%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET735+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 : n013.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 12:41:46 PM UTC 2026
% Result : Theorem 8.74s 2.10s
% Output : Refutation 9.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 212 ( 29 unt; 9 def)
% Number of atoms : 827 ( 96 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1065 ( 450 ~; 467 |; 109 &)
% ( 16 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-5 aty)
% Number of variables : 456 ( 0 sgn 424 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
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(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( member(X3,image3(X0,X1,X2))
<=> ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image3) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X3,X4)
& maps(X2,X4,X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& equal_set(image3(X0,X3,X4),image3(X1,X3,X4)) )
=> equal_maps(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII26) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X3,X4)
& maps(X2,X4,X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& equal_set(image3(X0,X3,X4),image3(X1,X3,X4)) )
=> equal_maps(X0,X1,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] :
( 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] :
( equal_set(X0,X1)
=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f41,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(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(flattening,[],[f41]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f48,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(X0,X1,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X3,X4)
& maps(X2,X4,X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& equal_set(image3(X0,X3,X4),image3(X1,X3,X4)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f49,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(X0,X1,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X3,X4)
& maps(X2,X4,X3)
& identity(compose_function(X2,X0,X3,X4,X3),X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& equal_set(image3(X0,X3,X4),image3(X1,X3,X4)) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f51]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f70,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,[],[f42]) ).
fof(f71,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,[],[f70]) ).
fof(f72,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(sK4(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& apply(X0,sK4(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,[sK4]),skolemize(X8,sK4(X0,X1,X3,X5,X6))],[f71]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& member(sK5(X0,X1,X2,X3),X2)
& member(sK6(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X4,sK5(X0,X1,X2,X3)),skolemize(X5,sK6(X0,X1,X2,X3)),skolemize(X6,sK7(X0,X1,X2,X3))],[f44]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X0,X5,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& member(sK9(X0,X1,X3),X1)
& apply(X0,sK9(X0,X1,X3),X3) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X5,sK9(X0,X1,X3))],[f80]) ).
fof(f89,plain,
( ~ equal_maps(sK12,sK13,sK15,sK16)
& maps(sK12,sK15,sK16)
& maps(sK13,sK15,sK16)
& maps(sK14,sK16,sK15)
& identity(compose_function(sK14,sK12,sK15,sK16,sK15),sK15)
& identity(compose_function(sK14,sK13,sK15,sK16,sK15),sK15)
& equal_set(image3(sK12,sK15,sK16),image3(sK13,sK15,sK16)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15),skolemize(X4,sK16)],[f49]) ).
fof(f90,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f94,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f118,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,[],[f69]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK4(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK4(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK4(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| apply(X0,sK9(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(sK9(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(X3,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f140,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X1)
| member(X3,image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f148,plain,
equal_set(image3(sK12,sK15,sK16),image3(sK13,sK15,sK16)),
inference(cnf_transformation,[],[f89]) ).
fof(f149,plain,
identity(compose_function(sK14,sK13,sK15,sK16,sK15),sK15),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
identity(compose_function(sK14,sK12,sK15,sK16,sK15),sK15),
inference(cnf_transformation,[],[f89]) ).
fof(f151,plain,
maps(sK14,sK16,sK15),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
maps(sK13,sK15,sK16),
inference(cnf_transformation,[],[f89]) ).
fof(f153,plain,
maps(sK12,sK15,sK16),
inference(cnf_transformation,[],[f89]) ).
fof(f154,plain,
~ equal_maps(sK12,sK13,sK15,sK16),
inference(cnf_transformation,[],[f89]) ).
fof(f158,definition,
sF17 = compose_function(sK14,sK12,sK15,sK16,sK15),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f159,plain,
compose_function(sK14,sK12,sK15,sK16,sK15) = sF17,
inference(reorient_equations,[],[f158]) ).
fof(f160,plain,
identity(sF17,sK15),
inference(definition_folding,[],[f150,f159]) ).
fof(f161,definition,
sF18 = compose_function(sK14,sK13,sK15,sK16,sK15),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f162,plain,
compose_function(sK14,sK13,sK15,sK16,sK15) = sF18,
inference(reorient_equations,[],[f161]) ).
fof(f163,plain,
identity(sF18,sK15),
inference(definition_folding,[],[f149,f162]) ).
fof(f164,definition,
sF19 = image3(sK12,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f165,plain,
image3(sK12,sK15,sK16) = sF19,
inference(reorient_equations,[],[f164]) ).
fof(f166,definition,
sF20 = image3(sK13,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f167,plain,
image3(sK13,sK15,sK16) = sF20,
inference(reorient_equations,[],[f166]) ).
fof(f168,plain,
equal_set(sF19,sF20),
inference(definition_folding,[],[f148,f167,f165]) ).
fof(f169,plain,
! [X0] :
( apply(sF17,X0,X0)
| ~ member(X0,sK15) ),
inference(resolution,[],[f160,f131]) ).
fof(f172,plain,
! [X0] :
( ~ member(X0,sF20)
| member(X0,sK16) ),
inference(superposition,[],[f139,f167]) ).
fof(f174,plain,
! [X0,X1] :
( apply(sK14,sK4(sK14,sK12,sK16,X0,X1),X1)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f121,f159]) ).
fof(f175,plain,
! [X0,X1] :
( apply(sK14,sK4(sK14,sK13,sK16,X0,X1),X1)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f121,f162]) ).
