TSTP Solution File: SEU180+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU180+2 : 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 : n006.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 09:28:03 EDT 2024
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 44
% Syntax : Number of formulae : 166 ( 24 unt; 0 def)
% Number of atoms : 463 ( 67 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 482 ( 185 ~; 171 |; 71 &)
% ( 31 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 13 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-2 aty)
% Number of variables : 256 ( 224 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7295,plain,
$false,
inference(avatar_sat_refutation,[],[f790,f2761,f4843,f5032,f5653,f6201,f7221,f7294]) ).
fof(f7294,plain,
spl55_2,
inference(avatar_contradiction_clause,[],[f7293]) ).
fof(f7293,plain,
( $false
| spl55_2 ),
inference(subsumption_resolution,[],[f7292,f420]) ).
fof(f420,plain,
relation(sK12),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
( ( ~ in(sK11,relation_field(sK12))
| ~ in(sK10,relation_field(sK12)) )
& in(ordered_pair(sK10,sK11),sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f164,f281]) ).
fof(f281,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) )
=> ( ( ~ in(sK11,relation_field(sK12))
| ~ in(sK10,relation_field(sK12)) )
& in(ordered_pair(sK10,sK11),sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
inference(negated_conjecture,[],[f108]) ).
fof(f108,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f7292,plain,
( ~ relation(sK12)
| spl55_2 ),
inference(subsumption_resolution,[],[f7265,f6175]) ).
fof(f6175,plain,
( ~ in(sK11,relation_rng(sK12))
| spl55_2 ),
inference(resolution,[],[f6126,f4784]) ).
fof(f4784,plain,
( ! [X0] :
( ~ subset(X0,relation_field(sK12))
| ~ in(sK11,X0) )
| spl55_2 ),
inference(resolution,[],[f4599,f483]) ).
fof(f483,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f4599,plain,
( ! [X0] :
( disjoint(singleton(sK11),X0)
| ~ subset(X0,relation_field(sK12)) )
| spl55_2 ),
inference(resolution,[],[f4306,f572]) ).
fof(f572,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f4306,plain,
( ! [X0] :
( disjoint(X0,singleton(sK11))
| ~ subset(X0,relation_field(sK12)) )
| spl55_2 ),
inference(resolution,[],[f494,f4150]) ).
fof(f4150,plain,
( disjoint(relation_field(sK12),singleton(sK11))
| spl55_2 ),
inference(trivial_inequality_removal,[],[f4128]) ).
fof(f4128,plain,
( relation_field(sK12) != relation_field(sK12)
| disjoint(relation_field(sK12),singleton(sK11))
| spl55_2 ),
inference(superposition,[],[f465,f3978]) ).
fof(f3978,plain,
( relation_field(sK12) = set_difference(relation_field(sK12),singleton(sK11))
| spl55_2 ),
inference(resolution,[],[f481,f789]) ).
fof(f789,plain,
( ~ in(sK11,relation_field(sK12))
| spl55_2 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f787,plain,
( spl55_2
<=> in(sK11,relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_2])]) ).
fof(f481,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f138]) ).
fof(f138,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f465,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f144]) ).
fof(f144,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f494,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| disjoint(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f206]) ).
fof(f206,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f6126,plain,
subset(relation_rng(sK12),relation_field(sK12)),
inference(superposition,[],[f849,f6113]) ).
fof(f6113,plain,
relation_field(sK12) = set_union2(relation_dom(sK12),relation_rng(sK12)),
inference(resolution,[],[f522,f420]) ).
fof(f522,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f849,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(superposition,[],[f436,f552]) ).
fof(f552,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f436,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f143]) ).
fof(f143,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f7265,plain,
( in(sK11,relation_rng(sK12))
| ~ relation(sK12) ),
inference(resolution,[],[f485,f421]) ).
fof(f421,plain,
in(ordered_pair(sK10,sK11),sK12),
inference(cnf_transformation,[],[f282]) ).
fof(f485,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f7221,plain,
spl55_1,
inference(avatar_contradiction_clause,[],[f7220]) ).
fof(f7220,plain,
( $false
| spl55_1 ),
inference(subsumption_resolution,[],[f7219,f420]) ).
fof(f7219,plain,
( ~ relation(sK12)
| spl55_1 ),
inference(subsumption_resolution,[],[f7192,f6162]) ).
fof(f6162,plain,
( ~ in(sK10,relation_dom(sK12))
| spl55_1 ),
inference(resolution,[],[f6119,f4729]) ).
fof(f4729,plain,
( ! [X0] :
( ~ subset(X0,relation_field(sK12))
| ~ in(sK10,X0) )
| spl55_1 ),
inference(resolution,[],[f4509,f483]) ).
