%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET727+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:45 PM UTC 2026
% Result : Theorem 4.17s 1.55s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 85 ( 41 unt; 0 def)
% Number of atoms : 289 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 297 ( 93 ~; 89 |; 83 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 250 ( 224 !; 26 ?)
% 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',equal_maps) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X3,X1)
& member(X4,X2) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> equal_maps(inverse_function(X0,X3,X4),X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII18) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> equal_maps(inverse_function(X0,X3,X4),X2,X4,X3) ),
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] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f34,plain,
! [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 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X2,X4,X3)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X2,X4,X3)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(flattening,[],[f35]) ).
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(ennf_transformation,[],[f32]) ).
fof(f38,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,[],[f37]) ).
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(ennf_transformation,[],[f34]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
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,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ~ equal_maps(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)
& maps(sK0,sK3,sK4)
& maps(sK1,sK4,sK3)
& maps(sK2,sK4,sK3)
& identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3)
& identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f36]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK5(X0,X2,X3),X2)
& apply(X0,X3,sK5(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,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f38]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& member(sK6(X0,X1,X2,X3),X2)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK8(X0,X1,X2,X3),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0,X1,X2,X3)),skolemize(X5,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f40]) ).
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(sK9(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK9(X0,X1,X3,X5,X6))
& apply(X0,sK9(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,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(nnf_transformation,[],[f45]) ).
fof(f53,plain,
identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4),
inference(cnf_transformation,[],[f46]) ).
fof(f54,plain,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f55,plain,
maps(sK2,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f56,plain,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f57,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
~ equal_maps(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f59,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,[],[f47]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK5(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK9(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK9(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK9(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
member(sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK3),
inference(unit_resulting_resolution,[],[f62,f58]) ).
fof(f76,plain,
apply(compose_function(sK1,sK0,sK3,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f68,f54,f75]) ).
fof(f77,plain,
member(sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK3),
inference(unit_resulting_resolution,[],[f63,f58]) ).
fof(f78,plain,
apply(compose_function(sK1,sK0,sK3,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f68,f54,f77]) ).
fof(f79,plain,
member(sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK4),
inference(unit_resulting_resolution,[],[f64,f58]) ).
fof(f80,plain,
apply(compose_function(sK0,sK2,sK4,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f68,f53,f79]) ).
fof(f81,plain,
member(sK5(sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK4),
inference(unit_resulting_resolution,[],[f61,f57,f75]) ).
fof(f88,plain,
apply(sK0,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK5(sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f60,f57,f75]) ).
fof(f99,plain,
sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3) != sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),
inference(unit_resulting_resolution,[],[f67,f58]) ).
fof(f103,plain,
apply(sK2,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f65,f58]) ).
fof(f107,plain,
apply(inverse_function(sK0,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f66,f58]) ).
fof(f135,plain,
apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f74,f79,f77,f107]) ).
fof(f216,plain,
apply(sK0,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK9(sK1,sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f70,f75,f75,f76]) ).
fof(f217,plain,
apply(sK1,sK9(sK1,sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f69,f75,f75,f76]) ).
fof(f218,plain,
member(sK9(sK1,sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK4),
inference(unit_resulting_resolution,[],[f71,f75,f75,f76]) ).
fof(f228,plain,
apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f70,f77,f77,f78]) ).
fof(f229,plain,
apply(sK1,sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f69,f77,f77,f78]) ).
fof(f230,plain,
member(sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK4),
inference(unit_resulting_resolution,[],[f71,f77,f77,f78]) ).
fof(f241,plain,
apply(sK2,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK9(sK0,sK2,sK3,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f70,f79,f79,f80]) ).
fof(f242,plain,
apply(sK0,sK9(sK0,sK2,sK3,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f69,f79,f79,f80]) ).
fof(f243,plain,
member(sK9(sK0,sK2,sK3,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK3),
inference(unit_resulting_resolution,[],[f71,f79,f79,f80]) ).
