :
( ~ member(sK6(sK0,sK5,sK6(sK1,sK4,X0)),sK5)
| ~ member(X0,sK3)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = sK6(sK0,sK5,sK6(sK1,sK4,X0))
| ~ member(sK6(sK1,sK4,X0),sK4) ),
inference(resolution,[],[f201,f98]) ).
fof(f212,plain,
! [X0] :
( ~ member(X0,sK3)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = sK6(sK0,sK5,sK6(sK1,sK4,X0))
| ~ member(sK6(sK1,sK4,X0),sK4) ),
inference(forward_subsumption_resolution,[],[f211,f95]) ).
fof(f213,plain,
! [X0] :
( ~ member(X0,sK3)
| sK6(sK0,sK5,sK6(sK2,sK4,X0)) = sK6(sK0,sK5,sK6(sK1,sK4,X0)) ),
inference(forward_subsumption_resolution,[],[f212,f94]) ).
fof(f228,plain,
! [X2,X0,X1] :
( equal_maps(X0,X1,sK3,X2)
| sK6(sK0,sK5,sK6(sK2,sK4,sK7(X0,X1,sK3,X2))) = sK6(sK0,sK5,sK6(sK1,sK4,sK7(X0,X1,sK3,X2))) ),
inference(resolution,[],[f213,f67]) ).
fof(f245,plain,
sK6(sK0,sK5,sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4))) = sK6(sK0,sK5,sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))),
inference(resolution,[],[f228,f60]) ).
fof(f252,plain,
( apply(sK0,sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK6(sK0,sK5,sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))))
| ~ member(sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK4) ),
inference(superposition,[],[f98,f245]) ).
fof(f255,definition,
( spl11_1
<=> member(sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f256,plain,
( member(sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ member(sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| spl11_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f264,definition,
( spl11_3
<=> apply(sK0,sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK6(sK0,sK5,sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)))) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f266,plain,
( apply(sK0,sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK6(sK0,sK5,sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( ~ spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f252,f264,f255]) ).
fof(f279,plain,
( ~ member(sK7(sK1,sK2,sK3,sK4),sK3)
| spl11_1 ),
inference(resolution,[],[f257,f93]) ).
fof(f291,plain,
( equal_maps(sK1,sK2,sK3,sK4)
| spl11_1 ),
inference(resolution,[],[f279,f67]) ).
fof(f292,plain,
( $false
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f291,f60]) ).
fof(f293,plain,
spl11_1,
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f334,plain,
( ~ member(sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)) = sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))
| ~ spl11_3 ),
inference(resolution,[],[f266,f111]) ).
fof(f341,definition,
( spl11_6
<=> member(sK7(sK1,sK2,sK3,sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f342,plain,
( member(sK7(sK1,sK2,sK3,sK4),sK3)
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f343,plain,
( ~ member(sK7(sK1,sK2,sK3,sK4),sK3)
| spl11_6 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f354,plain,
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)) = sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))
| ~ spl11_1
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f334,f256]) ).
fof(f357,definition,
( spl11_10
<=> sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)) = sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
fof(f359,plain,
( sK6(sK2,sK4,sK7(sK1,sK2,sK3,sK4)) = sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4))
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f361,definition,
( spl11_11
<=> member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f363,plain,
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),sK4)
| spl11_11 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f364,plain,
( spl11_10
| ~ spl11_11
| ~ spl11_1
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f354,f264,f255,f361,f357]) ).
fof(f381,plain,
( equal_maps(sK1,sK2,sK3,sK4)
| spl11_6 ),
inference(resolution,[],[f343,f67]) ).
fof(f382,plain,
( $false
| spl11_6 ),
inference(forward_subsumption_resolution,[],[f381,f60]) ).
fof(f383,plain,
spl11_6,
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f409,plain,
( ~ member(sK7(sK1,sK2,sK3,sK4),sK3)
| spl11_11 ),
inference(resolution,[],[f363,f94]) ).
fof(f410,plain,
( $false
| ~ spl11_6
| spl11_11 ),
inference(forward_subsumption_resolution,[],[f409,f342]) ).
fof(f411,plain,
( ~ spl11_6
| spl11_11 ),
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f430,plain,
( ! [X0,X1] :
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4)
| ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X1,X0)
| equal_maps(sK1,sK2,sK3,sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_10 ),
inference(superposition,[],[f191,f359]) ).
