TSTP Solution File: SEU039+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n004.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 18:31:47 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 27 unt; 0 def)
% Number of atoms : 429 ( 108 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 540 ( 203 ~; 198 |; 107 &)
% ( 13 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 194 ( 160 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f596,plain,
$false,
inference(subsumption_resolution,[],[f595,f240]) ).
fof(f240,plain,
~ in(sF19,sF21),
inference(definition_folding,[],[f183,f239,f238,f237]) ).
fof(f237,plain,
sF19 = apply(sK11,sK10),
introduced(function_definition,[]) ).
fof(f238,plain,
sF20 = relation_dom_restriction(sK11,sK9),
introduced(function_definition,[]) ).
fof(f239,plain,
relation_rng(sF20) = sF21,
introduced(function_definition,[]) ).
fof(f183,plain,
~ in(apply(sK11,sK10),relation_rng(relation_dom_restriction(sK11,sK9))),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( function(sK11)
& in(sK10,sK9)
& ~ in(apply(sK11,sK10),relation_rng(relation_dom_restriction(sK11,sK9)))
& relation(sK11)
& in(sK10,relation_dom(sK11)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f122,f123]) ).
fof(f123,plain,
( ? [X0,X1,X2] :
( function(X2)
& in(X1,X0)
& ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& relation(X2)
& in(X1,relation_dom(X2)) )
=> ( function(sK11)
& in(sK10,sK9)
& ~ in(apply(sK11,sK10),relation_rng(relation_dom_restriction(sK11,sK9)))
& relation(sK11)
& in(sK10,relation_dom(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
? [X0,X1,X2] :
( function(X2)
& in(X1,X0)
& ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& relation(X2)
& in(X1,relation_dom(X2)) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
? [X1,X0,X2] :
( function(X2)
& in(X0,X1)
& ~ in(apply(X2,X0),relation_rng(relation_dom_restriction(X2,X1)))
& relation(X2)
& in(X0,relation_dom(X2)) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
? [X2,X1,X0] :
( ~ in(apply(X2,X0),relation_rng(relation_dom_restriction(X2,X1)))
& in(X0,relation_dom(X2))
& in(X0,X1)
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
~ ! [X2,X1,X0] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
=> in(apply(X2,X0),relation_rng(relation_dom_restriction(X2,X1))) ) ),
inference(rectify,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X1,X0,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
! [X1,X0,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_1) ).
fof(f595,plain,
in(sF19,sF21),
inference(backward_demodulation,[],[f549,f594]) ).
fof(f594,plain,
sF19 = apply(sF20,sK10),
inference(forward_demodulation,[],[f587,f237]) ).
fof(f587,plain,
apply(sK11,sK10) = apply(sF20,sK10),
inference(resolution,[],[f456,f537]) ).
fof(f537,plain,
in(sK10,relation_dom(sF20)),
inference(forward_demodulation,[],[f535,f476]) ).
fof(f476,plain,
set_intersection2(sK9,sF22) = relation_dom(sF20),
inference(superposition,[],[f224,f468]) ).
fof(f468,plain,
relation_dom(sF20) = set_intersection2(sF22,sK9),
inference(forward_demodulation,[],[f467,f241]) ).
fof(f241,plain,
sF22 = relation_dom(sK11),
introduced(function_definition,[]) ).
fof(f467,plain,
relation_dom(sF20) = set_intersection2(relation_dom(sK11),sK9),
inference(subsumption_resolution,[],[f466,f269]) ).
fof(f269,plain,
relation(sF20),
inference(subsumption_resolution,[],[f268,f182]) ).
fof(f182,plain,
relation(sK11),
inference(cnf_transformation,[],[f124]) ).
fof(f268,plain,
( relation(sF20)
| ~ relation(sK11) ),
inference(superposition,[],[f226,f238]) ).
fof(f226,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X0)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X0] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f466,plain,
( relation_dom(sF20) = set_intersection2(relation_dom(sK11),sK9)
| ~ relation(sF20) ),
inference(subsumption_resolution,[],[f465,f182]) ).
