TSTP Solution File: SEU250+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU250+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May 5 09:30:25 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 178 ( 38 unt; 0 def)
% Number of atoms : 386 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 355 ( 147 ~; 131 |; 39 &)
% ( 19 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 17 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 174 ( 156 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f705,plain,
$false,
inference(avatar_sat_refutation,[],[f200,f242,f251,f274,f285,f306,f336,f337,f338,f404,f412,f413,f414,f415,f416,f417,f634,f647,f701]) ).
fof(f701,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f700]) ).
fof(f700,plain,
( $false
| spl9_1 ),
inference(subsumption_resolution,[],[f694,f90]) ).
fof(f90,plain,
relation(sK1),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ( ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)) )
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f49,f71]) ).
fof(f71,plain,
( ? [X0,X1] :
( ( ~ subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) )
& relation(X1) )
=> ( ( ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)) )
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0,X1] :
( ( ~ subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) )
& relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
inference(negated_conjecture,[],[f34]) ).
fof(f34,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f694,plain,
( ~ relation(sK1)
| spl9_1 ),
inference(resolution,[],[f679,f195]) ).
fof(f195,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1))
| spl9_1 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f193,plain,
( spl9_1
<=> subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f679,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(duplicate_literal_removal,[],[f669]) ).
fof(f669,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| subset(relation_field(relation_restriction(X0,X1)),relation_field(X0)) ),
inference(resolution,[],[f359,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f76,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f359,plain,
! [X2,X0,X1] :
( in(sK3(relation_field(relation_restriction(X0,X1)),X2),relation_field(X0))
| ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),X2) ),
inference(resolution,[],[f120,f114]) ).
fof(f114,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f647,plain,
( ~ spl9_15
| spl9_16
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f638,f197,f645,f641]) ).
fof(f641,plain,
( spl9_15
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f645,plain,
( spl9_16
<=> ! [X0] : ~ in(X0,relation_field(relation_restriction(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f197,plain,
( spl9_2
<=> subset(relation_field(relation_restriction(sK1,sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f638,plain,
( ! [X0] :
( ~ in(X0,relation_field(relation_restriction(sK1,sK0)))
| ~ empty(sK0) )
| ~ spl9_2 ),
inference(resolution,[],[f198,f190]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f123,f117]) ).
fof(f117,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f198,plain,
( subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f634,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f633,plain,
( $false
| spl9_2 ),
inference(subsumption_resolution,[],[f628,f90]) ).
fof(f628,plain,
( ~ relation(sK1)
| spl9_2 ),
inference(resolution,[],[f620,f199]) ).
fof(f199,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| spl9_2 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f620,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(duplicate_literal_removal,[],[f605]) ).
fof(f605,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),X1)
| subset(relation_field(relation_restriction(X0,X1)),X1) ),
inference(resolution,[],[f314,f115]) ).
fof(f314,plain,
! [X2,X0,X1] :
( in(sK3(relation_field(relation_restriction(X0,X1)),X2),X1)
| ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),X2) ),
inference(resolution,[],[f121,f114]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f417,plain,
( ~ spl9_12
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f405,plain,
( $false
| ~ spl9_12
| ~ spl9_13 ),
inference(resolution,[],[f400,f304]) ).
fof(f304,plain,
( empty(relation_field(empty_set))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f303,plain,
( spl9_12
<=> empty(relation_field(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f400,plain,
( ! [X1] : ~ empty(X1)
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f399,plain,
( spl9_13
<=> ! [X1] : ~ empty(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f416,plain,
( ~ spl9_11
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f406]) ).
fof(f406,plain,
( $false
| ~ spl9_11
| ~ spl9_13 ),
inference(resolution,[],[f400,f301]) ).
fof(f301,plain,
( empty(relation_dom(empty_set))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f299,plain,
( spl9_11
<=> empty(relation_dom(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f415,plain,
( ~ spl9_12
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f407,plain,
( $false
| ~ spl9_12
| ~ spl9_13 ),
inference(resolution,[],[f400,f349]) ).
fof(f349,plain,
( empty(relation_rng(empty_set))
| ~ spl9_12 ),
inference(subsumption_resolution,[],[f297,f304]) ).
fof(f297,plain,
( ~ empty(relation_field(empty_set))
| empty(relation_rng(empty_set)) ),
inference(superposition,[],[f107,f231]) ).
fof(f231,plain,
relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
inference(forward_demodulation,[],[f230,f135]) ).
fof(f135,plain,
empty_set = sK8,
inference(resolution,[],[f98,f131]) ).