fof(f440,plain,
( ! [X0,X1] :
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4)
| ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X1,X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_10 ),
inference(forward_subsumption_resolution,[],[f430,f60]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4)
| ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X1,X0) )
| ~ spl11_6
| ~ spl11_10 ),
inference(forward_subsumption_resolution,[],[f440,f342]) ).
fof(f447,definition,
( spl11_14
<=> sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
fof(f449,plain,
( sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)) = sK9(sK1,sK2,sK3,sK4)
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f451,definition,
( spl11_15
<=> ! [X0,X1] :
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),X0)
| ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| ~ maps(sK2,X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
fof(f452,plain,
( ! [X0,X1] :
( ~ member(sK6(sK1,sK4,sK7(sK1,sK2,sK3,sK4)),X0)
| ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| ~ maps(sK2,X1,X0) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f453,plain,
( spl11_14
| spl11_15
| ~ spl11_6
| ~ spl11_10 ),
inference(avatar_split_clause,[],[f445,f357,f341,f451,f447]) ).
fof(f490,plain,
( ! [X0,X1] :
( ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| sK9(sK1,sK2,sK3,sK4) = sK8(sK1,sK2,sK3,sK4)
| ~ member(sK8(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X1,X0)
| equal_maps(sK1,sK2,sK3,sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_14 ),
inference(superposition,[],[f205,f449]) ).
fof(f492,plain,
( ! [X0,X1] :
( ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| ~ member(sK8(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X1,X0)
| equal_maps(sK1,sK2,sK3,sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f490,f70]) ).
fof(f493,plain,
( ! [X0,X1] :
( ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| ~ member(sK8(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X1,X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f492,f60]) ).
fof(f494,plain,
( ! [X0,X1] :
( ~ member(sK9(sK1,sK2,sK3,sK4),X0)
| ~ member(sK7(sK1,sK2,sK3,sK4),X1)
| ~ member(sK8(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X1,X0) )
| ~ spl11_6
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f493,f342]) ).
fof(f569,plain,
( ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ member(sK8(sK1,sK2,sK3,sK4),sK4)
| ~ maps(sK1,X0,sK4)
| equal_maps(sK1,sK2,sK3,sK4) )
| ~ spl11_6
| ~ spl11_14 ),
inference(resolution,[],[f494,f65]) ).
fof(f587,definition,
( spl11_19
<=> ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
fof(f588,plain,
( ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X0,sK4) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f590,plain,
( ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X0,sK4)
| equal_maps(sK1,sK2,sK3,sK4) )
| ~ spl11_6
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f569,f66]) ).
fof(f591,plain,
( ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK1,X0,sK4) )
| ~ spl11_6
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f590,f60]) ).
fof(f592,plain,
( spl11_19
| ~ spl11_6
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f591,f447,f341,f587]) ).
fof(f633,plain,
( ! [X0] :
( ~ member(sK9(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X0,sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),sK3) )
| ~ spl11_15 ),
inference(resolution,[],[f452,f94]) ).
fof(f645,plain,
( ! [X0] :
( ~ member(sK9(sK1,sK2,sK3,sK4),sK4)
| ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X0,sK4) )
| ~ spl11_6
| ~ spl11_15 ),
inference(forward_subsumption_resolution,[],[f633,f342]) ).
fof(f647,definition,
( spl11_22
<=> ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
fof(f648,plain,
( ! [X0] :
( ~ member(sK7(sK1,sK2,sK3,sK4),X0)
| ~ maps(sK2,X0,sK4) )
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f650,definition,
( spl11_23
<=> member(sK9(sK1,sK2,sK3,sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl11_23])],[avatar_definition]) ).
fof(f652,plain,
( ~ member(sK9(sK1,sK2,sK3,sK4),sK4)
| spl11_23 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f654,plain,
( spl11_22
| ~ spl11_23
| ~ spl11_6
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f645,f451,f341,f650,f647]) ).
fof(f674,plain,
( equal_maps(sK1,sK2,sK3,sK4)
| spl11_23 ),
inference(resolution,[],[f652,f65]) ).
fof(f675,plain,
( $false
| spl11_23 ),
inference(forward_subsumption_resolution,[],[f674,f60]) ).