fof(f176,plain,
! [X0,X1] :
( apply(sK12,X0,sK4(sK14,sK12,sK16,X0,X1))
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f122,f159]) ).
fof(f177,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sK14,sK13,sK16,X0,X1))
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f122,f162]) ).
fof(f178,plain,
! [X0] :
( apply(sF18,X0,X0)
| ~ member(X0,sK15) ),
inference(resolution,[],[f163,f131]) ).
fof(f181,plain,
! [X0] :
( member(sK9(sK13,sK15,X0),sK15)
| ~ member(X0,sF20) ),
inference(superposition,[],[f138,f167]) ).
fof(f189,plain,
! [X0] :
( apply(sK13,sK9(sK13,sK15,X0),X0)
| ~ member(X0,sF20) ),
inference(superposition,[],[f137,f167]) ).
fof(f206,plain,
! [X0,X1] :
( member(sK4(sK14,sK12,sK16,X0,X1),sK16)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f123,f159]) ).
fof(f207,plain,
! [X0,X1] :
( member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(superposition,[],[f123,f162]) ).
fof(f228,plain,
subset(sF19,sF20),
inference(resolution,[],[f168,f94]) ).
fof(f250,plain,
! [X0] :
( apply(sK12,X0,sK3(sK12,sK16,X0))
| ~ member(X0,sK15) ),
inference(resolution,[],[f119,f153]) ).
fof(f251,plain,
! [X0] :
( apply(sK13,X0,sK3(sK13,sK16,X0))
| ~ member(X0,sK15) ),
inference(resolution,[],[f119,f152]) ).
fof(f252,plain,
! [X0] :
( apply(sK14,X0,sK3(sK14,sK15,X0))
| ~ member(X0,sK16) ),
inference(resolution,[],[f119,f151]) ).
fof(f253,plain,
! [X2,X0,X1] :
( member(sK3(sK12,sK16,X0),image3(sK12,X2,X1))
| ~ member(sK3(sK12,sK16,X0),X1)
| ~ member(X0,X2)
| ~ member(X0,sK15) ),
inference(resolution,[],[f250,f140]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK12,sK16,X0),X3)
| ~ apply(sK12,X0,X1)
| sK3(sK12,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK15)
| ~ maps(sK12,X2,X3) ),
inference(resolution,[],[f250,f118]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK13,sK16,X0),X3)
| ~ apply(sK13,X0,X1)
| sK3(sK13,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK15)
| ~ maps(sK13,X2,X3) ),
inference(resolution,[],[f251,f118]) ).
fof(f261,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK14,sK15,X0),X3)
| ~ apply(sK14,X0,X1)
| sK3(sK14,sK15,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK16)
| ~ maps(sK14,X2,X3) ),
inference(resolution,[],[f252,f118]) ).
fof(f295,plain,
! [X0] :
( member(sK3(sK12,sK16,X0),sK16)
| ~ member(X0,sK15) ),
inference(resolution,[],[f120,f153]) ).
fof(f296,plain,
! [X0] :
( member(sK3(sK13,sK16,X0),sK16)
| ~ member(X0,sK15) ),
inference(resolution,[],[f120,f152]) ).
fof(f297,plain,
! [X0] :
( member(sK3(sK14,sK15,X0),sK15)
| ~ member(X0,sK16) ),
inference(resolution,[],[f120,f151]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| ~ apply(sK12,X0,X1)
| sK3(sK12,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ member(X0,sK15)
| ~ maps(sK12,X2,sK16) ),
inference(resolution,[],[f295,f255]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ~ apply(sK12,X0,X1)
| ~ member(X0,sK15)
| sK3(sK12,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ maps(sK12,X2,sK16) ),
inference(duplicate_literal_removal,[],[f298]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| ~ apply(sK13,X0,X1)
| sK3(sK13,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ member(X0,sK15)
| ~ maps(sK13,X2,sK16) ),
inference(resolution,[],[f296,f258]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK15)
| sK3(sK13,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ maps(sK13,X2,sK16) ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ member(X0,sK16)
| ~ apply(sK14,X0,X1)
| sK3(sK14,sK15,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK15)
| ~ member(X0,sK16)
| ~ maps(sK14,X2,sK15) ),
inference(resolution,[],[f297,f261]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| sK3(sK14,sK15,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15) ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK12,sK16,X0,X1),sK16)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(sK4(sK14,sK12,sK16,X0,X1),X2)
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(resolution,[],[f303,f174]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| sK3(sK14,sK15,sK4(sK14,sK13,sK16,X0,X1)) = X1
| ~ member(sK4(sK14,sK13,sK16,X0,X1),X2)
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(resolution,[],[f303,f175]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| sK3(sK14,sK15,sK4(sK14,sK13,sK16,X0,X1)) = X1
| ~ member(sK4(sK14,sK13,sK16,X0,X1),X2)
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f306]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK12,sK16,X0,X1),sK16)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(sK4(sK14,sK12,sK16,X0,X1),X2)
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f305]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK16,X0,X1),X2)
| sK3(sK14,sK15,sK4(sK14,sK13,sK16,X0,X1)) = X1
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15) ),
inference(forward_subsumption_resolution,[],[f309,f207]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK12,sK16,X0,X1),X2)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(X1,sK15)
| ~ maps(sK14,X2,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15) ),
inference(forward_subsumption_resolution,[],[f310,f206]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| sK4(sK14,sK12,sK16,X0,X1) = sK3(sK12,sK16,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK12,sK16,X0,X1),sK16)
| ~ maps(sK12,X2,sK16)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(resolution,[],[f299,f176]) ).
