TSTP Solution File: SET746+4 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET746+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:22:06 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 25 unt; 0 def)
% Number of atoms : 360 ( 9 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 420 ( 132 ~; 126 |; 131 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-5 aty)
% Number of variables : 343 ( 285 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f146,plain,
$false,
inference(subsumption_resolution,[],[f145,f138]) ).
fof(f138,plain,
~ apply(sK7,sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),sK9(sK2,sK8,sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1)),
inference(unit_resulting_resolution,[],[f65,f88,f129,f82,f87,f83,f96,f95,f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ increasing(X4,X3,X1,X0,X2)
| ~ member(X5,X0)
| ~ apply(X1,X7,X6)
| ~ member(X8,X0)
| ~ apply(X4,X6,X8)
| ~ member(X7,X3)
| ~ member(X6,X3)
| ~ apply(X4,X7,X5)
| apply(X2,X5,X8) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7,X8] :
( apply(X2,X5,X8)
| ~ member(X6,X3)
| ~ member(X7,X3)
| ~ apply(X4,X6,X8)
| ~ member(X8,X0)
| ~ member(X5,X0)
| ~ apply(X1,X7,X6)
| ~ apply(X4,X7,X5) )
| ~ increasing(X4,X3,X1,X0,X2) )
& ( increasing(X4,X3,X1,X0,X2)
| ( ~ apply(X2,sK10(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
& member(sK11(X0,X1,X2,X3,X4),X3)
& member(sK12(X0,X1,X2,X3,X4),X3)
& apply(X4,sK11(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
& member(sK13(X0,X1,X2,X3,X4),X0)
& member(sK10(X0,X1,X2,X3,X4),X0)
& apply(X1,sK12(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& apply(X4,sK12(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f56,f57]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4] :
( ? [X9,X10,X11,X12] :
( ~ apply(X2,X9,X12)
& member(X10,X3)
& member(X11,X3)
& apply(X4,X10,X12)
& member(X12,X0)
& member(X9,X0)
& apply(X1,X11,X10)
& apply(X4,X11,X9) )
=> ( ~ apply(X2,sK10(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
& member(sK11(X0,X1,X2,X3,X4),X3)
& member(sK12(X0,X1,X2,X3,X4),X3)
& apply(X4,sK11(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
& member(sK13(X0,X1,X2,X3,X4),X0)
& member(sK10(X0,X1,X2,X3,X4),X0)
& apply(X1,sK12(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
& apply(X4,sK12(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7,X8] :
( apply(X2,X5,X8)
| ~ member(X6,X3)
| ~ member(X7,X3)
| ~ apply(X4,X6,X8)
| ~ member(X8,X0)
| ~ member(X5,X0)
| ~ apply(X1,X7,X6)
| ~ apply(X4,X7,X5) )
| ~ increasing(X4,X3,X1,X0,X2) )
& ( increasing(X4,X3,X1,X0,X2)
| ? [X9,X10,X11,X12] :
( ~ apply(X2,X9,X12)
& member(X10,X3)
& member(X11,X3)
& apply(X4,X10,X12)
& member(X12,X0)
& member(X9,X0)
& apply(X1,X11,X10)
& apply(X4,X11,X9) ) ) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X0,X4,X2,X1,X3] :
( ( ! [X6,X8,X5,X7] :
( apply(X2,X6,X7)
| ~ member(X8,X1)
| ~ member(X5,X1)
| ~ apply(X3,X8,X7)
| ~ member(X7,X0)
| ~ member(X6,X0)
| ~ apply(X4,X5,X8)
| ~ apply(X3,X5,X6) )
| ~ increasing(X3,X1,X4,X0,X2) )
& ( increasing(X3,X1,X4,X0,X2)
| ? [X6,X8,X5,X7] :
( ~ apply(X2,X6,X7)
& member(X8,X1)
& member(X5,X1)
& apply(X3,X8,X7)
& member(X7,X0)
& member(X6,X0)
& apply(X4,X5,X8)
& apply(X3,X5,X6) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X4,X2,X1,X3] :
( ! [X6,X8,X5,X7] :
( apply(X2,X6,X7)
| ~ member(X8,X1)
| ~ member(X5,X1)
| ~ apply(X3,X8,X7)
| ~ member(X7,X0)
| ~ member(X6,X0)
| ~ apply(X4,X5,X8)
| ~ apply(X3,X5,X6) )
<=> increasing(X3,X1,X4,X0,X2) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X2,X1,X3,X4] :
( increasing(X3,X1,X4,X0,X2)
<=> ! [X6,X8,X5,X7] :
( apply(X2,X6,X7)
| ~ member(X5,X1)
| ~ apply(X3,X5,X6)
| ~ member(X6,X0)
| ~ member(X7,X0)
| ~ apply(X3,X8,X7)
| ~ apply(X4,X5,X8)
| ~ member(X8,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X2,X1,X3,X4] :
( increasing(X3,X1,X4,X0,X2)
<=> ! [X6,X8,X5,X7] :
( ( member(X5,X1)
& apply(X3,X5,X6)
& member(X6,X0)
& member(X7,X0)
& apply(X3,X8,X7)
& apply(X4,X5,X8)
& member(X8,X1) )
=> apply(X2,X6,X7) ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1,X0,X15,X5,X14] :
( increasing(X5,X0,X14,X1,X15)
<=> ! [X12,X6,X7,X13] :
( ( member(X13,X0)
& apply(X14,X12,X13)
& member(X12,X0)
& member(X6,X1)
& apply(X5,X12,X6)
& apply(X5,X13,X7)
& member(X7,X1) )
=> apply(X15,X6,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',increasing_function) ).
