TSTP Solution File: SEU293+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 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 18:33:03 EDT 2022
% Result : Theorem 1.80s 0.60s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 114 ( 13 unt; 0 def)
% Number of atoms : 495 ( 80 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 604 ( 223 ~; 227 |; 103 &)
% ( 25 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 198 ( 162 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f609,plain,
$false,
inference(avatar_sat_refutation,[],[f277,f278,f279,f396,f408,f413,f503,f535,f608]) ).
fof(f608,plain,
( ~ spl25_1
| spl25_2
| ~ spl25_3
| ~ spl25_6 ),
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f607,plain,
( $false
| ~ spl25_1
| spl25_2
| ~ spl25_3
| ~ spl25_6 ),
inference(subsumption_resolution,[],[f606,f267]) ).
fof(f267,plain,
( in(sF23,sK20)
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f266,plain,
( spl25_1
<=> in(sF23,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).
fof(f606,plain,
( ~ in(sF23,sK20)
| spl25_2
| ~ spl25_3
| ~ spl25_6 ),
inference(subsumption_resolution,[],[f600,f272]) ).
fof(f272,plain,
( ~ in(sK21,sF24)
| spl25_2 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f270,plain,
( spl25_2
<=> in(sK21,sF24) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).
fof(f600,plain,
( in(sK21,sF24)
| ~ in(sF23,sK20)
| ~ spl25_3
| ~ spl25_6 ),
inference(superposition,[],[f504,f261]) ).
fof(f261,plain,
sF24 = relation_inverse_image(sK19,sK20),
introduced(function_definition,[]) ).
fof(f504,plain,
( ! [X0] :
( in(sK21,relation_inverse_image(sK19,X0))
| ~ in(sF23,X0) )
| ~ spl25_3
| ~ spl25_6 ),
inference(subsumption_resolution,[],[f450,f275]) ).
fof(f275,plain,
( in(sK21,sK17)
| ~ spl25_3 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f274,plain,
( spl25_3
<=> in(sK21,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
fof(f450,plain,
( ! [X0] :
( ~ in(sK21,sK17)
| in(sK21,relation_inverse_image(sK19,X0))
| ~ in(sF23,X0) )
| ~ spl25_6 ),
inference(forward_demodulation,[],[f449,f438]) ).
fof(f438,plain,
sK17 = relation_dom(sK19),
inference(backward_demodulation,[],[f385,f437]) ).
fof(f437,plain,
sK17 = relation_dom_as_subset(sK17,sK18,sK19),
inference(subsumption_resolution,[],[f436,f245]) ).
fof(f245,plain,
relation_of2_as_subset(sK19,sK17,sK18),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
( relation_of2_as_subset(sK19,sK17,sK18)
& ( ~ in(apply(sK19,sK21),sK20)
| ~ in(sK21,sK17)
| ~ in(sK21,relation_inverse_image(sK19,sK20)) )
& ( ( in(apply(sK19,sK21),sK20)
& in(sK21,sK17) )
| in(sK21,relation_inverse_image(sK19,sK20)) )
& quasi_total(sK19,sK17,sK18)
& empty_set != sK18
& function(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21])],[f162,f164,f163]) ).