fof(f465,plain,
( ~ relation(sK11)
| relation_dom(sF20) = set_intersection2(relation_dom(sK11),sK9)
| ~ relation(sF20) ),
inference(subsumption_resolution,[],[f464,f320]) ).
fof(f320,plain,
function(sF20),
inference(subsumption_resolution,[],[f319,f185]) ).
fof(f185,plain,
function(sK11),
inference(cnf_transformation,[],[f124]) ).
fof(f319,plain,
( ~ function(sK11)
| function(sF20) ),
inference(subsumption_resolution,[],[f318,f182]) ).
fof(f318,plain,
( ~ relation(sK11)
| function(sF20)
| ~ function(sK11) ),
inference(superposition,[],[f200,f238]) ).
fof(f200,plain,
! [X0,X1] :
( function(relation_dom_restriction(X1,X0))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( relation(relation_dom_restriction(X1,X0))
& function(relation_dom_restriction(X1,X0)) ) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
! [X1,X0] :
( ~ function(X0)
| ~ relation(X0)
| ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f464,plain,
( ~ function(sF20)
| ~ relation(sK11)
| ~ relation(sF20)
| relation_dom(sF20) = set_intersection2(relation_dom(sK11),sK9) ),
inference(subsumption_resolution,[],[f461,f185]) ).
fof(f461,plain,
( ~ function(sK11)
| ~ relation(sF20)
| ~ function(sF20)
| relation_dom(sF20) = set_intersection2(relation_dom(sK11),sK9)
| ~ relation(sK11) ),
inference(superposition,[],[f235,f238]) ).
fof(f235,plain,
! [X2,X1] :
( ~ function(relation_dom_restriction(X2,X1))
| ~ relation(relation_dom_restriction(X2,X1))
| ~ function(X2)
| relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1)
| ~ relation(X2) ),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
| relation_dom_restriction(X2,X1) != X0
| ~ relation(X2)
| ~ function(X2)
| ~ function(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( ~ relation(X0)
| ! [X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X2),X1)
| ( apply(X0,sK15(X0,X2)) != apply(X2,sK15(X0,X2))
& in(sK15(X0,X2),relation_dom(X0)) ) )
& ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ function(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f138,f139]) ).
fof(f139,plain,
! [X0,X2] :
( ? [X3] :
( apply(X0,X3) != apply(X2,X3)
& in(X3,relation_dom(X0)) )
=> ( apply(X0,sK15(X0,X2)) != apply(X2,sK15(X0,X2))
& in(sK15(X0,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X0,X1] :
( ~ relation(X0)
| ! [X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X2),X1)
| ? [X3] :
( apply(X0,X3) != apply(X2,X3)
& in(X3,relation_dom(X0)) ) )
& ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ function(X0) ),
inference(rectify,[],[f137]) ).
fof(f137,plain,
! [X1,X0] :
( ~ relation(X1)
| ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ function(X1) ),
inference(flattening,[],[f136]) ).
fof(f136,plain,
! [X1,X0] :
( ~ relation(X1)
| ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ function(X1) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X1,X0] :
( ~ relation(X1)
| ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ function(X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X1,X0] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f224,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f535,plain,
in(sK10,set_intersection2(sK9,sF22)),
inference(resolution,[],[f346,f242]) ).
fof(f242,plain,
in(sK10,sF22),
inference(definition_folding,[],[f181,f241]) ).
fof(f181,plain,
in(sK10,relation_dom(sK11)),
inference(cnf_transformation,[],[f124]) ).
fof(f346,plain,
! [X0] :
( ~ in(sK10,X0)
| in(sK10,set_intersection2(sK9,X0)) ),
inference(resolution,[],[f234,f184]) ).
fof(f184,plain,
in(sK10,sK9),
inference(cnf_transformation,[],[f124]) ).