fof(f95,plain,
apply(sK2,sK9(sK2,sK8,sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1),sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f86,f83,f84,f69]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X3,X1,X6,X2),X5,X4)
| ~ member(X5,X1)
| ~ member(X4,X2)
| apply(X0,sK9(X0,X3,X4,X5,X6),X4) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( ( apply(X3,X5,sK9(X0,X3,X4,X5,X6))
& apply(X0,sK9(X0,X3,X4,X5,X6),X4)
& member(sK9(X0,X3,X4,X5,X6),X6) )
| ~ apply(compose_function(X0,X3,X1,X6,X2),X5,X4) )
& ( apply(compose_function(X0,X3,X1,X6,X2),X5,X4)
| ! [X8] :
( ~ apply(X3,X5,X8)
| ~ apply(X0,X8,X4)
| ~ member(X8,X6) ) ) )
| ~ member(X4,X2)
| ~ member(X5,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f52,f53]) ).
fof(f53,plain,
! [X0,X3,X4,X5,X6] :
( ? [X7] :
( apply(X3,X5,X7)
& apply(X0,X7,X4)
& member(X7,X6) )
=> ( apply(X3,X5,sK9(X0,X3,X4,X5,X6))
& apply(X0,sK9(X0,X3,X4,X5,X6),X4)
& member(sK9(X0,X3,X4,X5,X6),X6) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( ? [X7] :
( apply(X3,X5,X7)
& apply(X0,X7,X4)
& member(X7,X6) )
| ~ apply(compose_function(X0,X3,X1,X6,X2),X5,X4) )
& ( apply(compose_function(X0,X3,X1,X6,X2),X5,X4)
| ! [X8] :
( ~ apply(X3,X5,X8)
| ~ apply(X0,X8,X4)
| ~ member(X8,X6) ) ) )
| ~ member(X4,X2)
| ~ member(X5,X1) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X4,X2,X6,X3,X5] :
( ( ( ? [X7] :
( apply(X2,X3,X7)
& apply(X0,X7,X6)
& member(X7,X5) )
| ~ apply(compose_function(X0,X2,X1,X5,X4),X3,X6) )
& ( apply(compose_function(X0,X2,X1,X5,X4),X3,X6)
| ! [X7] :
( ~ apply(X2,X3,X7)
| ~ apply(X0,X7,X6)
| ~ member(X7,X5) ) ) )
| ~ member(X6,X4)
| ~ member(X3,X1) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X4,X2,X6,X3,X5] :
( ( ? [X7] :
( apply(X2,X3,X7)
& apply(X0,X7,X6)
& member(X7,X5) )
<=> apply(compose_function(X0,X2,X1,X5,X4),X3,X6) )
| ~ member(X6,X4)
| ~ member(X3,X1) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X3,X2,X1,X5,X0,X6,X4] :
( ( ? [X7] :
( apply(X2,X3,X7)
& apply(X0,X7,X6)
& member(X7,X5) )
<=> apply(compose_function(X0,X2,X1,X5,X4),X3,X6) )
| ~ member(X3,X1)
| ~ member(X6,X4) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X3,X2,X1,X5,X0,X6,X4] :
( ( member(X3,X1)
& member(X6,X4) )
=> ( ? [X7] :
( apply(X2,X3,X7)
& apply(X0,X7,X6)
& member(X7,X5) )
<=> apply(compose_function(X0,X2,X1,X5,X4),X3,X6) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X9,X0,X5,X2,X10,X1,X11] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
<=> ? [X4] :
( apply(X9,X4,X11)
& member(X4,X1)
& apply(X5,X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f84,plain,
apply(compose_function(sK2,sK8,sK6,sK1,sK5),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f63,f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( apply(X4,sK11(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f63,plain,
~ increasing(compose_function(sK2,sK8,sK6,sK1,sK5),sK6,sK4,sK5,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
( maps(sK8,sK6,sK1)
& increasing(sK2,sK1,sK7,sK5,sK3)
& increasing(sK8,sK6,sK4,sK1,sK7)
& ~ increasing(compose_function(sK2,sK8,sK6,sK1,sK5),sK6,sK4,sK5,sK3)
& maps(sK2,sK1,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f48,f49]) ).