fof(f316,plain,
! [X2,X3,X0,X1] :
( ~ member(sK6(sK12,X0,X1,X2),sK16)
| sK6(sK12,X0,X1,X2) = sK3(sK12,sK16,sK5(sK12,X0,X1,X2))
| ~ member(sK5(sK12,X0,X1,X2),X3)
| ~ member(sK5(sK12,X0,X1,X2),sK15)
| ~ maps(sK12,X3,sK16)
| equal_maps(sK12,X0,X1,X2) ),
inference(resolution,[],[f299,f129]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| sK4(sK14,sK12,sK16,X0,X1) = sK3(sK12,sK16,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK12,sK16,X0,X1),sK16)
| ~ maps(sK12,X2,sK16)
| ~ apply(sF17,X0,X1)
| ~ member(X1,sK15) ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f322,plain,
! [X2,X0,X1] :
( ~ apply(sF17,X0,X1)
| sK4(sK14,sK12,sK16,X0,X1) = sK3(sK12,sK16,X0)
| ~ member(X0,X2)
| ~ maps(sK12,X2,sK16)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(forward_subsumption_resolution,[],[f320,f206]) ).
fof(f333,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| sK4(sK14,sK13,sK16,X0,X1) = sK3(sK13,sK16,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| ~ maps(sK13,X2,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(resolution,[],[f301,f177]) ).
fof(f336,plain,
! [X2,X3,X0,X1] :
( ~ member(sK7(X0,sK13,X1,X2),sK16)
| sK7(X0,sK13,X1,X2) = sK3(sK13,sK16,sK5(X0,sK13,X1,X2))
| ~ member(sK5(X0,sK13,X1,X2),X3)
| ~ member(sK5(X0,sK13,X1,X2),sK15)
| ~ maps(sK13,X3,sK16)
| equal_maps(X0,sK13,X1,X2) ),
inference(resolution,[],[f301,f128]) ).
fof(f337,plain,
! [X0,X1] :
( ~ member(sK9(sK13,sK15,X0),sK15)
| sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0
| ~ member(sK9(sK13,sK15,X0),X1)
| ~ member(X0,sK16)
| ~ maps(sK13,X1,sK16)
| ~ member(X0,sF20) ),
inference(resolution,[],[f301,f189]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ member(X0,sK15)
| sK4(sK14,sK13,sK16,X0,X1) = sK3(sK13,sK16,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| ~ maps(sK13,X2,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X1,sK15) ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f340,plain,
! [X0,X1] :
( sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0
| ~ member(sK9(sK13,sK15,X0),X1)
| ~ member(X0,sK16)
| ~ maps(sK13,X1,sK16)
| ~ member(X0,sF20) ),
inference(forward_subsumption_resolution,[],[f337,f181]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ apply(sF18,X0,X1)
| sK4(sK14,sK13,sK16,X0,X1) = sK3(sK13,sK16,X0)
| ~ member(X0,X2)
| ~ maps(sK13,X2,sK16)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(forward_subsumption_resolution,[],[f339,f207]) ).
fof(f342,plain,
! [X0,X1] :
( ~ member(sK9(sK13,sK15,X0),X1)
| sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0
| ~ maps(sK13,X1,sK16)
| ~ member(X0,sF20) ),
inference(forward_subsumption_resolution,[],[f340,f172]) ).
fof(f343,plain,
! [X0] :
( sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0
| ~ maps(sK13,sK15,sK16)
| ~ member(X0,sF20)
| ~ member(X0,sF20) ),
inference(resolution,[],[f342,f181]) ).
fof(f345,plain,
! [X0] :
( sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0
| ~ maps(sK13,sK15,sK16)
| ~ member(X0,sF20) ),
inference(duplicate_literal_removal,[],[f343]) ).
fof(f347,plain,
! [X0] :
( ~ member(X0,sF20)
| sK3(sK13,sK16,sK9(sK13,sK15,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f345,f152]) ).
fof(f352,plain,
! [X0,X1] :
( sK3(sK13,sK16,X0) = sK4(sK14,sK13,sK16,X0,X0)
| ~ member(X0,X1)
| ~ maps(sK13,X1,sK16)
| ~ member(X0,sK15)
| ~ member(X0,sK15)
| ~ member(X0,sK15) ),
inference(resolution,[],[f341,f178]) ).
fof(f355,plain,
! [X0,X1] :
( ~ maps(sK13,X1,sK16)
| ~ member(X0,X1)
| sK3(sK13,sK16,X0) = sK4(sK14,sK13,sK16,X0,X0)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f352]) ).
fof(f356,plain,
! [X0,X1] :
( sK3(sK12,sK16,X0) = sK4(sK14,sK12,sK16,X0,X0)
| ~ member(X0,X1)
| ~ maps(sK12,X1,sK16)
| ~ member(X0,sK15)
| ~ member(X0,sK15)
| ~ member(X0,sK15) ),
inference(resolution,[],[f322,f169]) ).
fof(f359,plain,
! [X0,X1] :
( ~ maps(sK12,X1,sK16)
| ~ member(X0,X1)
| sK3(sK12,sK16,X0) = sK4(sK14,sK12,sK16,X0,X0)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f356]) ).