fof(f163,plain,
( ? [X0,X1,X2,X3] :
( relation_of2_as_subset(X2,X0,X1)
& ? [X4] :
( ( ~ in(apply(X2,X4),X3)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X2,X3)) )
& ( ( in(apply(X2,X4),X3)
& in(X4,X0) )
| in(X4,relation_inverse_image(X2,X3)) ) )
& quasi_total(X2,X0,X1)
& empty_set != X1
& function(X2) )
=> ( relation_of2_as_subset(sK19,sK17,sK18)
& ? [X4] :
( ( ~ in(apply(sK19,X4),sK20)
| ~ in(X4,sK17)
| ~ in(X4,relation_inverse_image(sK19,sK20)) )
& ( ( in(apply(sK19,X4),sK20)
& in(X4,sK17) )
| in(X4,relation_inverse_image(sK19,sK20)) ) )
& quasi_total(sK19,sK17,sK18)
& empty_set != sK18
& function(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
( ? [X4] :
( ( ~ in(apply(sK19,X4),sK20)
| ~ in(X4,sK17)
| ~ in(X4,relation_inverse_image(sK19,sK20)) )
& ( ( in(apply(sK19,X4),sK20)
& in(X4,sK17) )
| in(X4,relation_inverse_image(sK19,sK20)) ) )
=> ( ( ~ in(apply(sK19,sK21),sK20)
| ~ in(sK21,sK17)
| ~ in(sK21,relation_inverse_image(sK19,sK20)) )
& ( ( in(apply(sK19,sK21),sK20)
& in(sK21,sK17) )
| in(sK21,relation_inverse_image(sK19,sK20)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X2,X0,X1)
& ? [X4] :
( ( ~ in(apply(X2,X4),X3)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X2,X3)) )
& ( ( in(apply(X2,X4),X3)
& in(X4,X0) )
| in(X4,relation_inverse_image(X2,X3)) ) )
& quasi_total(X2,X0,X1)
& empty_set != X1
& function(X2) ),
inference(rectify,[],[f161]) ).
fof(f161,plain,
? [X1,X3,X2,X0] :
( relation_of2_as_subset(X2,X1,X3)
& ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,X1)
| ~ in(X4,relation_inverse_image(X2,X0)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,X1) )
| in(X4,relation_inverse_image(X2,X0)) ) )
& quasi_total(X2,X1,X3)
& empty_set != X3
& function(X2) ),
inference(flattening,[],[f160]) ).
fof(f160,plain,
? [X1,X3,X2,X0] :
( relation_of2_as_subset(X2,X1,X3)
& ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,X1)
| ~ in(X4,relation_inverse_image(X2,X0)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,X1) )
| in(X4,relation_inverse_image(X2,X0)) ) )
& quasi_total(X2,X1,X3)
& empty_set != X3
& function(X2) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
? [X1,X3,X2,X0] :
( relation_of2_as_subset(X2,X1,X3)
& ? [X4] :
( in(X4,relation_inverse_image(X2,X0))
<~> ( in(apply(X2,X4),X0)
& in(X4,X1) ) )
& quasi_total(X2,X1,X3)
& empty_set != X3
& function(X2) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
? [X3,X0,X2,X1] :
( ? [X4] :
( in(X4,relation_inverse_image(X2,X0))
<~> ( in(apply(X2,X4),X0)
& in(X4,X1) ) )
& empty_set != X3
& relation_of2_as_subset(X2,X1,X3)
& quasi_total(X2,X1,X3)
& function(X2) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
~ ! [X3,X0,X2,X1] :
( ( relation_of2_as_subset(X2,X1,X3)
& quasi_total(X2,X1,X3)
& function(X2) )
=> ( empty_set != X3
=> ! [X4] :
( ( in(apply(X2,X4),X0)
& in(X4,X1) )
<=> in(X4,relation_inverse_image(X2,X0)) ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X2,X0,X3,X1] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( empty_set != X1
=> ! [X4] :
( ( in(X4,X0)
& in(apply(X3,X4),X2) )
<=> in(X4,relation_inverse_image(X3,X2)) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X2,X0,X3,X1] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( empty_set != X1
=> ! [X4] :
( ( in(X4,X0)
& in(apply(X3,X4),X2) )
<=> in(X4,relation_inverse_image(X3,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f436,plain,
( ~ relation_of2_as_subset(sK19,sK17,sK18)
| sK17 = relation_dom_as_subset(sK17,sK18,sK19) ),
inference(subsumption_resolution,[],[f433,f240]) ).
fof(f240,plain,
empty_set != sK18,
inference(cnf_transformation,[],[f165]) ).
fof(f433,plain,
( empty_set = sK18
| ~ relation_of2_as_subset(sK19,sK17,sK18)
| sK17 = relation_dom_as_subset(sK17,sK18,sK19) ),
inference(resolution,[],[f221,f241]) ).
