TSTP Solution File: SEU039+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n027.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 : Thu Aug 31 17:55:03 EDT 2023
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 87 ( 28 unt; 0 def)
% Number of atoms : 399 ( 105 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 498 ( 186 ~; 183 |; 100 &)
% ( 11 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 184 (; 153 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f864,plain,
$false,
inference(subsumption_resolution,[],[f863,f218]) ).
fof(f218,plain,
~ in(sF19,sF21),
inference(definition_folding,[],[f132,f217,f216,f215]) ).
fof(f215,plain,
apply(sK2,sK1) = sF19,
introduced(function_definition,[]) ).
fof(f216,plain,
relation_dom_restriction(sK2,sK0) = sF20,
introduced(function_definition,[]) ).
fof(f217,plain,
relation_rng(sF20) = sF21,
introduced(function_definition,[]) ).
fof(f132,plain,
~ in(apply(sK2,sK1),relation_rng(relation_dom_restriction(sK2,sK0))),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ~ in(apply(sK2,sK1),relation_rng(relation_dom_restriction(sK2,sK0)))
& in(sK1,sK0)
& in(sK1,relation_dom(sK2))
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f52,f88]) ).
fof(f88,plain,
( ? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) )
=> ( ~ in(apply(sK2,sK1),relation_rng(relation_dom_restriction(sK2,sK0)))
& in(sK1,sK0)
& in(sK1,relation_dom(sK2))
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,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,
! [X0,X1,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/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',t73_funct_1) ).
fof(f863,plain,
in(sF19,sF21),
inference(backward_demodulation,[],[f652,f860]) ).
fof(f860,plain,
sF19 = apply(sF20,sK1),
inference(forward_demodulation,[],[f853,f215]) ).
fof(f853,plain,
apply(sK2,sK1) = apply(sF20,sK1),
inference(resolution,[],[f453,f131]) ).
fof(f131,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f89]) ).
fof(f453,plain,
! [X0] :
( ~ in(X0,sK0)
| apply(sK2,X0) = apply(sF20,X0) ),
inference(subsumption_resolution,[],[f452,f128]) ).
fof(f128,plain,
relation(sK2),
inference(cnf_transformation,[],[f89]) ).
fof(f452,plain,
! [X0] :
( apply(sK2,X0) = apply(sF20,X0)
| ~ in(X0,sK0)
| ~ relation(sK2) ),
inference(subsumption_resolution,[],[f449,f129]) ).
fof(f129,plain,
function(sK2),
inference(cnf_transformation,[],[f89]) ).
fof(f449,plain,
! [X0] :
( apply(sK2,X0) = apply(sF20,X0)
| ~ in(X0,sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[],[f182,f216]) ).
fof(f182,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',t72_funct_1) ).
fof(f652,plain,
in(apply(sF20,sK1),sF21),
inference(forward_demodulation,[],[f651,f217]) ).
fof(f651,plain,
in(apply(sF20,sK1),relation_rng(sF20)),
inference(subsumption_resolution,[],[f650,f261]) ).
fof(f261,plain,
relation(sF20),
inference(subsumption_resolution,[],[f260,f128]) ).
fof(f260,plain,
( relation(sF20)
| ~ relation(sK2) ),
inference(superposition,[],[f166,f216]) ).
fof(f166,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',dt_k7_relat_1) ).
fof(f650,plain,
( in(apply(sF20,sK1),relation_rng(sF20))
| ~ relation(sF20) ),
inference(subsumption_resolution,[],[f644,f337]) ).
fof(f337,plain,
function(sF20),
inference(subsumption_resolution,[],[f336,f128]) ).
fof(f336,plain,
( function(sF20)
| ~ relation(sK2) ),
inference(subsumption_resolution,[],[f335,f129]) ).
fof(f335,plain,
( function(sF20)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[],[f173,f216]) ).
fof(f173,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',fc4_funct_1) ).
fof(f644,plain,
( in(apply(sF20,sK1),relation_rng(sF20))
| ~ function(sF20)
| ~ relation(sF20) ),
inference(resolution,[],[f629,f207]) ).
fof(f207,plain,
! [X0,X6] :
( ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK4(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK4(X0,X1),X1) )
& ( ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
& in(sK5(X0,X1),relation_dom(X0)) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK6(X0,X5)) = X5
& in(sK6(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f93,f96,f95,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK4(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK4(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK4(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
& in(sK5(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK6(X0,X5)) = X5
& in(sK6(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',d5_funct_1) ).
fof(f629,plain,
in(sK1,relation_dom(sF20)),
inference(backward_demodulation,[],[f421,f616]) ).
fof(f616,plain,
set_intersection2(sK0,sF22) = relation_dom(sF20),
inference(superposition,[],[f610,f165]) ).