fof(f368,plain,
! [X0,X1] :
( sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(X1,sK15)
| ~ maps(sK14,sK16,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK15) ),
inference(resolution,[],[f313,f206]) ).
fof(f370,plain,
! [X0,X1] :
( sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(X1,sK15)
| ~ maps(sK14,sK16,sK15)
| ~ apply(sF17,X0,X1)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f368]) ).
fof(f371,plain,
! [X0,X1] :
( ~ apply(sF17,X0,X1)
| ~ member(X1,sK15)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X1)) = X1
| ~ member(X0,sK15) ),
inference(forward_subsumption_resolution,[],[f370,f151]) ).
fof(f372,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X0)) = X0
| ~ member(X0,sK15)
| ~ member(X0,sK15) ),
inference(resolution,[],[f371,f169]) ).
fof(f375,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK14,sK15,sK4(sK14,sK12,sK16,X0,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f372]) ).
fof(f390,plain,
! [X2,X0,X1] :
( sK7(X0,sK13,X1,sK16) = sK3(sK13,sK16,sK5(X0,sK13,X1,sK16))
| ~ member(sK5(X0,sK13,X1,sK16),X2)
| ~ member(sK5(X0,sK13,X1,sK16),sK15)
| ~ maps(sK13,X2,sK16)
| equal_maps(X0,sK13,X1,sK16)
| equal_maps(X0,sK13,X1,sK16) ),
inference(resolution,[],[f336,f125]) ).
fof(f391,plain,
! [X2,X0,X1] :
( ~ member(sK5(X0,sK13,X1,sK16),sK15)
| ~ member(sK5(X0,sK13,X1,sK16),X2)
| sK7(X0,sK13,X1,sK16) = sK3(sK13,sK16,sK5(X0,sK13,X1,sK16))
| ~ maps(sK13,X2,sK16)
| equal_maps(X0,sK13,X1,sK16) ),
inference(duplicate_literal_removal,[],[f390]) ).
fof(f394,plain,
! [X0,X1] :
( ~ member(sK5(X0,sK13,sK15,sK16),X1)
| sK7(X0,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(X0,sK13,sK15,sK16))
| ~ maps(sK13,X1,sK16)
| equal_maps(X0,sK13,sK15,sK16)
| equal_maps(X0,sK13,sK15,sK16) ),
inference(resolution,[],[f391,f127]) ).
fof(f395,plain,
! [X0,X1] :
( ~ member(sK5(X0,sK13,sK15,sK16),X1)
| sK7(X0,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(X0,sK13,sK15,sK16))
| ~ maps(sK13,X1,sK16)
| equal_maps(X0,sK13,sK15,sK16) ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f402,plain,
! [X2,X0,X1] :
( sK6(sK12,X0,X1,sK16) = sK3(sK12,sK16,sK5(sK12,X0,X1,sK16))
| ~ member(sK5(sK12,X0,X1,sK16),X2)
| ~ member(sK5(sK12,X0,X1,sK16),sK15)
| ~ maps(sK12,X2,sK16)
| equal_maps(sK12,X0,X1,sK16)
| equal_maps(sK12,X0,X1,sK16) ),
inference(resolution,[],[f316,f126]) ).
fof(f403,plain,
! [X2,X0,X1] :
( ~ member(sK5(sK12,X0,X1,sK16),sK15)
| ~ member(sK5(sK12,X0,X1,sK16),X2)
| sK6(sK12,X0,X1,sK16) = sK3(sK12,sK16,sK5(sK12,X0,X1,sK16))
| ~ maps(sK12,X2,sK16)
| equal_maps(sK12,X0,X1,sK16) ),
inference(duplicate_literal_removal,[],[f402]) ).
fof(f404,plain,
! [X0,X1] :
( ~ member(sK5(sK12,X0,sK15,sK16),X1)
| sK6(sK12,X0,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,X0,sK15,sK16))
| ~ maps(sK12,X1,sK16)
| equal_maps(sK12,X0,sK15,sK16)
| equal_maps(sK12,X0,sK15,sK16) ),
inference(resolution,[],[f403,f127]) ).
fof(f405,plain,
! [X0,X1] :
( ~ member(sK5(sK12,X0,sK15,sK16),X1)
| sK6(sK12,X0,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,X0,sK15,sK16))
| ~ maps(sK12,X1,sK16)
| equal_maps(sK12,X0,sK15,sK16) ),
inference(duplicate_literal_removal,[],[f404]) ).
fof(f411,plain,
! [X0] :
( sK6(sK12,X0,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,X0,sK15,sK16))
| ~ maps(sK12,sK15,sK16)
| equal_maps(sK12,X0,sK15,sK16)
| equal_maps(sK12,X0,sK15,sK16) ),
inference(resolution,[],[f405,f127]) ).
fof(f413,plain,
! [X0] :
( sK6(sK12,X0,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,X0,sK15,sK16))
| ~ maps(sK12,sK15,sK16)
| equal_maps(sK12,X0,sK15,sK16) ),
inference(duplicate_literal_removal,[],[f411]) ).
fof(f415,plain,
! [X0] :
( equal_maps(sK12,X0,sK15,sK16)
| sK6(sK12,X0,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,X0,sK15,sK16)) ),
inference(forward_subsumption_resolution,[],[f413,f153]) ).