fof(f978,plain,
sK5(sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)) = sK9(sK1,sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f57,f75,f81,f88,f218,f216]) ).
fof(f1002,plain,
apply(inverse_function(sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK9(sK1,sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f73,f75,f218,f217]) ).
fof(f1015,plain,
apply(inverse_function(sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK5(sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(forward_demodulation,[],[f1002,f978]) ).
fof(f1024,plain,
sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3) = sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f57,f77,f79,f135,f230,f228]) ).
fof(f1067,plain,
~ apply(sK1,sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f56,f75,f77,f99,f230,f229]) ).
fof(f1085,plain,
~ apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(forward_demodulation,[],[f1067,f1024]) ).
fof(f1090,plain,
~ apply(inverse_function(sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f74,f75,f79,f1085]) ).
fof(f1102,plain,
sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3) = sK9(sK0,sK2,sK3,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f55,f79,f75,f103,f243,f241]) ).
fof(f1161,plain,
apply(inverse_function(sK0,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK9(sK0,sK2,sK3,sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3))),
inference(unit_resulting_resolution,[],[f73,f79,f243,f242]) ).
fof(f1178,plain,
apply(inverse_function(sK0,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(forward_demodulation,[],[f1161,f1102]) ).
fof(f1299,plain,
apply(sK0,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f74,f79,f75,f1178]) ).
fof(f1445,plain,
sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3) = sK5(sK0,sK4,sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f57,f75,f79,f81,f88,f1299]) ).
fof(f1519,plain,
apply(inverse_function(sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK2,sK4,sK3)),
inference(superposition,[],[f1015,f1445]) ).
fof(f1520,plain,
$false,
inference(forward_subsumption_resolution,[],[f1519,f1090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET727+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n006.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:39:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.17/1.55 % (3535258)Detected formulas, will run a generic FOF schedule.
% 4.17/1.55 % (3535266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3003242093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.17/1.55 % (3535266)Refutation not found, incomplete strategy
% 4.17/1.55 % (3535266)------------------------------
% 4.17/1.55 % (3535266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535266)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535266)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.55 % (3535266)Time elapsed: 0.010 s
% 4.17/1.55 % (3535266)Peak memory usage: 89 MB
% 4.17/1.55 % (3535266)Instructions burned: 27 (million)
% 4.17/1.55 % (3535269)dis-21_1_sil=8000:lcm=predicate:random_seed=2993802859:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.17/1.55 % (3535263)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=998654375:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.17/1.55 % (3535265)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=2947355539:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.17/1.55 % (3535267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2893936686:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.17/1.55 % (3535264)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=2531391231:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.17/1.55 % (3535268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1277556061:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.17/1.55 % (3535267)Instruction limit reached!
% 4.17/1.55 % (3535267)------------------------------
% 4.17/1.55 % (3535267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535267)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535267)Termination reason: Instruction limit
% 4.17/1.55 % (3535267)Termination phase: Saturation
% 4.17/1.55 % (3535267)Time elapsed: 0.069 s
% 4.17/1.55 % (3535267)Peak memory usage: 89 MB
% 4.17/1.55 % (3535267)Instructions burned: 119 (million)
% 4.17/1.55 % (3535269)Instruction limit reached!
% 4.17/1.55 % (3535269)------------------------------
% 4.17/1.55 % (3535269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535269)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535269)Termination reason: Instruction limit
% 4.17/1.55 % (3535269)Termination phase: Saturation
% 4.17/1.55 % (3535269)Time elapsed: 0.078 s
% 4.17/1.55 % (3535269)Peak memory usage: 89 MB
% 4.17/1.55 % (3535269)Instructions burned: 130 (million)
% 4.17/1.55 % (3535268)Instruction limit reached!