fof(f131,plain,
empty(sK8),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( function(sK8)
& empty(sK8)
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f27,f88]) ).
fof(f88,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK8)
& empty(sK8)
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f98,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f230,plain,
relation_field(sK8) = set_union2(relation_dom(sK8),relation_rng(sK8)),
inference(resolution,[],[f95,f130]) ).
fof(f130,plain,
relation(sK8),
inference(cnf_transformation,[],[f89]) ).
fof(f95,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f107,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f414,plain,
~ spl9_13,
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f408,plain,
( $false
| ~ spl9_13 ),
inference(resolution,[],[f400,f92]) ).
fof(f92,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f413,plain,
~ spl9_13,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f410,plain,
( $false
| ~ spl9_13 ),
inference(resolution,[],[f400,f125]) ).
fof(f125,plain,
empty(sK5),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f26,f82]) ).
fof(f82,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f412,plain,
~ spl9_13,
inference(avatar_contradiction_clause,[],[f411]) ).
fof(f411,plain,
( $false
| ~ spl9_13 ),
inference(resolution,[],[f400,f131]) ).
fof(f404,plain,
( spl9_13
| spl9_14
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f391,f303,f402,f399]) ).
fof(f402,plain,
( spl9_14
<=> ! [X0] : ~ in(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f391,plain,
( ! [X0,X1] :
( ~ in(X0,empty_set)
| ~ empty(X1) )
| ~ spl9_12 ),
inference(resolution,[],[f384,f190]) ).
fof(f384,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl9_12 ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f370,plain,
( ! [X0] :
( subset(empty_set,X0)
| subset(empty_set,X0) )
| ~ spl9_12 ),
inference(resolution,[],[f366,f115]) ).
fof(f366,plain,
( ! [X0,X1] :
( in(sK3(empty_set,X0),X1)
| subset(empty_set,X0) )
| ~ spl9_12 ),
inference(resolution,[],[f348,f114]) ).
fof(f348,plain,
( ! [X0,X1] :
( ~ in(X0,empty_set)
| in(X0,X1) )
| ~ spl9_12 ),
inference(superposition,[],[f316,f344]) ).
fof(f344,plain,
( empty_set = relation_field(empty_set)
| ~ spl9_12 ),
inference(resolution,[],[f304,f98]) ).
fof(f316,plain,
! [X0,X1] :
( ~ in(X1,relation_field(empty_set))
| in(X1,X0) ),
inference(subsumption_resolution,[],[f315,f138]) ).
fof(f138,plain,
relation(empty_set),
inference(superposition,[],[f130,f135]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(X1,relation_field(empty_set))
| in(X1,X0)
| ~ relation(empty_set) ),
inference(superposition,[],[f121,f294]) ).
fof(f294,plain,
! [X0] : empty_set = relation_restriction(empty_set,X0),
inference(forward_demodulation,[],[f293,f143]) ).
fof(f143,plain,
! [X0] : empty_set = set_intersection2(empty_set,X0),
inference(superposition,[],[f105,f93]) ).
fof(f93,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f105,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/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f293,plain,
! [X0] : relation_restriction(empty_set,X0) = set_intersection2(empty_set,cartesian_product2(X0,X0)),
inference(forward_demodulation,[],[f291,f135]) ).
fof(f291,plain,
! [X0] : relation_restriction(sK8,X0) = set_intersection2(sK8,cartesian_product2(X0,X0)),
inference(resolution,[],[f96,f130]) ).
fof(f96,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f338,plain,
spl9_12,
inference(avatar_contradiction_clause,[],[f332]) ).
fof(f332,plain,
( $false
| spl9_12 ),
inference(resolution,[],[f321,f92]) ).
fof(f321,plain,
( ! [X0] : ~ empty(X0)
| spl9_12 ),
inference(resolution,[],[f319,f119]) ).
fof(f119,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f319,plain,
( ! [X0] : in(sK2(relation_field(empty_set)),X0)
| spl9_12 ),
inference(subsumption_resolution,[],[f317,f305]) ).
fof(f305,plain,
( ~ empty(relation_field(empty_set))
| spl9_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f317,plain,
! [X0] :
( in(sK2(relation_field(empty_set)),X0)
| empty(relation_field(empty_set)) ),
inference(resolution,[],[f316,f173]) ).
fof(f173,plain,
! [X0] :
( in(sK2(X0),X0)
| empty(X0) ),
inference(resolution,[],[f110,f101]) ).
fof(f101,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f73]) ).