fof(f416,plain,
sK6(sK12,sK13,sK15,sK16) = sK3(sK12,sK16,sK5(sK12,sK13,sK15,sK16)),
inference(resolution,[],[f415,f154]) ).
fof(f421,definition,
( spl21_1
<=> member(sK5(sK12,sK13,sK15,sK16),sK15) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f422,plain,
( member(sK5(sK12,sK13,sK15,sK16),sK15)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f423,plain,
( ~ member(sK5(sK12,sK13,sK15,sK16),sK15)
| spl21_1 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f438,plain,
( equal_maps(sK12,sK13,sK15,sK16)
| spl21_1 ),
inference(resolution,[],[f423,f127]) ).
fof(f439,plain,
( $false
| spl21_1 ),
inference(forward_subsumption_resolution,[],[f438,f154]) ).
fof(f440,plain,
spl21_1,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f444,plain,
( sK5(sK12,sK13,sK15,sK16) = sK3(sK14,sK15,sK4(sK14,sK12,sK16,sK5(sK12,sK13,sK15,sK16),sK5(sK12,sK13,sK15,sK16)))
| ~ spl21_1 ),
inference(resolution,[],[f422,f375]) ).
fof(f523,plain,
( sK7(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(sK12,sK13,sK15,sK16))
| ~ maps(sK13,sK15,sK16)
| equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_1 ),
inference(resolution,[],[f395,f422]) ).
fof(f527,plain,
( sK7(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(sK12,sK13,sK15,sK16))
| equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_1 ),
inference(forward_subsumption_resolution,[],[f523,f152]) ).
fof(f529,plain,
( sK7(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(sK12,sK13,sK15,sK16))
| ~ spl21_1 ),
inference(forward_subsumption_resolution,[],[f527,f154]) ).
fof(f560,plain,
! [X0] :
( member(sK3(sK12,sK16,X0),sF19)
| ~ member(sK3(sK12,sK16,X0),sK16)
| ~ member(X0,sK15)
| ~ member(X0,sK15) ),
inference(superposition,[],[f253,f165]) ).
fof(f561,plain,
! [X0] :
( member(sK3(sK12,sK16,X0),sF19)
| ~ member(sK3(sK12,sK16,X0),sK16)
| ~ member(X0,sK15) ),
inference(duplicate_literal_removal,[],[f560]) ).
fof(f563,plain,
! [X0] :
( member(sK3(sK12,sK16,X0),sF19)
| ~ member(X0,sK15) ),
inference(forward_subsumption_resolution,[],[f561,f295]) ).
fof(f567,plain,
( member(sK6(sK12,sK13,sK15,sK16),sF19)
| ~ member(sK5(sK12,sK13,sK15,sK16),sK15) ),
inference(superposition,[],[f563,f416]) ).
fof(f569,plain,
( member(sK6(sK12,sK13,sK15,sK16),sF19)
| ~ spl21_1 ),
inference(forward_subsumption_resolution,[],[f567,f422]) ).
fof(f688,plain,
( ! [X0] :
( member(sK6(sK12,sK13,sK15,sK16),X0)
| ~ subset(sF19,X0) )
| ~ spl21_1 ),
inference(resolution,[],[f90,f569]) ).
fof(f882,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK12,sK16,X0) = sK4(sK14,sK12,sK16,X0,X0)
| ~ member(X0,sK15) ),
inference(resolution,[],[f359,f153]) ).
fof(f883,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK12,sK16,X0) = sK4(sK14,sK12,sK16,X0,X0) ),
inference(duplicate_literal_removal,[],[f882]) ).
fof(f889,plain,
( sK3(sK12,sK16,sK5(sK12,sK13,sK15,sK16)) = sK4(sK14,sK12,sK16,sK5(sK12,sK13,sK15,sK16),sK5(sK12,sK13,sK15,sK16))
| ~ spl21_1 ),
inference(resolution,[],[f883,f422]) ).
fof(f899,plain,
( sK6(sK12,sK13,sK15,sK16) = sK4(sK14,sK12,sK16,sK5(sK12,sK13,sK15,sK16),sK5(sK12,sK13,sK15,sK16))
| ~ spl21_1 ),
inference(forward_demodulation,[],[f889,f416]) ).
fof(f902,plain,
( sK5(sK12,sK13,sK15,sK16) = sK3(sK14,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ spl21_1 ),
inference(superposition,[],[f444,f899]) ).
fof(f944,definition,
( spl21_31
<=> ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| ~ maps(sK14,X0,sK15) ) ),
introduced(definition,[new_symbols(definition,[spl21_31])],[avatar_definition]) ).
fof(f945,plain,
( ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| ~ maps(sK14,X0,sK15) )
| ~ spl21_31 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f953,plain,
( ~ maps(sK14,sK16,sK15)
| equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_31 ),
inference(resolution,[],[f945,f126]) ).
fof(f965,plain,
( equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_31 ),
inference(forward_subsumption_resolution,[],[f953,f151]) ).
fof(f968,plain,
( $false
| ~ spl21_31 ),
inference(forward_subsumption_resolution,[],[f965,f154]) ).
fof(f969,plain,
~ spl21_31,
inference(avatar_contradiction_clause,[],[f968]) ).
fof(f1003,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK13,sK16,X0) = sK4(sK14,sK13,sK16,X0,X0)
| ~ member(X0,sK15) ),
inference(resolution,[],[f355,f152]) ).