fof(f676,plain,
spl11_23,
inference(avatar_contradiction_clause,[],[f675]) ).
fof(f725,plain,
( ~ maps(sK1,sK3,sK4)
| equal_maps(sK1,sK2,sK3,sK4)
| ~ spl11_19 ),
inference(resolution,[],[f588,f67]) ).
fof(f732,plain,
( equal_maps(sK1,sK2,sK3,sK4)
| ~ spl11_19 ),
inference(forward_subsumption_resolution,[],[f725,f58]) ).
fof(f733,plain,
( $false
| ~ spl11_19 ),
inference(forward_subsumption_resolution,[],[f732,f60]) ).
fof(f734,plain,
~ spl11_19,
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f746,plain,
( ~ maps(sK2,sK3,sK4)
| equal_maps(sK1,sK2,sK3,sK4)
| ~ spl11_22 ),
inference(resolution,[],[f648,f67]) ).
fof(f753,plain,
( equal_maps(sK1,sK2,sK3,sK4)
| ~ spl11_22 ),
inference(forward_subsumption_resolution,[],[f746,f57]) ).
fof(f754,plain,
( $false
| ~ spl11_22 ),
inference(forward_subsumption_resolution,[],[f753,f60]) ).
fof(f755,plain,
~ spl11_22,
inference(avatar_contradiction_clause,[],[f754]) ).
cnf(s2,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f267]) ).
cnf(s5,plain,
spl11_1,
inference(sat_conversion,[],[f293]) ).
cnf(s7,plain,
( ~ spl11_1
| ~ spl11_3
| spl11_10
| ~ spl11_11 ),
inference(sat_conversion,[],[f364]) ).
cnf(s9,plain,
spl11_6,
inference(sat_conversion,[],[f383]) ).
cnf(s15,plain,
( ~ spl11_6
| spl11_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s17,plain,
( ~ spl11_6
| ~ spl11_10
| spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f453]) ).
cnf(s20,plain,
( ~ spl11_6
| ~ spl11_14
| spl11_19 ),
inference(sat_conversion,[],[f592]) ).
cnf(s23,plain,
( ~ spl11_6
| ~ spl11_15
| spl11_22
| ~ spl11_23 ),
inference(sat_conversion,[],[f654]) ).
cnf(s24,plain,
spl11_23,
inference(sat_conversion,[],[f676]) ).
cnf(s29,plain,
~ spl11_19,
inference(sat_conversion,[],[f734]) ).
cnf(s31,plain,
~ spl11_22,
inference(sat_conversion,[],[f755]) ).
cnf(s32,plain,
( ~ spl11_6
| ~ spl11_15 ),
inference(rat,[],[s23,s24,s31]) ).
cnf(s34,plain,
( ~ spl11_6
| ~ spl11_14 ),
inference(rat,[],[s20,s29]) ).
cnf(s36,plain,
~ spl11_15,
inference(rat,[],[s32,s9]) ).
cnf(s37,plain,
~ spl11_14,
inference(rat,[],[s34,s9]) ).
cnf(s38,plain,
~ spl11_10,
inference(rat,[],[s17,s36,s37,s9]) ).
cnf(s39,plain,
spl11_11,
inference(rat,[],[s15,s9]) ).
cnf(s41,plain,
( ~ spl11_1
| ~ spl11_3 ),
inference(rat,[],[s7,s39,s38]) ).
cnf(s43,plain,
~ spl11_3,
inference(rat,[],[s41,s5]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s2,s43,s5]) ).
fof(f756,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET723+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 02:38:53 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.92/0.97 % (2958063)Detected formulas, will run a generic FOF schedule.
% 0.92/0.97 % (2958068)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=1872141433:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.92/0.97 % (2958072)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3762530865:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.92/0.97 % (2958071)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3502648137:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.92/0.97 % (2958070)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=348827579:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.92/0.97 % (2958074)dis-21_1_sil=8000:lcm=predicate:random_seed=2202278457: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)
% 0.92/0.97 % (2958069)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=1405571590:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.92/0.97 % (2958073)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3441751242:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.92/0.97 % (2958071)Instruction limit reached!