fof(f4509,plain,
( ! [X0] :
( disjoint(singleton(sK10),X0)
| ~ subset(X0,relation_field(sK12)) )
| spl55_1 ),
inference(resolution,[],[f4305,f572]) ).
fof(f4305,plain,
( ! [X0] :
( disjoint(X0,singleton(sK10))
| ~ subset(X0,relation_field(sK12)) )
| spl55_1 ),
inference(resolution,[],[f494,f4027]) ).
fof(f4027,plain,
( disjoint(relation_field(sK12),singleton(sK10))
| spl55_1 ),
inference(trivial_inequality_removal,[],[f4005]) ).
fof(f4005,plain,
( relation_field(sK12) != relation_field(sK12)
| disjoint(relation_field(sK12),singleton(sK10))
| spl55_1 ),
inference(superposition,[],[f465,f3977]) ).
fof(f3977,plain,
( relation_field(sK12) = set_difference(relation_field(sK12),singleton(sK10))
| spl55_1 ),
inference(resolution,[],[f481,f785]) ).
fof(f785,plain,
( ~ in(sK10,relation_field(sK12))
| spl55_1 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f783,plain,
( spl55_1
<=> in(sK10,relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_1])]) ).
fof(f6119,plain,
subset(relation_dom(sK12),relation_field(sK12)),
inference(superposition,[],[f436,f6113]) ).
fof(f7192,plain,
( in(sK10,relation_dom(sK12))
| ~ relation(sK12) ),
inference(resolution,[],[f484,f421]) ).
fof(f484,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f196]) ).
fof(f6201,plain,
( ~ spl55_11
| ~ spl55_12
| spl55_9 ),
inference(avatar_split_clause,[],[f6159,f5646,f6198,f6194]) ).
fof(f6194,plain,
( spl55_11
<=> relation(relation_dom(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_11])]) ).
fof(f6198,plain,
( spl55_12
<=> relation(relation_rng(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_12])]) ).
fof(f5646,plain,
( spl55_9
<=> relation(relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_9])]) ).
fof(f6159,plain,
( ~ relation(relation_rng(sK12))
| ~ relation(relation_dom(sK12))
| spl55_9 ),
inference(subsumption_resolution,[],[f6123,f5647]) ).
fof(f5647,plain,
( ~ relation(relation_field(sK12))
| spl55_9 ),
inference(avatar_component_clause,[],[f5646]) ).
fof(f6123,plain,
( relation(relation_field(sK12))
| ~ relation(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[],[f594,f6113]) ).
fof(f594,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f248]) ).
fof(f248,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f5653,plain,
( spl55_9
| ~ spl55_10
| spl55_1 ),
inference(avatar_split_clause,[],[f4253,f783,f5650,f5646]) ).
fof(f5650,plain,
( spl55_10
<=> in(sK24(relation_field(sK12)),singleton(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_10])]) ).
fof(f4253,plain,
( ~ in(sK24(relation_field(sK12)),singleton(sK10))
| relation(relation_field(sK12))
| spl55_1 ),
inference(resolution,[],[f4032,f533]) ).
fof(f533,plain,
! [X0] :
( in(sK24(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK24(X0)
& in(sK24(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK25(X4),sK26(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f324,f326,f325]) ).
fof(f325,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK24(X0)
& in(sK24(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK25(X4),sK26(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f323]) ).
fof(f323,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f4032,plain,
( ! [X0] :
( ~ in(X0,relation_field(sK12))
| ~ in(X0,singleton(sK10)) )
| spl55_1 ),
inference(resolution,[],[f4027,f446]) ).
fof(f446,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK15(X0,X1),X1)
& in(sK15(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f174,f288]) ).
fof(f288,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK15(X0,X1),X1)
& in(sK15(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f174,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f5032,plain,
( ~ spl55_7
| ~ spl55_8
| spl55_1 ),
inference(avatar_split_clause,[],[f5002,f783,f5029,f5025]) ).
fof(f5025,plain,
( spl55_7
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_7])]) ).
fof(f5029,plain,
( spl55_8
<=> in(empty_set,relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_8])]) ).
fof(f5002,plain,
( ~ in(empty_set,relation_field(sK12))
| ~ empty(sK10)
| spl55_1 ),
inference(resolution,[],[f4747,f3471]) ).
fof(f3471,plain,
! [X0] :
( in(X0,singleton(empty_set))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f3469,f512]) ).
fof(f512,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f3469,plain,
! [X0] :
( ~ empty(X0)
| in(X0,singleton(empty_set))
| empty(singleton(empty_set)) ),
inference(resolution,[],[f3466,f554]) ).
fof(f554,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f3466,plain,
! [X0] :
( element(X0,singleton(empty_set))
| ~ empty(X0) ),
inference(superposition,[],[f3453,f423]) ).
