%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET747+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 : n009.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 12:41:49 PM UTC 2026
% Result : Theorem 3.94s 1.54s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 29 unt; 0 def)
% Number of atoms : 338 ( 9 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 411 ( 145 ~; 143 |; 97 &)
% ( 9 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-5 aty)
% Number of variables : 320 ( 286 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/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(f26,axiom,
! [X0,X1,X2,X3,X4] :
( increasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( ( member(X5,X1)
& member(X6,X3)
& member(X7,X1)
& member(X8,X3)
& apply(X2,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X7,X8) )
=> apply(X4,X6,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',increasing_function) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( decreasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( ( member(X5,X1)
& member(X6,X3)
& member(X7,X1)
& member(X8,X3)
& apply(X2,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X7,X8) )
=> apply(X4,X8,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decreasing_function) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& increasing(X0,X2,X5,X3,X6)
& decreasing(X1,X3,X6,X4,X7) )
=> decreasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII38) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& increasing(X0,X2,X5,X3,X6)
& decreasing(X1,X3,X6,X4,X7) )
=> decreasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( increasing(X0,X1,X2,X3,X4)
=> ! [X5,X6,X7,X8] :
( ( member(X5,X1)
& member(X6,X3)
& member(X7,X1)
& member(X8,X3)
& apply(X2,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X7,X8) )
=> apply(X4,X6,X8) ) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ decreasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& increasing(X0,X2,X5,X3,X6)
& decreasing(X1,X3,X6,X4,X7) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ decreasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& increasing(X0,X2,X5,X3,X6)
& decreasing(X1,X3,X6,X4,X7) ),
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,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(f39,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,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6,X7,X8] :
( apply(X4,X6,X8)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8) )
| ~ increasing(X0,X1,X2,X3,X4) ),
inference(ennf_transformation,[],[f33]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5,X6,X7,X8] :
( apply(X4,X6,X8)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8) )
| ~ increasing(X0,X1,X2,X3,X4) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( decreasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( apply(X4,X8,X6)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( decreasing(X0,X1,X2,X3,X4)
<=> ! [X5,X6,X7,X8] :
( apply(X4,X8,X6)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
( ~ decreasing(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)
& maps(sK0,sK2,sK3)
& maps(sK1,sK3,sK4)
& increasing(sK0,sK2,sK5,sK3,sK6)
& decreasing(sK1,sK3,sK6,sK4,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f35]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK8(X0,X2,X3),X2)
& apply(X0,X3,sK8(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,[sK8]),skolemize(X4,sK8(X0,X2,X3))],[f37]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [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,[],[f39]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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))],[f47]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( ( decreasing(X0,X1,X2,X3,X4)
| ? [X5,X6,X7,X8] :
( ~ apply(X4,X8,X6)
& member(X5,X1)
& member(X6,X3)
& member(X7,X1)
& member(X8,X3)
& apply(X2,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X7,X8) ) )
& ( ! [X5,X6,X7,X8] :
( apply(X4,X8,X6)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8) )
| ~ decreasing(X0,X1,X2,X3,X4) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( ( decreasing(X0,X1,X2,X3,X4)
| ? [X5,X6,X7,X8] :
( ~ apply(X4,X8,X6)
& member(X5,X1)
& member(X6,X3)
& member(X7,X1)
& member(X8,X3)
& apply(X2,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X7,X8) ) )
& ( ! [X9,X10,X11,X12] :
( apply(X4,X12,X10)
| ~ member(X9,X1)
| ~ member(X10,X3)
| ~ member(X11,X1)
| ~ member(X12,X3)
| ~ apply(X2,X9,X11)
| ~ apply(X0,X9,X10)
| ~ apply(X0,X11,X12) )
| ~ decreasing(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ( decreasing(X0,X1,X2,X3,X4)
| ( ~ apply(X4,sK13(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& member(sK10(X0,X1,X2,X3,X4),X1)
& member(sK11(X0,X1,X2,X3,X4),X3)
& member(sK12(X0,X1,X2,X3,X4),X1)
& member(sK13(X0,X1,X2,X3,X4),X3)
& apply(X2,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
& apply(X0,sK10(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& apply(X0,sK12(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4)) ) )
& ( ! [X9,X10,X11,X12] :
( apply(X4,X12,X10)
| ~ member(X9,X1)
| ~ member(X10,X3)
| ~ member(X11,X1)
| ~ member(X12,X3)
| ~ apply(X2,X9,X11)
| ~ apply(X0,X9,X10)
| ~ apply(X0,X11,X12) )
| ~ decreasing(X0,X1,X2,X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X5,sK10(X0,X1,X2,X3,X4)),skolemize(X6,sK11(X0,X1,X2,X3,X4)),skolemize(X7,sK12(X0,X1,X2,X3,X4)),skolemize(X8,sK13(X0,X1,X2,X3,X4))],[f50]) ).