% 0.92/0.97 % (2958071)------------------------------
% 0.92/0.97 % (2958071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.92/0.97 % (2958071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.97 % (2958071)CaDiCaL version: 2.1.3
% 0.92/0.97 % (2958071)Termination reason: Instruction limit
% 0.92/0.97 % (2958071)Termination phase: Saturation
% 0.92/0.97 % (2958071)Time elapsed: 0.032 s
% 0.92/0.97 % (2958071)Peak memory usage: 89 MB
% 0.92/0.97 % (2958071)Instructions burned: 110 (million)
% 0.92/0.97 % (2958072)Instruction limit reached!
% 0.92/0.97 % (2958072)------------------------------
% 0.92/0.97 % (2958072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.92/0.97 % (2958072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.97 % (2958072)CaDiCaL version: 2.1.3
% 0.92/0.97 % (2958072)Termination reason: Instruction limit
% 0.92/0.97 % (2958072)Termination phase: Saturation
% 0.92/0.97 % (2958072)Time elapsed: 0.037 s
% 0.92/0.97 % (2958072)Peak memory usage: 88 MB
% 0.92/0.97 % (2958072)Instructions burned: 119 (million)
% 0.92/0.97 % (2958074)Instruction limit reached!
% 0.92/0.97 % (2958074)------------------------------
% 0.92/0.97 % (2958074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.92/0.97 % (2958074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.97 % (2958074)CaDiCaL version: 2.1.3
% 0.92/0.97 % (2958074)Termination reason: Instruction limit
% 0.92/0.97 % (2958074)Termination phase: Saturation
% 0.92/0.97 % (2958074)Time elapsed: 0.042 s
% 0.92/0.97 % (2958074)Peak memory usage: 89 MB
% 0.92/0.97 % (2958074)Instructions burned: 132 (million)
% 0.92/0.97 % (2958073)Instruction limit reached!
% 0.92/0.97 % (2958073)------------------------------
% 0.92/0.97 % (2958073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.92/0.97 % (2958073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.97 % (2958073)CaDiCaL version: 2.1.3
% 0.92/0.97 % (2958073)Termination reason: Instruction limit
% 0.92/0.97 % (2958073)Termination phase: Saturation
% 0.92/0.97 % (2958073)Time elapsed: 0.057 s
% 0.92/0.97 % (2958073)Peak memory usage: 90 MB
% 0.92/0.97 % (2958073)Instructions burned: 141 (million)
% 0.92/0.97 % (2958082)lrs+10_1_sil=8000:sp=occurrence:random_seed=717376742:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.92/0.97 % (2958083)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2461368773:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.92/0.97 % (2958084)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4205460470:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 0.92/0.97 % (2958082)First to succeed.
% 0.92/0.97 % (2958083)Also succeeded, but the first one will report.
% 0.92/0.97 % (2958082)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2958063"
% 0.92/0.97 % (2958085)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=74121871:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 0.92/0.97 % (2958084)Also succeeded, but the first one will report.
% 0.92/0.97 % (2958085)Instruction limit reached!
% 0.92/0.97 % (2958085)------------------------------
% 0.92/0.97 % (2958085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.92/0.97 % (2958085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.97 % (2958085)CaDiCaL version: 2.1.3
% 0.92/0.97 % (2958085)Termination reason: Instruction limit
% 0.92/0.97 % (2958085)Termination phase: Saturation
% 0.92/0.97 % (2958085)Time elapsed: 0.071 s
% 0.92/0.97 % (2958085)Peak memory usage: 89 MB
% 0.92/0.97 % (2958085)Instructions burned: 250 (million)
% 0.92/0.97 % (2958082)Refutation found. Thanks to Tanya!
% 0.92/0.97 % SZS status Theorem for theBenchmark
% 0.92/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.08 % (2958082)------------------------------
% 3.37/1.08 % (2958082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.08 % (2958082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.08 % (2958082)CaDiCaL version: 2.1.3
% 3.37/1.08 % (2958082)Termination reason: Refutation
% 3.37/1.08 % (2958082)Time elapsed: 0.025 s
% 3.37/1.08 % (2958082)Peak memory usage: 90 MB
% 3.37/1.08 % (2958082)Instructions burned: 69 (million)
% 3.37/1.08 % (2958082)------------------------------
% 3.37/1.08 % (2958082)------------------------------
% 3.37/1.08 % (2958063)Success in time 0.453 s
% 3.37/1.08 % Vampire exiting
%------------------------------------------------------------------------------