fof(f165,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',commutativity_k3_xboole_0) ).
fof(f610,plain,
set_intersection2(sF22,sK0) = relation_dom(sF20),
inference(superposition,[],[f599,f216]) ).
fof(f599,plain,
! [X6] : relation_dom(relation_dom_restriction(sK2,X6)) = set_intersection2(sF22,X6),
inference(forward_demodulation,[],[f598,f219]) ).
fof(f219,plain,
relation_dom(sK2) = sF22,
introduced(function_definition,[]) ).
fof(f598,plain,
! [X6] : set_intersection2(relation_dom(sK2),X6) = relation_dom(relation_dom_restriction(sK2,X6)),
inference(subsumption_resolution,[],[f589,f128]) ).
fof(f589,plain,
! [X6] :
( set_intersection2(relation_dom(sK2),X6) = relation_dom(relation_dom_restriction(sK2,X6))
| ~ relation(sK2) ),
inference(resolution,[],[f556,f129]) ).
fof(f556,plain,
! [X2,X0] :
( ~ function(X2)
| set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2) ),
inference(subsumption_resolution,[],[f555,f166]) ).
fof(f555,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(subsumption_resolution,[],[f211,f173]) ).
fof(f211,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f174]) ).
fof(f174,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X1,sK9(X1,X2)) != apply(X2,sK9(X1,X2))
& in(sK9(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f104,f105]) ).
fof(f105,plain,
! [X1,X2] :
( ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK9(X1,X2)) != apply(X2,sK9(X1,X2))
& in(sK9(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [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(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [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(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',t68_funct_1) ).
fof(f421,plain,
in(sK1,set_intersection2(sK0,sF22)),
inference(forward_demodulation,[],[f418,f165]) ).
fof(f418,plain,
in(sK1,set_intersection2(sF22,sK0)),
inference(resolution,[],[f393,f220]) ).
fof(f220,plain,
in(sK1,sF22),
inference(definition_folding,[],[f130,f219]) ).
fof(f130,plain,
in(sK1,relation_dom(sK2)),
inference(cnf_transformation,[],[f89]) ).
fof(f393,plain,
! [X4] :
( ~ in(sK1,X4)
| in(sK1,set_intersection2(X4,sK0)) ),
inference(resolution,[],[f212,f131]) ).
fof(f212,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f186]) ).
fof(f186,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( in(sK10(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0) )
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( in(sK10(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0) )
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077',d3_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 01:56:32 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077
% 0.15/0.35 % (17274)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (17280)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.41 % (17275)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.41 % (17278)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.41 % (17277)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.41 % (17276)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.41 % (17279)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.41 % (17281)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.44 % (17280)First to succeed.
% 0.21/0.44 % (17279)Also succeeded, but the first one will report.
% 0.21/0.44 % (17280)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for Vampire---4
% 0.21/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.44 % (17280)------------------------------
% 0.21/0.44 % (17280)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 % (17280)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 % (17280)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (17280)Memory used [KB]: 5884
% 0.21/0.44 % (17280)Time elapsed: 0.027 s
% 0.21/0.44 % (17280)------------------------------
% 0.21/0.44 % (17280)------------------------------
% 0.21/0.44 % (17274)Success in time 0.088 s
% 0.21/0.44 17275 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077
% 0.21/0.44 % (17275)------------------------------
% 0.21/0.44 % (17275)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 % (17275)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 17276 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077
% 0.21/0.44 % (17276)------------------------------
% 0.21/0.44 % (17276)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 17277 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.yIpTw8ZNTb/Vampire---4.8_17077
% 0.21/0.44 % (17277)------------------------------
% 0.21/0.44 % (17277)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 % (17275)Termination reason: Unknown
% 0.21/0.44 % (17275)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (17276)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 % (17277)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 % (17275)Memory used [KB]: 5500
% 0.21/0.44 % (17276)Termination reason: Unknown
% 0.21/0.44 % (17277)Termination reason: Unknown
% 0.21/0.44 % (17275)Time elapsed: 0.031 s
% 0.21/0.44 % (17276)Termination phase: Saturation
% 0.21/0.44 % (17277)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 % (17275)------------------------------
% 0.21/0.44 % (17275)------------------------------
% 0.21/0.44 % (17276)Memory used [KB]: 1023
% 0.21/0.44 % (17277)Memory used [KB]: 1151
% 0.21/0.44 % (17276)Time elapsed: 0.031 s
% 0.21/0.44 % (17277)Time elapsed: 0.031 s
% 0.21/0.44 % (17276)------------------------------
% 0.21/0.44 % (17276)------------------------------
% 0.21/0.44 % (17277)------------------------------
% 0.21/0.44 % (17277)------------------------------
% 0.21/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------