fof(f1004,plain,
! [X0] :
( ~ member(X0,sK15)
| sK3(sK13,sK16,X0) = sK4(sK14,sK13,sK16,X0,X0) ),
inference(duplicate_literal_removal,[],[f1003]) ).
fof(f1129,plain,
( ~ subset(sF19,sF20)
| sK6(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)))
| ~ spl21_1 ),
inference(resolution,[],[f688,f347]) ).
fof(f1131,plain,
( sK6(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)))
| ~ spl21_1 ),
inference(forward_subsumption_resolution,[],[f1129,f228]) ).
fof(f1140,definition,
( spl21_39
<=> member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15) ),
introduced(definition,[new_symbols(definition,[spl21_39])],[avatar_definition]) ).
fof(f1141,plain,
( member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15)
| ~ spl21_39 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1142,plain,
( ~ member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15)
| spl21_39 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1152,definition,
( spl21_42
<=> member(sK6(sK12,sK13,sK15,sK16),sF20) ),
introduced(definition,[new_symbols(definition,[spl21_42])],[avatar_definition]) ).
fof(f1153,plain,
( ~ member(sK6(sK12,sK13,sK15,sK16),sF20)
| spl21_42 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1169,plain,
( ~ member(sK6(sK12,sK13,sK15,sK16),sF20)
| spl21_39 ),
inference(resolution,[],[f1142,f181]) ).
fof(f1170,plain,
( ~ spl21_42
| spl21_39 ),
inference(avatar_split_clause,[],[f1169,f1140,f1152]) ).
fof(f1171,plain,
( ~ subset(sF19,sF20)
| ~ spl21_1
| spl21_42 ),
inference(resolution,[],[f1153,f688]) ).
fof(f1172,plain,
( $false
| ~ spl21_1
| spl21_42 ),
inference(forward_subsumption_resolution,[],[f1171,f228]) ).
fof(f1173,plain,
( ~ spl21_1
| spl21_42 ),
inference(avatar_contradiction_clause,[],[f1172]) ).
fof(f1175,plain,
( sK3(sK13,sK16,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))) = sK4(sK14,sK13,sK16,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)))
| ~ spl21_39 ),
inference(resolution,[],[f1141,f1004]) ).
fof(f1180,plain,
( sK6(sK12,sK13,sK15,sK16) = sK4(sK14,sK13,sK16,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)))
| ~ spl21_1
| ~ spl21_39 ),
inference(forward_demodulation,[],[f1175,f1131]) ).
fof(f1184,plain,
( ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| sK3(sK14,sK15,sK6(sK12,sK13,sK15,sK16)) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15)
| ~ maps(sK14,X0,sK15)
| ~ apply(sF18,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)))
| ~ member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15) )
| ~ spl21_1
| ~ spl21_39 ),
inference(superposition,[],[f312,f1180]) ).
fof(f1193,plain,
( ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| sK3(sK14,sK15,sK6(sK12,sK13,sK15,sK16)) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15)
| ~ maps(sK14,X0,sK15)
| ~ apply(sF18,sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))) )
| ~ spl21_1
| ~ spl21_39 ),
inference(duplicate_literal_removal,[],[f1184]) ).
fof(f1196,plain,
( ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| sK3(sK14,sK15,sK6(sK12,sK13,sK15,sK16)) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ member(sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)),sK15)
| ~ maps(sK14,X0,sK15) )
| ~ spl21_1
| ~ spl21_39 ),
inference(forward_subsumption_resolution,[],[f1193,f178]) ).
fof(f1199,plain,
( ! [X0] :
( ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| sK3(sK14,sK15,sK6(sK12,sK13,sK15,sK16)) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ maps(sK14,X0,sK15) )
| ~ spl21_1
| ~ spl21_39 ),
inference(forward_subsumption_resolution,[],[f1196,f1141]) ).
fof(f1200,plain,
( ! [X0] :
( sK5(sK12,sK13,sK15,sK16) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ member(sK6(sK12,sK13,sK15,sK16),X0)
| ~ maps(sK14,X0,sK15) )
| ~ spl21_1
| ~ spl21_39 ),
inference(forward_demodulation,[],[f1199,f902]) ).
fof(f1202,definition,
( spl21_46
<=> sK5(sK12,sK13,sK15,sK16) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16)) ),
introduced(definition,[new_symbols(definition,[spl21_46])],[avatar_definition]) ).
fof(f1204,plain,
( sK5(sK12,sK13,sK15,sK16) = sK9(sK13,sK15,sK6(sK12,sK13,sK15,sK16))
| ~ spl21_46 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1205,plain,
( spl21_31
| spl21_46
| ~ spl21_1
| ~ spl21_39 ),
inference(avatar_split_clause,[],[f1200,f1140,f421,f1202,f944]) ).
fof(f1208,plain,
( sK6(sK12,sK13,sK15,sK16) = sK3(sK13,sK16,sK5(sK12,sK13,sK15,sK16))
| ~ spl21_1
| ~ spl21_46 ),
inference(superposition,[],[f1131,f1204]) ).
fof(f1214,plain,
( sK6(sK12,sK13,sK15,sK16) = sK7(sK12,sK13,sK15,sK16)
| ~ spl21_1
| ~ spl21_46 ),
inference(forward_demodulation,[],[f1208,f529]) ).
fof(f1233,plain,
( sK6(sK12,sK13,sK15,sK16) != sK6(sK12,sK13,sK15,sK16)
| equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_1
| ~ spl21_46 ),
inference(superposition,[],[f130,f1214]) ).