fof(f241,plain,
quasi_total(sK19,sK17,sK18),
inference(cnf_transformation,[],[f165]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ quasi_total(X2,X1,X0)
| ~ relation_of2_as_subset(X2,X1,X0)
| empty_set = X0
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ( ( ( ( relation_dom_as_subset(X1,X0,X2) = X1
| ~ quasi_total(X2,X1,X0) )
& ( quasi_total(X2,X1,X0)
| relation_dom_as_subset(X1,X0,X2) != X1 ) )
| ( empty_set = X0
& empty_set != X1 ) )
& ( empty_set != X0
| ( ( empty_set = X2
| ~ quasi_total(X2,X1,X0) )
& ( quasi_total(X2,X1,X0)
| empty_set != X2 ) )
| empty_set = X1 ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f142]) ).
fof(f142,plain,
! [X1,X2,X0] :
( ( ( ( ( relation_dom_as_subset(X2,X1,X0) = X2
| ~ quasi_total(X0,X2,X1) )
& ( quasi_total(X0,X2,X1)
| relation_dom_as_subset(X2,X1,X0) != X2 ) )
| ( empty_set = X1
& empty_set != X2 ) )
& ( empty_set != X1
| ( ( empty_set = X0
| ~ quasi_total(X0,X2,X1) )
& ( quasi_total(X0,X2,X1)
| empty_set != X0 ) )
| empty_set = X2 ) )
| ~ relation_of2_as_subset(X0,X2,X1) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X1,X2,X0] :
( ( ( ( relation_dom_as_subset(X2,X1,X0) = X2
<=> quasi_total(X0,X2,X1) )
| ( empty_set = X1
& empty_set != X2 ) )
& ( empty_set != X1
| ( empty_set = X0
<=> quasi_total(X0,X2,X1) )
| empty_set = X2 ) )
| ~ relation_of2_as_subset(X0,X2,X1) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X2,X1] :
( ( ( empty_set = X2
| ( empty_set = X0
<=> quasi_total(X0,X2,X1) )
| empty_set != X1 )
& ( ( relation_dom_as_subset(X2,X1,X0) = X2
<=> quasi_total(X0,X2,X1) )
| ( empty_set = X1
& empty_set != X2 ) ) )
| ~ relation_of2_as_subset(X0,X2,X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X2,X1] :
( relation_of2_as_subset(X0,X2,X1)
=> ( ( empty_set = X1
=> ( empty_set = X2
| ( empty_set = X0
<=> quasi_total(X0,X2,X1) ) ) )
& ( ( empty_set = X1
=> empty_set = X2 )
=> ( relation_dom_as_subset(X2,X1,X0) = X2
<=> quasi_total(X0,X2,X1) ) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X2,X1,X0] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( empty_set = X1
=> ( ( empty_set = X2
<=> quasi_total(X2,X0,X1) )
| empty_set = X0 ) )
& ( ( empty_set = X1
=> empty_set = X0 )
=> ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f385,plain,
relation_dom_as_subset(sK17,sK18,sK19) = relation_dom(sK19),
inference(resolution,[],[f247,f347]) ).
fof(f347,plain,
relation_of2(sK19,sK17,sK18),
inference(resolution,[],[f248,f245]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X1,X2,X0)
| relation_of2(X1,X2,X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X1,X2,X0)
| ~ relation_of2(X1,X2,X0) )
& ( relation_of2(X1,X2,X0)
| ~ relation_of2_as_subset(X1,X2,X0) ) ),
inference(rectify,[],[f166]) ).
fof(f166,plain,
! [X0,X2,X1] :
( ( relation_of2_as_subset(X2,X1,X0)
| ~ relation_of2(X2,X1,X0) )
& ( relation_of2(X2,X1,X0)
| ~ relation_of2_as_subset(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X2,X1] :
( relation_of2_as_subset(X2,X1,X0)
<=> relation_of2(X2,X1,X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X1,X0,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ relation_of2(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ relation_of2(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X2,X1] :
( relation_of2(X1,X0,X2)
=> relation_dom_as_subset(X0,X2,X1) = relation_dom(X1) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X0,X2,X1] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f449,plain,
( ! [X0] :
( ~ in(sK21,relation_dom(sK19))
| in(sK21,relation_inverse_image(sK19,X0))
| ~ in(sF23,X0) )
| ~ spl25_6 ),
inference(subsumption_resolution,[],[f448,f391]) ).