% 4.17/1.55 % (3535268)------------------------------
% 4.17/1.55 % (3535268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535268)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535268)Termination reason: Instruction limit
% 4.17/1.55 % (3535268)Termination phase: Saturation
% 4.17/1.55 % (3535268)Time elapsed: 0.095 s
% 4.17/1.55 % (3535268)Peak memory usage: 89 MB
% 4.17/1.55 % (3535268)Instructions burned: 139 (million)
% 4.17/1.55 % (3535266)------------------------------
% 4.17/1.55 % (3535266)------------------------------
% 4.17/1.55 % (3535280)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=349478527:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.17/1.55 % (3535278)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3592440499:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.17/1.55 % (3535277)lrs+10_1_sil=8000:sp=occurrence:random_seed=2002655763:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.17/1.55 % (3535279)lrs+1011_1_sil=32000:sp=occurrence:random_seed=747160446:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.17/1.55 % (3535280)Instruction limit reached!
% 4.17/1.55 % (3535280)------------------------------
% 4.17/1.55 % (3535280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535280)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535280)Termination reason: Instruction limit
% 4.17/1.55 % (3535280)Termination phase: Saturation
% 4.17/1.55 % (3535280)Time elapsed: 0.065 s
% 4.17/1.55 % (3535280)Peak memory usage: 92 MB
% 4.17/1.55 % (3535280)Instructions burned: 252 (million)
% 4.17/1.55 % (3535278)First to succeed.
% 4.17/1.55 % (3535278)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3535258"
% 4.17/1.55 % (3535285)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1757527049:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.17/1.55 % (3535285)Refutation not found, incomplete strategy
% 4.17/1.55 % (3535285)------------------------------
% 4.17/1.55 % (3535285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535285)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535285)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.55 % (3535285)Time elapsed: 0.001 s
% 4.17/1.55 % (3535285)Peak memory usage: 88 MB
% 4.17/1.55 % (3535285)Instructions burned: 1 (million)
% 4.17/1.55 % (3535277)Instruction limit reached!
% 4.17/1.55 % (3535277)------------------------------
% 4.17/1.55 % (3535277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535277)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535277)Termination reason: Instruction limit
% 4.17/1.55 % (3535277)Termination phase: Saturation
% 4.17/1.55 % (3535277)Time elapsed: 0.166 s
% 4.17/1.55 % (3535277)Peak memory usage: 93 MB
% 4.17/1.55 % (3535277)Instructions burned: 285 (million)
% 4.17/1.55 % (3535279)Instruction limit reached!
% 4.17/1.55 % (3535279)------------------------------
% 4.17/1.55 % (3535279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.55 % (3535279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.55 % (3535279)CaDiCaL version: 2.1.3
% 4.17/1.55 % (3535279)Termination reason: Instruction limit
% 4.17/1.55 % (3535279)Termination phase: Saturation
% 4.17/1.55 % (3535279)Time elapsed: 0.227 s
% 4.17/1.55 % (3535279)Peak memory usage: 93 MB
% 4.17/1.55 % (3535279)Instructions burned: 326 (million)
% 4.17/1.55 % (3535285)------------------------------
% 4.17/1.55 % (3535285)------------------------------
% 4.17/1.55 % (3535287)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3333906899:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.17/1.55 % (3535278)Refutation found. Thanks to Tanya!
% 4.17/1.55 % SZS status Theorem for theBenchmark
% 4.17/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.44/1.75 % (3535278)------------------------------
% 5.44/1.75 % (3535278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.75 % (3535278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.75 % (3535278)CaDiCaL version: 2.1.3
% 5.44/1.75 % (3535278)Termination reason: Refutation
% 5.44/1.75 % (3535278)Time elapsed: 0.081 s
% 5.44/1.75 % (3535278)Peak memory usage: 90 MB
% 5.44/1.75 % (3535278)Instructions burned: 151 (million)
% 5.44/1.75 % (3535278)------------------------------
% 5.44/1.75 % (3535278)------------------------------
% 5.44/1.75 % (3535258)Success in time 0.685 s
% 5.44/1.75 % Vampire exiting
%------------------------------------------------------------------------------