fof(f49,plain,
( ? [X0,X1,X2,X3,X4,X5,X6,X7] :
( maps(X7,X5,X0)
& increasing(X1,X0,X6,X4,X2)
& increasing(X7,X5,X3,X0,X6)
& ~ increasing(compose_function(X1,X7,X5,X0,X4),X5,X3,X4,X2)
& maps(X1,X0,X4) )
=> ( maps(sK8,sK6,sK1)
& increasing(sK2,sK1,sK7,sK5,sK3)
& increasing(sK8,sK6,sK4,sK1,sK7)
& ~ increasing(compose_function(sK2,sK8,sK6,sK1,sK5),sK6,sK4,sK5,sK3)
& maps(sK2,sK1,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( maps(X7,X5,X0)
& increasing(X1,X0,X6,X4,X2)
& increasing(X7,X5,X3,X0,X6)
& ~ increasing(compose_function(X1,X7,X5,X0,X4),X5,X3,X4,X2)
& maps(X1,X0,X4) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
? [X2,X4,X6,X3,X1,X0,X5,X7] :
( maps(X7,X0,X2)
& increasing(X4,X2,X5,X1,X6)
& increasing(X7,X0,X3,X2,X5)
& ~ increasing(compose_function(X4,X7,X0,X2,X1),X0,X3,X1,X6)
& maps(X4,X2,X1) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X4,X2,X3,X7,X6,X5,X0,X1] :
( ~ increasing(compose_function(X4,X7,X0,X2,X1),X0,X3,X1,X6)
& maps(X7,X0,X2)
& maps(X4,X2,X1)
& increasing(X4,X2,X5,X1,X6)
& increasing(X7,X0,X3,X2,X5) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X4,X2,X3,X7,X6,X5,X0,X1] :
( ( maps(X7,X0,X2)
& maps(X4,X2,X1)
& increasing(X4,X2,X5,X1,X6)
& increasing(X7,X0,X3,X2,X5) )
=> increasing(compose_function(X4,X7,X0,X2,X1),X0,X3,X1,X6) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X10,X1,X14,X9,X15,X16,X5] :
( ( maps(X5,X0,X1)
& maps(X9,X1,X10)
& increasing(X9,X1,X15,X10,X16)
& increasing(X5,X0,X14,X1,X15) )
=> increasing(compose_function(X9,X5,X0,X1,X10),X0,X14,X10,X16) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X10,X1,X14,X9,X15,X16,X5] :
( ( maps(X5,X0,X1)
& maps(X9,X1,X10)
& increasing(X9,X1,X15,X10,X16)
& increasing(X5,X0,X14,X1,X15) )
=> increasing(compose_function(X9,X5,X0,X1,X10),X0,X14,X10,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII37) ).
fof(f86,plain,
member(sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK6),
inference(unit_resulting_resolution,[],[f63,f77]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( member(sK11(X0,X1,X2,X3,X4),X3)
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f96,plain,
member(sK9(sK2,sK8,sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1),sK1),
inference(unit_resulting_resolution,[],[f83,f86,f84,f68]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X3,X1,X6,X2),X5,X4)
| member(sK9(X0,X3,X4,X5,X6),X6)
| ~ member(X5,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f83,plain,
member(sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK5),
inference(unit_resulting_resolution,[],[f63,f74]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X4] :
( member(sK13(X0,X1,X2,X3,X4),X0)
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f87,plain,
~ apply(sK3,sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f63,f78]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X2,sK10(X0,X1,X2,X3,X4),sK13(X0,X1,X2,X3,X4))
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f82,plain,
member(sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK5),
inference(unit_resulting_resolution,[],[f63,f73]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( member(sK10(X0,X1,X2,X3,X4),X0)
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f129,plain,
apply(sK2,sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(backward_demodulation,[],[f92,f122]) ).