fof(f391,plain,
( relation(sK19)
| ~ spl25_6 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl25_6
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_6])]) ).
fof(f448,plain,
! [X0] :
( ~ in(sF23,X0)
| in(sK21,relation_inverse_image(sK19,X0))
| ~ in(sK21,relation_dom(sK19))
| ~ relation(sK19) ),
inference(subsumption_resolution,[],[f447,f239]) ).
fof(f239,plain,
function(sK19),
inference(cnf_transformation,[],[f165]) ).
fof(f447,plain,
! [X0] :
( ~ function(sK19)
| ~ relation(sK19)
| ~ in(sK21,relation_dom(sK19))
| ~ in(sF23,X0)
| in(sK21,relation_inverse_image(sK19,X0)) ),
inference(superposition,[],[f252,f260]) ).
fof(f260,plain,
sF23 = apply(sK19,sK21),
introduced(function_definition,[]) ).
fof(f252,plain,
! [X2,X3,X0] :
( ~ in(apply(X0,X3),X2)
| ~ function(X0)
| in(X3,relation_inverse_image(X0,X2))
| ~ in(X3,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f195]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0))
| relation_inverse_image(X0,X2) != X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X2)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X1) ) )
| relation_inverse_image(X0,X2) != X1 )
& ( relation_inverse_image(X0,X2) = X1
| ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
| ~ in(sK4(X0,X1,X2),relation_dom(X0))
| ~ in(sK4(X0,X1,X2),X1) )
& ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
& in(sK4(X0,X1,X2),relation_dom(X0)) )
| in(sK4(X0,X1,X2),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f125,f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(apply(X0,X4),X2)
| ~ in(X4,relation_dom(X0))
| ~ in(X4,X1) )
& ( ( in(apply(X0,X4),X2)
& in(X4,relation_dom(X0)) )
| in(X4,X1) ) )
=> ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
| ~ in(sK4(X0,X1,X2),relation_dom(X0))
| ~ in(sK4(X0,X1,X2),X1) )
& ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
& in(sK4(X0,X1,X2),relation_dom(X0)) )
| in(sK4(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X2)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X1) ) )
| relation_inverse_image(X0,X2) != X1 )
& ( relation_inverse_image(X0,X2) = X1
| ? [X4] :
( ( ~ in(apply(X0,X4),X2)
| ~ in(X4,relation_dom(X0))
| ~ in(X4,X1) )
& ( ( in(apply(X0,X4),X2)
& in(X4,relation_dom(X0)) )
| in(X4,X1) ) ) ) ) ),
inference(rectify,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) ) ) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 ) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f535,plain,
( spl25_1
| ~ spl25_2
| ~ spl25_8 ),
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f534,plain,
( $false
| spl25_1
| ~ spl25_2
| ~ spl25_8 ),
inference(subsumption_resolution,[],[f533,f271]) ).
fof(f271,plain,
( in(sK21,sF24)
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f533,plain,
( ~ in(sK21,sF24)
| spl25_1
| ~ spl25_8 ),
inference(subsumption_resolution,[],[f527,f268]) ).
fof(f268,plain,
( ~ in(sF23,sK20)
| spl25_1 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f527,plain,
( in(sF23,sK20)
| ~ in(sK21,sF24)
| ~ spl25_8 ),
inference(superposition,[],[f412,f260]) ).
fof(f412,plain,
( ! [X0] :
( in(apply(sK19,X0),sK20)
| ~ in(X0,sF24) )
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f411,plain,
( spl25_8
<=> ! [X0] :
( ~ in(X0,sF24)
| in(apply(sK19,X0),sK20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_8])]) ).