fof(f73,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f110,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f337,plain,
spl9_12,
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f334,plain,
( $false
| spl9_12 ),
inference(resolution,[],[f321,f125]) ).
fof(f336,plain,
spl9_12,
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f335,plain,
( $false
| spl9_12 ),
inference(resolution,[],[f321,f131]) ).
fof(f306,plain,
( spl9_11
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f296,f303,f299]) ).
fof(f296,plain,
( ~ empty(relation_field(empty_set))
| empty(relation_dom(empty_set)) ),
inference(superposition,[],[f108,f231]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f285,plain,
( spl9_9
| ~ spl9_10 ),
inference(avatar_split_clause,[],[f275,f282,f278]) ).
fof(f278,plain,
( spl9_9
<=> empty(relation_dom(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f282,plain,
( spl9_10
<=> empty(relation_field(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f275,plain,
( ~ empty(relation_field(sK7))
| empty(relation_dom(sK7)) ),
inference(superposition,[],[f108,f229]) ).
fof(f229,plain,
relation_field(sK7) = set_union2(relation_dom(sK7),relation_rng(sK7)),
inference(resolution,[],[f95,f128]) ).
fof(f128,plain,
relation(sK7),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f48,f86]) ).
fof(f86,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK7)
& relation(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f274,plain,
( spl9_7
| ~ spl9_8 ),
inference(avatar_split_clause,[],[f264,f271,f267]) ).
fof(f267,plain,
( spl9_7
<=> empty(relation_dom(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f271,plain,
( spl9_8
<=> empty(relation_field(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f264,plain,
( ~ empty(relation_field(sK6))
| empty(relation_dom(sK6)) ),
inference(superposition,[],[f108,f228]) ).
fof(f228,plain,
relation_field(sK6) = set_union2(relation_dom(sK6),relation_rng(sK6)),
inference(resolution,[],[f95,f126]) ).
fof(f126,plain,
relation(sK6),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f25,f84]) ).
fof(f84,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK6)
& relation(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f251,plain,
( spl9_5
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f219,f248,f244]) ).
fof(f244,plain,
( spl9_5
<=> empty(powerset(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f248,plain,
( spl9_6
<=> in(powerset(empty_set),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f219,plain,
( ~ in(powerset(empty_set),empty_set)
| empty(powerset(empty_set)) ),
inference(superposition,[],[f176,f208]) ).
fof(f208,plain,
empty_set = sK2(powerset(empty_set)),
inference(resolution,[],[f206,f92]) ).
fof(f206,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK2(powerset(X0)) ),
inference(resolution,[],[f203,f98]) ).
fof(f203,plain,
! [X0] :
( empty(sK2(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f189,f173]) ).
fof(f189,plain,
! [X0,X1] :
( ~ in(X1,sK2(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f123,f101]) ).
fof(f176,plain,
! [X0] :
( ~ in(X0,sK2(X0))
| empty(X0) ),
inference(resolution,[],[f173,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f242,plain,
( spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f232,f239,f235]) ).
fof(f235,plain,
( spl9_3
<=> empty(relation_dom(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f239,plain,
( spl9_4
<=> empty(relation_field(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f232,plain,
( ~ empty(relation_field(sK1))
| empty(relation_dom(sK1)) ),
inference(superposition,[],[f108,f227]) ).
fof(f227,plain,
relation_field(sK1) = set_union2(relation_dom(sK1),relation_rng(sK1)),
inference(resolution,[],[f95,f90]) ).
fof(f200,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f91,f197,f193]) ).
fof(f91,plain,
( ~ subset(relation_field(relation_restriction(sK1,sK0)),sK0)
| ~ subset(relation_field(relation_restriction(sK1,sK0)),relation_field(sK1)) ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU250+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n004.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 : Fri May 3 11:40:33 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (1654)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (1660)WARNING: value z3 for option sas not known
% 0.15/0.38 % (1659)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (1661)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (1660)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (1658)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (1664)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (1665)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 % (1662)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 TRYING [2]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [4]
% 0.22/0.40 % (1660)First to succeed.
% 0.22/0.40 TRYING [5]
% 0.22/0.40 % (1660)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1654"
% 0.22/0.40 % (1660)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (1660)------------------------------
% 0.22/0.40 % (1660)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (1660)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (1660)Memory used [KB]: 1045
% 0.22/0.40 % (1660)Time elapsed: 0.025 s
% 0.22/0.40 % (1660)Instructions burned: 34 (million)
% 0.22/0.40 % (1654)Success in time 0.041 s
%------------------------------------------------------------------------------