fof(f122,plain,
sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))) = sK9(sK2,sK8,sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1),
inference(unit_resulting_resolution,[],[f66,f85,f88,f89,f93,f94,f61]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ apply(X2,X3,X5)
| ~ member(X3,X0)
| ~ maps(X2,X0,X1)
| ~ apply(X2,X3,X4)
| ~ member(X5,X1)
| ~ member(X4,X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ maps(X2,X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ apply(X2,X3,X5)
| X4 = X5
| ~ member(X3,X0)
| ~ apply(X2,X3,X4)
| ~ member(X4,X1) )
& ! [X6] :
( ~ member(X6,X0)
| ( apply(X2,X6,sK0(X1,X2,X6))
& member(sK0(X1,X2,X6),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f45,f46]) ).
fof(f46,plain,
! [X1,X2,X6] :
( ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) )
=> ( apply(X2,X6,sK0(X1,X2,X6))
& member(sK0(X1,X2,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ maps(X2,X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ apply(X2,X3,X5)
| X4 = X5
| ~ member(X3,X0)
| ~ apply(X2,X3,X4)
| ~ member(X4,X1) )
& ! [X6] :
( ~ member(X6,X0)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) ) ) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X1,X0,X2] :
( ~ maps(X2,X1,X0)
| ( ! [X3,X4,X5] :
( ~ member(X5,X0)
| ~ apply(X2,X3,X5)
| X4 = X5
| ~ member(X3,X1)
| ~ apply(X2,X3,X4)
| ~ member(X4,X0) )
& ! [X6] :
( ~ member(X6,X1)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ( ! [X3,X5,X4] :
( X4 = X5
| ~ apply(X2,X3,X5)
| ~ apply(X2,X3,X4)
| ~ member(X4,X0)
| ~ member(X5,X0)
| ~ member(X3,X1) )
& ! [X6] :
( ~ member(X6,X1)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) )
| ~ maps(X2,X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( maps(X2,X1,X0)
=> ( ! [X3,X5,X4] :
( ( member(X4,X0)
& member(X5,X0)
& member(X3,X1) )
=> ( ( apply(X2,X3,X5)
& apply(X2,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f33,plain,
! [X2,X0,X1] :
( maps(X2,X1,X0)
<=> ( ! [X3,X5,X4] :
( ( member(X4,X0)
& member(X5,X0)
& member(X3,X1) )
=> ( ( apply(X2,X3,X5)
& apply(X2,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X0,X5] :
( maps(X5,X0,X1)
<=> ( ! [X2,X6,X7] :
( ( member(X6,X1)
& member(X2,X0)
& member(X7,X1) )
=> ( ( apply(X5,X2,X6)
& apply(X5,X2,X7) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( member(X4,X1)
& apply(X5,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f94,plain,
apply(sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK9(sK2,sK8,sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1)),
inference(unit_resulting_resolution,[],[f85,f82,f80,f70]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X3,X1,X6,X2),X5,X4)
| ~ member(X5,X1)
| ~ member(X4,X2)
| apply(X3,X5,sK9(X0,X3,X4,X5,X6)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f80,plain,
apply(compose_function(sK2,sK8,sK6,sK1,sK5),sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f63,f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4] :
( apply(X4,sK12(X0,X1,X2,X3,X4),sK10(X0,X1,X2,X3,X4))
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f93,plain,
member(sK9(sK2,sK8,sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1),sK1),
inference(unit_resulting_resolution,[],[f82,f85,f80,f68]) ).
fof(f89,plain,
apply(sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)))),
inference(unit_resulting_resolution,[],[f66,f85,f60]) ).
fof(f60,plain,
! [X2,X0,X1,X6] :
( ~ maps(X2,X0,X1)
| ~ member(X6,X0)
| apply(X2,X6,sK0(X1,X2,X6)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f85,plain,
member(sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK6),
inference(unit_resulting_resolution,[],[f63,f76]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2,X3,X4),X3)
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f66,plain,
maps(sK8,sK6,sK1),
inference(cnf_transformation,[],[f50]) ).
fof(f92,plain,
apply(sK2,sK9(sK2,sK8,sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1),sK10(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f85,f82,f80,f69]) ).
fof(f88,plain,
member(sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),sK1),
inference(unit_resulting_resolution,[],[f66,f85,f59]) ).
fof(f59,plain,
! [X2,X0,X1,X6] :
( ~ maps(X2,X0,X1)
| member(sK0(X1,X2,X6),X1)
| ~ member(X6,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
increasing(sK2,sK1,sK7,sK5,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f145,plain,
apply(sK7,sK0(sK1,sK8,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),sK9(sK2,sK8,sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1)),
inference(unit_resulting_resolution,[],[f64,f88,f89,f85,f81,f86,f96,f97,f79]) ).