fof(f503,plain,
( ~ spl25_2
| spl25_3
| ~ spl25_7 ),
inference(avatar_contradiction_clause,[],[f502]) ).
fof(f502,plain,
( $false
| ~ spl25_2
| spl25_3
| ~ spl25_7 ),
inference(subsumption_resolution,[],[f500,f276]) ).
fof(f276,plain,
( ~ in(sK21,sK17)
| spl25_3 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f500,plain,
( in(sK21,sK17)
| ~ spl25_2
| ~ spl25_7 ),
inference(resolution,[],[f442,f271]) ).
fof(f442,plain,
( ! [X0] :
( ~ in(X0,sF24)
| in(X0,sK17) )
| ~ spl25_7 ),
inference(backward_demodulation,[],[f395,f438]) ).
fof(f395,plain,
( ! [X0] :
( in(X0,relation_dom(sK19))
| ~ in(X0,sF24) )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f394,plain,
( spl25_7
<=> ! [X0] :
( in(X0,relation_dom(sK19))
| ~ in(X0,sF24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).
fof(f413,plain,
( spl25_8
| ~ spl25_6 ),
inference(avatar_split_clause,[],[f409,f390,f411]) ).
fof(f409,plain,
! [X0] :
( ~ relation(sK19)
| ~ in(X0,sF24)
| in(apply(sK19,X0),sK20) ),
inference(subsumption_resolution,[],[f399,f239]) ).
fof(f399,plain,
! [X0] :
( in(apply(sK19,X0),sK20)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,sF24) ),
inference(superposition,[],[f253,f261]) ).
fof(f253,plain,
! [X2,X3,X0] :
( ~ in(X3,relation_inverse_image(X0,X2))
| in(apply(X0,X3),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f194]) ).
fof(f194,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(apply(X0,X3),X2)
| ~ in(X3,X1)
| relation_inverse_image(X0,X2) != X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f408,plain,
spl25_6,
inference(avatar_split_clause,[],[f405,f390]) ).
fof(f405,plain,
relation(sK19),
inference(resolution,[],[f363,f245]) ).
fof(f363,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f181,f223]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
! [X0,X2,X1] :
( ~ element(X1,powerset(cartesian_product2(X0,X2)))
| relation(X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X2,X1] :
( element(X1,powerset(cartesian_product2(X0,X2)))
=> relation(X1) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X2,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f181,plain,
! [X2,X0,X1] :
( element(X1,powerset(cartesian_product2(X2,X0)))
| ~ relation_of2_as_subset(X1,X2,X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( element(X1,powerset(cartesian_product2(X2,X0)))
| ~ relation_of2_as_subset(X1,X2,X0) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X2,X0,X1] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( relation_of2_as_subset(X0,X1,X2)
=> element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f396,plain,
( ~ spl25_6
| spl25_7 ),
inference(avatar_split_clause,[],[f388,f394,f390]) ).
fof(f388,plain,
! [X0] :
( in(X0,relation_dom(sK19))
| ~ in(X0,sF24)
| ~ relation(sK19) ),
inference(subsumption_resolution,[],[f387,f239]) ).
fof(f387,plain,
! [X0] :
( ~ function(sK19)
| ~ relation(sK19)
| in(X0,relation_dom(sK19))
| ~ in(X0,sF24) ),
inference(superposition,[],[f254,f261]) ).
fof(f254,plain,
! [X2,X3,X0] :
( ~ in(X3,relation_inverse_image(X0,X2))
| ~ relation(X0)
| in(X3,relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X3,relation_dom(X0))
| ~ in(X3,X1)
| relation_inverse_image(X0,X2) != X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f279,plain,
( spl25_2
| spl25_1 ),
inference(avatar_split_clause,[],[f263,f266,f270]) ).
fof(f263,plain,
( in(sF23,sK20)
| in(sK21,sF24) ),
inference(definition_folding,[],[f243,f261,f260]) ).