fof(f52,plain,
decreasing(sK1,sK3,sK6,sK4,sK7),
inference(cnf_transformation,[],[f44]) ).
fof(f53,plain,
increasing(sK0,sK2,sK5,sK3,sK6),
inference(cnf_transformation,[],[f44]) ).
fof(f55,plain,
maps(sK0,sK2,sK3),
inference(cnf_transformation,[],[f44]) ).
fof(f56,plain,
~ decreasing(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),
inference(cnf_transformation,[],[f44]) ).
fof(f57,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(f58,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK8(X0,X2,X3)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK8(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,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,[],[f48]) ).
fof(f61,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,[],[f48]) ).
fof(f62,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,[],[f48]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ increasing(X0,X1,X2,X3,X4)
| ~ member(X5,X1)
| ~ member(X6,X3)
| ~ member(X7,X1)
| ~ member(X8,X3)
| ~ apply(X2,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X7,X8)
| apply(X4,X6,X8) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X2,X3,X10,X0,X11,X1,X9,X4,X12] :
( ~ decreasing(X0,X1,X2,X3,X4)
| ~ member(X9,X1)
| ~ member(X10,X3)
| ~ member(X11,X1)
| ~ member(X12,X3)
| ~ apply(X2,X9,X11)
| ~ apply(X0,X9,X10)
| ~ apply(X0,X11,X12)
| apply(X4,X12,X10) ),
inference(cnf_transformation,[],[f51]) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK12(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK10(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X4] :
( apply(X2,sK10(X0,X1,X2,X3,X4),sK12(X0,X1,X2,X3,X4))
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X4] :
( member(sK13(X0,X1,X2,X3,X4),X3)
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2,X3,X4),X1)
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4] :
( member(sK11(X0,X1,X2,X3,X4),X3)
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( member(sK10(X0,X1,X2,X3,X4),X1)
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X4,sK13(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
| decreasing(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
member(sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4),
inference(unit_resulting_resolution,[],[f69,f56]) ).
fof(f75,plain,
member(sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2),
inference(unit_resulting_resolution,[],[f70,f56]) ).
fof(f76,plain,
apply(sK0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f58,f55,f75]) ).
fof(f77,plain,
member(sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(unit_resulting_resolution,[],[f59,f55,f75]) ).
fof(f78,plain,
member(sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK4),
inference(unit_resulting_resolution,[],[f71,f56]) ).
fof(f79,plain,
member(sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK2),
inference(unit_resulting_resolution,[],[f72,f56]) ).
fof(f80,plain,
apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f58,f55,f79]) ).
fof(f81,plain,
member(sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(unit_resulting_resolution,[],[f59,f55,f79]) ).
fof(f82,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f66,f56]) ).
fof(f85,plain,
apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f67,f56]) ).
fof(f88,plain,
apply(sK5,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f68,f56]) ).
fof(f89,plain,
~ apply(sK7,sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f73,f56]) ).
fof(f95,plain,
apply(sK0,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f61,f74,f75,f82]) ).
fof(f96,plain,
apply(sK1,sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f60,f74,f75,f82]) ).
fof(f97,plain,
member(sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(unit_resulting_resolution,[],[f62,f74,f75,f82]) ).
fof(f99,plain,
apply(sK6,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f64,f77,f76,f81,f80,f75,f88,f79,f53]) ).
fof(f102,plain,
apply(sK0,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f61,f78,f79,f85]) ).
fof(f103,plain,
apply(sK1,sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f60,f78,f79,f85]) ).
fof(f104,plain,
member(sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK3),
inference(unit_resulting_resolution,[],[f62,f78,f79,f85]) ).
fof(f112,plain,
sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f57,f55,f75,f77,f76,f97,f95]) ).
fof(f126,plain,
sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)) = sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),
inference(unit_resulting_resolution,[],[f57,f55,f79,f81,f80,f104,f102]) ).
fof(f140,plain,
~ apply(sK6,sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK9(sK1,sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK13(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(unit_resulting_resolution,[],[f65,f52,f74,f97,f96,f89,f78,f104,f103]) ).
fof(f141,plain,
~ apply(sK6,sK9(sK1,sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7),sK11(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(forward_demodulation,[],[f140,f112]) ).
fof(f142,plain,
~ apply(sK6,sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7)),sK8(sK0,sK3,sK12(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(forward_demodulation,[],[f141,f126]) ).
fof(f143,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET747+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:41:30 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.94/1.54 % (2615191)Detected formulas, will run a generic FOF schedule.