fof(f234,plain,
! [X2,X3,X0] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| in(X3,set_intersection2(X2,X0)) ),
inference(equality_resolution,[],[f197]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2)
| set_intersection2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 )
& ( set_intersection2(X2,X0) = X1
| ( ( ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X2) )
& ( in(sK13(X0,X1,X2),X1)
| ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X2) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f130,f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X0)
| ~ in(X4,X2) )
& ( in(X4,X1)
| ( in(X4,X0)
& in(X4,X2) ) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X2) )
& ( in(sK13(X0,X1,X2),X1)
| ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 )
& ( set_intersection2(X2,X0) = X1
| ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X0)
| ~ in(X4,X2) )
& ( in(X4,X1)
| ( in(X4,X0)
& in(X4,X2) ) ) ) ) ),
inference(rectify,[],[f129]) ).
fof(f129,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( ( in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) ) )
| set_intersection2(X0,X2) != X1 )
& ( set_intersection2(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X1)
| ( in(X3,X2)
& in(X3,X0) ) ) ) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( ( in(X3,X2)
& in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) ) )
| set_intersection2(X0,X2) != X1 )
& ( set_intersection2(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X1)
| ( in(X3,X2)
& in(X3,X0) ) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X2,X1,X0] :
( ! [X3] :
( ( in(X3,X2)
& in(X3,X0) )
<=> in(X3,X1) )
<=> set_intersection2(X0,X2) = X1 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X1] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X1)
& in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f456,plain,
! [X0] :
( ~ in(X0,relation_dom(sF20))
| apply(sF20,X0) = apply(sK11,X0) ),
inference(subsumption_resolution,[],[f455,f182]) ).
fof(f455,plain,
! [X0] :
( apply(sF20,X0) = apply(sK11,X0)
| ~ in(X0,relation_dom(sF20))
| ~ relation(sK11) ),
inference(subsumption_resolution,[],[f454,f185]) ).
fof(f454,plain,
! [X0] :
( apply(sF20,X0) = apply(sK11,X0)
| ~ function(sK11)
| ~ relation(sK11)
| ~ in(X0,relation_dom(sF20)) ),
inference(superposition,[],[f244,f238]) ).
fof(f244,plain,
! [X2,X1,X4] :
( ~ in(X4,relation_dom(relation_dom_restriction(X2,X1)))
| apply(relation_dom_restriction(X2,X1),X4) = apply(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(subsumption_resolution,[],[f243,f200]) ).
fof(f243,plain,
! [X2,X1,X4] :
( ~ function(X2)
| apply(relation_dom_restriction(X2,X1),X4) = apply(X2,X4)
| ~ function(relation_dom_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(subsumption_resolution,[],[f236,f226]) ).
fof(f236,plain,
! [X2,X1,X4] :
( ~ relation(relation_dom_restriction(X2,X1))
| ~ relation(X2)
| ~ function(X2)
| apply(relation_dom_restriction(X2,X1),X4) = apply(X2,X4)
| ~ function(relation_dom_restriction(X2,X1))
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(equality_resolution,[],[f207]) ).
fof(f207,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0))
| relation_dom_restriction(X2,X1) != X0
| ~ relation(X2)
| ~ function(X2)
| ~ function(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f549,plain,
in(apply(sF20,sK10),sF21),
inference(forward_demodulation,[],[f548,f239]) ).
fof(f548,plain,
in(apply(sF20,sK10),relation_rng(sF20)),
inference(subsumption_resolution,[],[f547,f269]) ).
fof(f547,plain,
( ~ relation(sF20)
| in(apply(sF20,sK10),relation_rng(sF20)) ),
inference(subsumption_resolution,[],[f541,f320]) ).
fof(f541,plain,
( in(apply(sF20,sK10),relation_rng(sF20))
| ~ function(sF20)
| ~ relation(sF20) ),
inference(resolution,[],[f537,f231]) ).
fof(f231,plain,
! [X0,X7] :
( ~ in(X7,relation_dom(X0))
| ~ relation(X0)
| in(apply(X0,X7),relation_rng(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f230]) ).