fof(f243,plain,
( in(apply(sK19,sK21),sK20)
| in(sK21,relation_inverse_image(sK19,sK20)) ),
inference(cnf_transformation,[],[f165]) ).
fof(f278,plain,
( spl25_2
| spl25_3 ),
inference(avatar_split_clause,[],[f264,f274,f270]) ).
fof(f264,plain,
( in(sK21,sK17)
| in(sK21,sF24) ),
inference(definition_folding,[],[f242,f261]) ).
fof(f242,plain,
( in(sK21,sK17)
| in(sK21,relation_inverse_image(sK19,sK20)) ),
inference(cnf_transformation,[],[f165]) ).
fof(f277,plain,
( ~ spl25_1
| ~ spl25_2
| ~ spl25_3 ),
inference(avatar_split_clause,[],[f262,f274,f270,f266]) ).
fof(f262,plain,
( ~ in(sK21,sK17)
| ~ in(sK21,sF24)
| ~ in(sF23,sK20) ),
inference(definition_folding,[],[f244,f261,f260]) ).
fof(f244,plain,
( ~ in(apply(sK19,sK21),sK20)
| ~ in(sK21,sK17)
| ~ in(sK21,relation_inverse_image(sK19,sK20)) ),
inference(cnf_transformation,[],[f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:04:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.53 % (21106)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.54 % (21089)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54 % (21098)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)
% 0.19/0.54 % (21090)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54 % (21090)Instruction limit reached!
% 0.19/0.54 % (21090)------------------------------
% 0.19/0.54 % (21090)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (21090)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (21090)Termination reason: Unknown
% 0.19/0.54 % (21090)Termination phase: Preprocessing 3
% 0.19/0.54
% 0.19/0.54 % (21090)Memory used [KB]: 895
% 0.19/0.54 % (21090)Time elapsed: 0.003 s
% 0.19/0.54 % (21090)Instructions burned: 2 (million)
% 0.19/0.54 % (21090)------------------------------
% 0.19/0.54 % (21090)------------------------------
% 0.19/0.54 % (21097)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)
% 0.19/0.54 % (21088)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)
% 0.19/0.55 TRYING [1]
% 0.19/0.55 % (21105)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)
% 0.19/0.55 % (21104)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)
% 0.19/0.55 % (21096)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)
% 0.19/0.55 TRYING [2]
% 0.19/0.55 % (21089)Instruction limit reached!
% 0.19/0.55 % (21089)------------------------------
% 0.19/0.55 % (21089)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56 % (21089)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56 % (21089)Termination reason: Unknown
% 0.19/0.56 % (21089)Termination phase: Saturation
% 0.19/0.56
% 0.19/0.56 % (21089)Memory used [KB]: 5628
% 0.19/0.56 % (21089)Time elapsed: 0.128 s
% 0.19/0.56 % (21089)Instructions burned: 7 (million)
% 0.19/0.56 % (21089)------------------------------
% 0.19/0.56 % (21089)------------------------------
% 0.19/0.56 TRYING [3]
% 1.71/0.58 % (21106)First to succeed.
% 1.71/0.59 % (21087)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)
% 1.71/0.59 % (21085)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)
% 1.71/0.60 TRYING [4]
% 1.71/0.60 % (21097)Also succeeded, but the first one will report.
% 1.80/0.60 % (21106)Refutation found. Thanks to Tanya!
% 1.80/0.60 % SZS status Theorem for theBenchmark
% 1.80/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.60 % (21106)------------------------------
% 1.80/0.60 % (21106)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.80/0.60 % (21106)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.80/0.60 % (21106)Termination reason: Refutation
% 1.80/0.60
% 1.80/0.60 % (21106)Memory used [KB]: 5756
% 1.80/0.60 % (21106)Time elapsed: 0.162 s
% 1.80/0.60 % (21106)Instructions burned: 17 (million)
% 1.80/0.60 % (21106)------------------------------
% 1.80/0.60 % (21106)------------------------------
% 1.80/0.60 % (21081)Success in time 0.246 s
%------------------------------------------------------------------------------