%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET748+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 : n015.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 3.90s 1.57s
% Output : Refutation 5.50s
% 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)
& decreasing(X0,X2,X5,X3,X6)
& increasing(X1,X3,X6,X4,X7) )
=> decreasing(compose_function(X1,X0,X2,X3,X4),X2,X5,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII39) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& decreasing(X0,X2,X5,X3,X6)
& increasing(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)
& decreasing(X0,X2,X5,X3,X6)
& increasing(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)
& decreasing(X0,X2,X5,X3,X6)
& increasing(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)
& decreasing(sK0,sK2,sK5,sK3,sK6)
& increasing(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,
increasing(sK1,sK3,sK6,sK4,sK7),
inference(cnf_transformation,[],[f44]) ).
fof(f53,plain,
decreasing(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(f101,plain,
apply(sK6,sK8(sK0,sK3,sK12(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,[],[f65,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(f127,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(f141,plain,
~ apply(sK6,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)),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,[],[f64,f52,f97,f96,f74,f89,f78,f104,f103]) ).
fof(f142,plain,
~ apply(sK6,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)),sK8(sK0,sK3,sK10(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK5,sK4,sK7))),
inference(forward_demodulation,[],[f141,f127]) ).
fof(f143,plain,
~ apply(sK6,sK8(sK0,sK3,sK12(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(forward_demodulation,[],[f142,f112]) ).
fof(f144,plain,
$false,
inference(forward_subsumption_resolution,[],[f143,f101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET748+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:46:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.90/1.57 % (2213428)Detected formulas, will run a generic FOF schedule.
% 3.90/1.57 % (2213433)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=141680804:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.90/1.57 % (2213435)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=1894267920:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.90/1.57 % (2213438)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1082952589:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.90/1.57 % (2213436)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2258343643:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.90/1.57 % (2213439)dis-21_1_sil=8000:lcm=predicate:random_seed=1755930528: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)
% 3.90/1.57 % (2213434)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=3858046927:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.90/1.57 % (2213436)Refutation not found, incomplete strategy
% 3.90/1.57 % (2213436)------------------------------
% 3.90/1.57 % (2213436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213436)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213436)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.57 % (2213436)Time elapsed: 0.013 s
% 3.90/1.57 % (2213436)Peak memory usage: 88 MB
% 3.90/1.57 % (2213436)Instructions burned: 18 (million)
% 3.90/1.57 % (2213437)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3073217458:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.90/1.57 % (2213439)Instruction limit reached!
% 3.90/1.57 % (2213439)------------------------------
% 3.90/1.57 % (2213439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213439)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213439)Termination reason: Instruction limit
% 3.90/1.57 % (2213439)Termination phase: Saturation
% 3.90/1.57 % (2213439)Time elapsed: 0.076 s
% 3.90/1.57 % (2213439)Peak memory usage: 89 MB
% 3.90/1.57 % (2213439)Instructions burned: 130 (million)
% 3.90/1.57 % (2213438)Instruction limit reached!
% 3.90/1.57 % (2213438)------------------------------
% 3.90/1.57 % (2213438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213438)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213438)Termination reason: Instruction limit
% 3.90/1.57 % (2213438)Termination phase: Saturation
% 3.90/1.57 % (2213438)Time elapsed: 0.094 s
% 3.90/1.57 % (2213438)Peak memory usage: 89 MB
% 3.90/1.57 % (2213438)Instructions burned: 140 (million)
% 3.90/1.57 % (2213437)Instruction limit reached!
% 3.90/1.57 % (2213437)------------------------------
% 3.90/1.57 % (2213437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213437)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213437)Termination reason: Instruction limit
% 3.90/1.57 % (2213437)Termination phase: Saturation
% 3.90/1.57 % (2213437)Time elapsed: 0.073 s
% 3.90/1.57 % (2213437)Peak memory usage: 89 MB
% 3.90/1.57 % (2213437)Instructions burned: 120 (million)
% 3.90/1.57 % (2213447)lrs+10_1_sil=8000:sp=occurrence:random_seed=2196044397:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.90/1.57 % (2213449)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3317725889:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.90/1.57 % (2213448)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4092911341:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.90/1.57 % (2213436)------------------------------
% 3.90/1.57 % (2213436)------------------------------
% 3.90/1.57 % (2213448)First to succeed.
% 3.90/1.57 % (2213448)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2213428"
% 3.90/1.57 % (2213433)Also succeeded, but the first one will report.
% 3.90/1.57 % (2213447)Instruction limit reached!
% 3.90/1.57 % (2213447)------------------------------
% 3.90/1.57 % (2213447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213447)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213447)Termination reason: Instruction limit
% 3.90/1.57 % (2213447)Termination phase: Saturation
% 3.90/1.57 % (2213447)Time elapsed: 0.167 s
% 3.90/1.57 % (2213447)Peak memory usage: 92 MB
% 3.90/1.57 % (2213447)Instructions burned: 286 (million)
% 3.90/1.57 % (2213453)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=2310222050:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.90/1.57 % (2213449)Instruction limit reached!
% 3.90/1.57 % (2213449)------------------------------
% 3.90/1.57 % (2213449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (2213449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (2213449)CaDiCaL version: 2.1.3
% 3.90/1.57 % (2213449)Termination reason: Instruction limit
% 3.90/1.57 % (2213449)Termination phase: Saturation
% 3.90/1.57 % (2213449)Time elapsed: 0.223 s
% 3.90/1.57 % (2213449)Peak memory usage: 92 MB
% 3.90/1.57 % (2213449)Instructions burned: 326 (million)
% 3.90/1.57 % (2213448)Refutation found. Thanks to Tanya!
% 3.90/1.57 % SZS status Theorem for theBenchmark
% 3.90/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 5.50/1.77 % (2213448)------------------------------
% 5.50/1.77 % (2213448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.77 % (2213448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.77 % (2213448)CaDiCaL version: 2.1.3
% 5.50/1.77 % (2213448)Termination reason: Refutation
% 5.50/1.77 % (2213448)Time elapsed: 0.017 s
% 5.50/1.77 % (2213448)Peak memory usage: 88 MB
% 5.50/1.77 % (2213448)Instructions burned: 30 (million)
% 5.50/1.77 % (2213448)------------------------------
% 5.50/1.77 % (2213448)------------------------------
% 5.50/1.77 % (2213428)Success in time 0.7 s
% 5.50/1.77 % Vampire exiting
%------------------------------------------------------------------------------