fof(f97,plain,
apply(sK8,sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK9(sK2,sK8,sK13(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK1)),
inference(unit_resulting_resolution,[],[f86,f83,f84,f70]) ).
fof(f81,plain,
apply(sK4,sK12(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5)),sK11(sK5,sK4,sK3,sK6,compose_function(sK2,sK8,sK6,sK1,sK5))),
inference(unit_resulting_resolution,[],[f63,f72]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( apply(X1,sK12(X0,X1,X2,X3,X4),sK11(X0,X1,X2,X3,X4))
| increasing(X4,X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f64,plain,
increasing(sK8,sK6,sK4,sK1,sK7),
inference(cnf_transformation,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET746+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:17:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51 % (11983)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51 % (12001)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.51 % (11976)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (11993)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (11978)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (11983)Instruction limit reached!
% 0.20/0.52 % (11983)------------------------------
% 0.20/0.52 % (11983)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (11983)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (11983)Termination reason: Unknown
% 0.20/0.52 % (11983)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (11983)Memory used [KB]: 6140
% 0.20/0.52 % (11983)Time elapsed: 0.109 s
% 0.20/0.52 % (11983)Instructions burned: 8 (million)
% 0.20/0.52 % (11983)------------------------------
% 0.20/0.52 % (11983)------------------------------
% 0.20/0.52 % (11985)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (11977)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.53 % (11973)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.53 % (11975)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (11976)Instruction limit reached!
% 0.20/0.53 % (11976)------------------------------
% 0.20/0.53 % (11976)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (11976)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (11976)Termination reason: Unknown
% 0.20/0.53 % (11976)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (11976)Memory used [KB]: 6268
% 0.20/0.53 % (11976)Time elapsed: 0.118 s
% 0.20/0.53 % (11976)Instructions burned: 13 (million)
% 0.20/0.53 % (11976)------------------------------
% 0.20/0.53 % (11976)------------------------------
% 0.20/0.53 % (11992)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.53 % (11974)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.53 % (12000)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.53 % (11974)Instruction limit reached!
% 0.20/0.53 % (11974)------------------------------
% 0.20/0.53 % (11974)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (11974)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (11974)Termination reason: Unknown
% 0.20/0.53 % (11974)Termination phase: Property scanning
% 0.20/0.53
% 0.20/0.53 % (11974)Memory used [KB]: 1535
% 0.20/0.53 % (11974)Time elapsed: 0.003 s
% 0.20/0.53 % (11974)Instructions burned: 3 (million)
% 0.20/0.53 % (11974)------------------------------
% 0.20/0.53 % (11974)------------------------------
% 0.20/0.53 % (11975)First to succeed.
% 0.20/0.54 % (11999)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.54 % (11984)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.54 % (11972)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.54 % (11988)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (11991)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.54 % (11991)Refutation not found, incomplete strategy% (11991)------------------------------
% 0.20/0.54 % (11991)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (11982)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.54 % (11991)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (11991)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54
% 0.20/0.54 % (11991)Memory used [KB]: 6012
% 0.20/0.54 % (11991)Time elapsed: 0.129 s
% 0.20/0.54 % (11991)Instructions burned: 3 (million)
% 0.20/0.54 % (11991)------------------------------
% 0.20/0.54 % (11991)------------------------------
% 0.20/0.54 % (11998)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.55 % (11994)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.55 % (11987)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55 % (11981)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.55 % (11986)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.55 % (11986)Instruction limit reached!
% 0.20/0.55 % (11986)------------------------------
% 0.20/0.55 % (11986)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (11986)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (11986)Termination reason: Unknown
% 0.20/0.55 % (11986)Termination phase: Property scanning
% 0.20/0.55
% 0.20/0.55 % (11986)Memory used [KB]: 1535
% 0.20/0.55 % (11986)Time elapsed: 0.004 s
% 0.20/0.55 % (11986)Instructions burned: 3 (million)
% 0.20/0.55 % (11986)------------------------------
% 0.20/0.55 % (11986)------------------------------
% 0.20/0.55 % (11989)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.55 % (11975)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Theorem for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (11975)------------------------------
% 0.20/0.55 % (11975)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (11975)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (11975)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (11975)Memory used [KB]: 6268
% 0.20/0.55 % (11975)Time elapsed: 0.127 s
% 0.20/0.55 % (11975)Instructions burned: 18 (million)
% 0.20/0.55 % (11975)------------------------------
% 0.20/0.55 % (11975)------------------------------
% 0.20/0.55 % (11969)Success in time 0.19 s
%------------------------------------------------------------------------------