fof(f230,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),X1)
| ~ in(X7,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X7,X5] :
( in(X5,X1)
| apply(X0,X7) != X5
| ~ in(X7,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) )
& ( in(sK1(X0,X1),X1)
| ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) ) ) )
& ( ! [X5] :
( ( ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] :
( apply(X0,X7) != X5
| ~ in(X7,relation_dom(X0)) ) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f105,f108,f107,f106]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) ) )
=> ( ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) )
& ( in(sK1(X0,X1),X1)
| ? [X4] :
( apply(X0,X4) = sK1(X0,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK1(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0,X5] :
( ? [X6] :
( apply(X0,X6) = X5
& in(X6,relation_dom(X0)) )
=> ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) ) ) )
& ( ! [X5] :
( ( ? [X6] :
( apply(X0,X6) = X5
& in(X6,relation_dom(X0)) )
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] :
( apply(X0,X7) != X5
| ~ in(X7,relation_dom(X0)) ) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( in(X2,X1)
| ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) )
& ( ! [X2] :
( ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
<=> in(X2,X1) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
<=> in(X2,X1) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n004.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 14:34:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % (6652)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.50 % (6645)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.52 % (6629)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (6627)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.52 % (6626)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (6626)Refutation not found, incomplete strategy% (6626)------------------------------
% 0.20/0.53 % (6626)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (6626)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (6626)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (6626)Memory used [KB]: 5628
% 0.20/0.53 % (6626)Time elapsed: 0.129 s
% 0.20/0.53 % (6626)Instructions burned: 8 (million)
% 0.20/0.53 % (6626)------------------------------
% 0.20/0.53 % (6626)------------------------------
% 0.20/0.53 % (6625)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53 % (6632)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53 % (6647)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53 % (6634)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (6632)Instruction limit reached!
% 0.20/0.53 % (6632)------------------------------
% 0.20/0.53 % (6632)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (6632)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (6632)Termination reason: Unknown
% 0.20/0.53 % (6632)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (6632)Memory used [KB]: 5500
% 0.20/0.53 % (6632)Time elapsed: 0.124 s
% 0.20/0.53 % (6632)Instructions burned: 7 (million)
% 0.20/0.53 % (6632)------------------------------
% 0.20/0.53 % (6632)------------------------------
% 0.20/0.53 % (6651)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53 % (6630)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.54 % (6652)First to succeed.
% 0.20/0.54 % (6654)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.54 % (6640)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.54 % (6653)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (6643)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54 % (6639)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (6641)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54 % (6642)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54 % (6628)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (6648)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.54 % (6646)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.55 % (6644)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (6631)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (6633)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55 % (6633)Instruction limit reached!
% 0.20/0.55 % (6633)------------------------------
% 0.20/0.55 % (6633)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (6633)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (6633)Termination reason: Unknown
% 0.20/0.55 % (6633)Termination phase: Property scanning
% 0.20/0.55
% 0.20/0.55 % (6633)Memory used [KB]: 1023
% 0.20/0.55 % (6633)Time elapsed: 0.003 s
% 0.20/0.55 % (6633)Instructions burned: 3 (million)
% 0.20/0.55 % (6633)------------------------------
% 0.20/0.55 % (6633)------------------------------
% 0.20/0.55 TRYING [1]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 TRYING [1]
% 0.20/0.55 % (6637)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.55 % (6635)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55 % (6636)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (6638)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.55 TRYING [2]
% 0.20/0.55 % (6652)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 % (6652)------------------------------
% 0.20/0.55 % (6652)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (6652)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (6652)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (6652)Memory used [KB]: 1407
% 0.20/0.55 % (6652)Time elapsed: 0.128 s
% 0.20/0.55 % (6652)Instructions burned: 25 (million)
% 0.20/0.55 % (6652)------------------------------
% 0.20/0.55 % (6652)------------------------------
% 0.20/0.55 % (6624)Success in time 0.196 s
%------------------------------------------------------------------------------