fof(f1234,plain,
( equal_maps(sK12,sK13,sK15,sK16)
| ~ spl21_1
| ~ spl21_46 ),
inference(trivial_inequality_removal,[],[f1233]) ).
fof(f1235,plain,
( $false
| ~ spl21_1
| ~ spl21_46 ),
inference(forward_subsumption_resolution,[],[f1234,f154]) ).
fof(f1236,plain,
( ~ spl21_1
| ~ spl21_46 ),
inference(avatar_contradiction_clause,[],[f1235]) ).
cnf(s4,plain,
spl21_1,
inference(sat_conversion,[],[f440]) ).
cnf(s33,plain,
~ spl21_31,
inference(sat_conversion,[],[f969]) ).
cnf(s44,plain,
( spl21_39
| ~ spl21_42 ),
inference(sat_conversion,[],[f1170]) ).
cnf(s45,plain,
( ~ spl21_1
| spl21_42 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s46,plain,
( ~ spl21_1
| spl21_31
| ~ spl21_39
| spl21_46 ),
inference(sat_conversion,[],[f1205]) ).
cnf(s47,plain,
( ~ spl21_1
| ~ spl21_46 ),
inference(sat_conversion,[],[f1236]) ).
cnf(s51,plain,
~ spl21_46,
inference(rat,[],[s47,s4]) ).
cnf(s52,plain,
~ spl21_39,
inference(rat,[],[s46,s51,s33,s4]) ).
cnf(s53,plain,
spl21_42,
inference(rat,[],[s45,s4]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s44,s53,s52]) ).
fof(f1246,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET735+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 02:39:22 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 8.74/2.10 % (753984)Detected formulas, will run a generic FOF schedule.
% 8.74/2.10 % (753991)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=2389541513:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.74/2.10 % (753995)dis-21_1_sil=8000:lcm=predicate:random_seed=626535611: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)
% 8.74/2.10 % (753989)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=2136486274:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.74/2.10 % (753993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1297869423:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.74/2.10 % (753992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2505057980:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.74/2.10 % (753990)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=1620156904:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.74/2.10 % (753994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1087064098:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.74/2.10 % (753992)Refutation not found, incomplete strategy
% 8.74/2.10 % (753992)------------------------------
% 8.74/2.10 % (753992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (753992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (753992)CaDiCaL version: 2.1.3
% 8.74/2.10 % (753992)Termination reason: Refutation not found, incomplete strategy
% 8.74/2.10 % (753992)Time elapsed: 0.022 s
% 8.74/2.10 % (753992)Peak memory usage: 89 MB
% 8.74/2.10 % (753992)Instructions burned: 33 (million)
% 8.74/2.10 % (753993)Instruction limit reached!
% 8.74/2.10 % (753993)------------------------------
% 8.74/2.10 % (753993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (753993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (753993)CaDiCaL version: 2.1.3
% 8.74/2.10 % (753993)Termination reason: Instruction limit
% 8.74/2.10 % (753993)Termination phase: Saturation
% 8.74/2.10 % (753993)Time elapsed: 0.071 s
% 8.74/2.10 % (753993)Peak memory usage: 88 MB
% 8.74/2.10 % (753993)Instructions burned: 120 (million)
% 8.74/2.10 % (753995)Instruction limit reached!
% 8.74/2.10 % (753995)------------------------------
% 8.74/2.10 % (753995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (753995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (753995)CaDiCaL version: 2.1.3
% 8.74/2.10 % (753995)Termination reason: Instruction limit
% 8.74/2.10 % (753995)Termination phase: Saturation
% 8.74/2.10 % (753995)Time elapsed: 0.080 s
% 8.74/2.10 % (753995)Peak memory usage: 89 MB
% 8.74/2.10 % (753995)Instructions burned: 130 (million)
% 8.74/2.10 % (753994)Instruction limit reached!
% 8.74/2.10 % (753994)------------------------------
% 8.74/2.10 % (753994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (753994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (753994)CaDiCaL version: 2.1.3
% 8.74/2.10 % (753994)Termination reason: Instruction limit
% 8.74/2.10 % (753994)Termination phase: Saturation
% 8.74/2.10 % (753994)Time elapsed: 0.093 s
% 8.74/2.10 % (753994)Peak memory usage: 89 MB
% 8.74/2.10 % (753994)Instructions burned: 139 (million)
% 8.74/2.10 % (754003)lrs+10_1_sil=8000:sp=occurrence:random_seed=398711015:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.74/2.10 % (754004)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1913059460:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.74/2.10 % (754005)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2948387938:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.74/2.10 % (753992)------------------------------
% 8.74/2.10 % (753992)------------------------------
% 8.74/2.10 % (754004)Instruction limit reached!
% 8.74/2.10 % (754004)------------------------------
% 8.74/2.10 % (754004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754004)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754004)Termination reason: Instruction limit
% 8.74/2.10 % (754004)Termination phase: Saturation
% 8.74/2.10 % (754004)Time elapsed: 0.076 s
% 8.74/2.10 % (754004)Peak memory usage: 89 MB
% 8.74/2.10 % (754004)Instructions burned: 157 (million)
% 8.74/2.10 % (754003)Instruction limit reached!