% 3.94/1.54 % (2615196)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=611087293:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.94/1.54 % (2615198)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=1632460583:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.94/1.54 % (2615199)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3397001786:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.94/1.54 % (2615200)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2687257862:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.94/1.54 % (2615201)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2942129775:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.94/1.54 % (2615197)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=1799199241:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.94/1.54 % (2615202)dis-21_1_sil=8000:lcm=predicate:random_seed=3825309570: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)
% 3.94/1.54 % (2615199)Refutation not found, incomplete strategy
% 3.94/1.54 % (2615199)------------------------------
% 3.94/1.54 % (2615199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615199)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615199)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.54 % (2615199)Time elapsed: 0.013 s
% 3.94/1.54 % (2615199)Peak memory usage: 88 MB
% 3.94/1.54 % (2615199)Instructions burned: 18 (million)
% 3.94/1.54 % (2615202)Instruction limit reached!
% 3.94/1.54 % (2615202)------------------------------
% 3.94/1.54 % (2615202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615202)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615202)Termination reason: Instruction limit
% 3.94/1.54 % (2615202)Termination phase: Saturation
% 3.94/1.54 % (2615202)Time elapsed: 0.071 s
% 3.94/1.54 % (2615202)Peak memory usage: 88 MB
% 3.94/1.54 % (2615202)Instructions burned: 129 (million)
% 3.94/1.54 % (2615200)Instruction limit reached!
% 3.94/1.54 % (2615200)------------------------------
% 3.94/1.54 % (2615200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615200)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615200)Termination reason: Instruction limit
% 3.94/1.54 % (2615200)Termination phase: Saturation
% 3.94/1.54 % (2615200)Time elapsed: 0.071 s
% 3.94/1.54 % (2615200)Peak memory usage: 88 MB
% 3.94/1.54 % (2615200)Instructions burned: 120 (million)
% 3.94/1.54 % (2615201)Instruction limit reached!
% 3.94/1.54 % (2615201)------------------------------
% 3.94/1.54 % (2615201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615201)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615201)Termination reason: Instruction limit
% 3.94/1.54 % (2615201)Termination phase: Saturation
% 3.94/1.54 % (2615201)Time elapsed: 0.091 s
% 3.94/1.54 % (2615201)Peak memory usage: 89 MB
% 3.94/1.54 % (2615201)Instructions burned: 140 (million)
% 3.94/1.54 % (2615211)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1718184736:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.94/1.54 % (2615210)lrs+10_1_sil=8000:sp=occurrence:random_seed=4102775122:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.94/1.54 % (2615211)First to succeed.
% 3.94/1.54 % (2615211)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2615191"
% 3.94/1.54 % (2615212)lrs+1011_1_sil=32000:sp=occurrence:random_seed=299520959:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.94/1.54 % (2615199)------------------------------
% 3.94/1.54 % (2615199)------------------------------
% 3.94/1.54 % (2615196)Also succeeded, but the first one will report.
% 3.94/1.54 % (2615210)Instruction limit reached!
% 3.94/1.54 % (2615210)------------------------------
% 3.94/1.54 % (2615210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615210)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615210)Termination reason: Instruction limit
% 3.94/1.54 % (2615210)Termination phase: Saturation
% 3.94/1.54 % (2615210)Time elapsed: 0.166 s
% 3.94/1.54 % (2615210)Peak memory usage: 93 MB
% 3.94/1.54 % (2615210)Instructions burned: 286 (million)
% 3.94/1.54 % (2615216)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=2788211981:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.94/1.54 % (2615212)Instruction limit reached!
% 3.94/1.54 % (2615212)------------------------------
% 3.94/1.54 % (2615212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.54 % (2615212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.54 % (2615212)CaDiCaL version: 2.1.3
% 3.94/1.54 % (2615212)Termination reason: Instruction limit
% 3.94/1.54 % (2615212)Termination phase: Saturation
% 3.94/1.54 % (2615212)Time elapsed: 0.223 s
% 3.94/1.54 % (2615212)Peak memory usage: 92 MB
% 3.94/1.54 % (2615212)Instructions burned: 325 (million)
% 3.94/1.54 % (2615211)Refutation found. Thanks to Tanya!
% 3.94/1.54 % SZS status Theorem for theBenchmark
% 3.94/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.73 % (2615211)------------------------------
% 5.38/1.73 % (2615211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.73 % (2615211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.73 % (2615211)CaDiCaL version: 2.1.3
% 5.38/1.73 % (2615211)Termination reason: Refutation
% 5.38/1.73 % (2615211)Time elapsed: 0.018 s
% 5.38/1.73 % (2615211)Peak memory usage: 88 MB
% 5.38/1.73 % (2615211)Instructions burned: 30 (million)
% 5.38/1.73 % (2615211)------------------------------
% 5.38/1.73 % (2615211)------------------------------
% 5.38/1.73 % (2615191)Success in time 0.67 s
% 5.38/1.73 % Vampire exiting
%------------------------------------------------------------------------------