fof(f423,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f98]) ).
fof(f98,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f3453,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ empty(X0) ),
inference(resolution,[],[f462,f625]) ).
fof(f625,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f462,plain,
! [X0,X1] :
( in(sK16(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f192,f291]) ).
fof(f291,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f4747,plain,
( ! [X0] :
( ~ in(sK10,singleton(X0))
| ~ in(X0,relation_field(sK12)) )
| spl55_1 ),
inference(resolution,[],[f4729,f473]) ).
fof(f473,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f298,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f4843,plain,
( spl55_5
| ~ spl55_6
| spl55_1 ),
inference(avatar_split_clause,[],[f4694,f783,f4840,f4836]) ).
fof(f4836,plain,
( spl55_5
<=> empty(relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_5])]) ).
fof(f4840,plain,
( spl55_6
<=> subset(relation_field(sK12),singleton(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_6])]) ).
fof(f4694,plain,
( ~ subset(relation_field(sK12),singleton(sK10))
| empty(relation_field(sK12))
| spl55_1 ),
inference(resolution,[],[f4303,f2208]) ).
fof(f2208,plain,
! [X0] :
( ~ disjoint(X0,X0)
| empty(X0) ),
inference(superposition,[],[f2170,f548]) ).
fof(f548,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f2170,plain,
! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(resolution,[],[f2145,f443]) ).
fof(f443,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK14(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f173,f286]) ).
fof(f286,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK14(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f173,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f2145,plain,
! [X0] :
( in(sK28(X0),X0)
| empty(X0) ),
inference(resolution,[],[f554,f537]) ).
fof(f537,plain,
! [X0] : element(sK28(X0),X0),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] : element(sK28(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f50,f332]) ).
fof(f332,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK28(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f4303,plain,
( ! [X0] :
( disjoint(X0,relation_field(sK12))
| ~ subset(X0,singleton(sK10)) )
| spl55_1 ),
inference(resolution,[],[f494,f4035]) ).
fof(f4035,plain,
( disjoint(singleton(sK10),relation_field(sK12))
| spl55_1 ),
inference(resolution,[],[f4027,f572]) ).
fof(f2761,plain,
( ~ spl55_3
| spl55_4 ),
inference(avatar_split_clause,[],[f2752,f2758,f2754]) ).
fof(f2754,plain,
( spl55_3
<=> sP1(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_3])]) ).
fof(f2758,plain,
( spl55_4
<=> sP0(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_4])]) ).
fof(f2752,plain,
( sP0(empty_set,empty_set)
| ~ sP1(empty_set,empty_set) ),
inference(forward_demodulation,[],[f2751,f687]) ).
fof(f687,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f686]) ).
fof(f686,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f568]) ).
fof(f568,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP1(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP1(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f227,f264,f263]) ).
fof(f263,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f264,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f227,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f2751,plain,
( ~ sP1(empty_set,empty_set)
| sP0(empty_set,set_meet(empty_set)) ),
inference(superposition,[],[f685,f687]) ).
fof(f685,plain,
! [X1] :
( ~ sP1(set_meet(X1),X1)
| sP0(X1,set_meet(X1)) ),
inference(equality_resolution,[],[f558]) ).
fof(f558,plain,
! [X0,X1] :
( sP0(X1,X0)
| set_meet(X1) != X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f341]) ).
fof(f341,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f264]) ).
fof(f790,plain,
( ~ spl55_1
| ~ spl55_2 ),
inference(avatar_split_clause,[],[f422,f787,f783]) ).
fof(f422,plain,
( ~ in(sK11,relation_field(sK12))
| ~ in(sK10,relation_field(sK12)) ),
inference(cnf_transformation,[],[f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:13:34 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.35 % (27190)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (27198)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (27197)WARNING: value z3 for option sas not known
% 0.21/0.37 % (27195)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (27196)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (27197)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)
% 0.21/0.37 % (27199)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)
% 0.21/0.37 % (27200)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)
% 0.21/0.37 % (27201)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.45 TRYING [1]
% 0.21/0.46 TRYING [4]
% 0.21/0.47 TRYING [2]
% 0.21/0.54 % (27197)First to succeed.
% 0.21/0.54 % (27197)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27190"
% 0.21/0.54 % (27197)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Theorem for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (27197)------------------------------
% 0.21/0.54 % (27197)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.54 % (27197)Termination reason: Refutation
% 0.21/0.54
% 0.21/0.54 % (27197)Memory used [KB]: 4086
% 0.21/0.54 % (27197)Time elapsed: 0.167 s
% 0.21/0.54 % (27197)Instructions burned: 350 (million)
% 0.21/0.54 % (27190)Success in time 0.187 s
%------------------------------------------------------------------------------