% 8.74/2.10 % (754003)------------------------------
% 8.74/2.10 % (754003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754003)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754003)Termination reason: Instruction limit
% 8.74/2.10 % (754003)Termination phase: Saturation
% 8.74/2.10 % (754003)Time elapsed: 0.171 s
% 8.74/2.10 % (754003)Peak memory usage: 92 MB
% 8.74/2.10 % (754003)Instructions burned: 286 (million)
% 8.74/2.10 % (754009)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=158532780:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.74/2.10 % (754010)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2476350755:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.74/2.10 % (754010)Refutation not found, incomplete strategy
% 8.74/2.10 % (754010)------------------------------
% 8.74/2.10 % (754010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754010)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754010)Termination reason: Refutation not found, incomplete strategy
% 8.74/2.10 % (754010)Time elapsed: 0.002 s
% 8.74/2.10 % (754010)Peak memory usage: 88 MB
% 8.74/2.10 % (754010)Instructions burned: 1 (million)
% 8.74/2.10 % (754005)Instruction limit reached!
% 8.74/2.10 % (754005)------------------------------
% 8.74/2.10 % (754005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754005)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754005)Termination reason: Instruction limit
% 8.74/2.10 % (754005)Termination phase: Saturation
% 8.74/2.10 % (754005)Time elapsed: 0.219 s
% 8.74/2.10 % (754005)Peak memory usage: 92 MB
% 8.74/2.10 % (754005)Instructions burned: 325 (million)
% 8.74/2.10 % (754011)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2490441819:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.74/2.10 % (754009)Instruction limit reached!
% 8.74/2.10 % (754009)------------------------------
% 8.74/2.10 % (754009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754009)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754009)Termination reason: Instruction limit
% 8.74/2.10 % (754009)Termination phase: Saturation
% 8.74/2.10 % (754009)Time elapsed: 0.128 s
% 8.74/2.10 % (754009)Peak memory usage: 92 MB
% 8.74/2.10 % (754009)Instructions burned: 248 (million)
% 8.74/2.10 % (754014)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=882269878:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.74/2.10 % (754010)------------------------------
% 8.74/2.10 % (754010)------------------------------
% 8.74/2.10 % (754014)Instruction limit reached!
% 8.74/2.10 % (754014)------------------------------
% 8.74/2.10 % (754014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754014)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754014)Termination reason: Instruction limit
% 8.74/2.10 % (754014)Termination phase: Saturation
% 8.74/2.10 % (754014)Time elapsed: 0.077 s
% 8.74/2.10 % (754014)Peak memory usage: 90 MB
% 8.74/2.10 % (754014)Instructions burned: 114 (million)
% 8.74/2.10 % (754016)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3189314730:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.74/2.10 % (754016)Instruction limit reached!
% 8.74/2.10 % (754016)------------------------------
% 8.74/2.10 % (754016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754016)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754016)Termination reason: Instruction limit
% 8.74/2.10 % (754016)Termination phase: Saturation
% 8.74/2.10 % (754016)Time elapsed: 0.069 s
% 8.74/2.10 % (754016)Peak memory usage: 89 MB
% 8.74/2.10 % (754016)Instructions burned: 128 (million)
% 8.74/2.10 % (754018)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=102605467:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.74/2.10 % (754020)lrs+10_1_sil=8000:sp=occurrence:random_seed=2896129250:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.74/2.10 % (753989)First to succeed.
% 8.74/2.10 % (753989)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-753984"
% 8.74/2.10 % (754018)Instruction limit reached!
% 8.74/2.10 % (754018)------------------------------
% 8.74/2.10 % (754018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754018)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754018)Termination reason: Instruction limit
% 8.74/2.10 % (754018)Termination phase: Saturation
% 8.74/2.10 % (754018)Time elapsed: 0.070 s
% 8.74/2.10 % (754018)Peak memory usage: 89 MB
% 8.74/2.10 % (754018)Instructions burned: 116 (million)
% 8.74/2.10 % (754021)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4148762274:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 8.74/2.10 % (754021)Refutation not found, incomplete strategy
% 8.74/2.10 % (754021)------------------------------
% 8.74/2.10 % (754021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.74/2.10 % (754021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.74/2.10 % (754021)CaDiCaL version: 2.1.3
% 8.74/2.10 % (754021)Termination reason: Refutation not found, incomplete strategy
% 8.74/2.10 % (754021)Time elapsed: 0.002 s
% 8.74/2.10 % (754021)Peak memory usage: 88 MB
% 8.74/2.10 % (754021)Instructions burned: 1 (million)
% 8.74/2.10 % (754024)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=189731272:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.74/2.10 % (753989)Refutation found. Thanks to Tanya!
% 8.74/2.10 % SZS status Theorem for theBenchmark
% 8.74/2.10 % SZS output start Proof for theBenchmark
% See solution above
% 9.32/2.28 % (753989)------------------------------
% 9.32/2.28 % (753989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.28 % (753989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.28 % (753989)CaDiCaL version: 2.1.3
% 9.32/2.28 % (753989)Termination reason: Refutation
% 9.32/2.28 % (753989)Time elapsed: 0.832 s
% 9.32/2.28 % (753989)Peak memory usage: 131 MB
% 9.32/2.28 % (753989)Instructions burned: 1234 (million)
% 9.32/2.28 % (753989)------------------------------
% 9.32/2.28 % (753989)------------------------------
% 9.32/2.28 % (753984)Success in time 1.242 s
% 9.32/2.28 % Vampire exiting
%------------------------------------------------------------------------------