TSTP Solution File: SEV421_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV421_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 : Tue May 21 04:15:45 EDT 2024
% Result : Theorem 0.13s 0.35s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 43
% Syntax : Number of formulae : 127 ( 15 unt; 15 typ; 0 def)
% Number of atoms : 299 ( 140 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 308 ( 121 ~; 107 |; 48 &)
% ( 25 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 121 ( 12 atm; 32 fun; 46 num; 31 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 193 ( 175 !; 18 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
set: $tType ).
tff(type_def_6,type,
element: $tType ).
tff(func_def_0,type,
empty_set: set ).
tff(func_def_1,type,
singleton: element > set ).
tff(func_def_2,type,
intersection: ( set * set ) > set ).
tff(func_def_3,type,
union: ( set * set ) > set ).
tff(func_def_4,type,
difference: ( set * set ) > set ).
tff(func_def_5,type,
complement: set > set ).
tff(func_def_6,type,
cardinality: set > $int ).
tff(func_def_11,type,
sK0: element ).
tff(func_def_12,type,
sK1: set ).
tff(func_def_13,type,
sK2: $int ).
tff(func_def_14,type,
sK3: set > element ).
tff(pred_def_1,type,
member: ( element * set ) > $o ).
tff(pred_def_2,type,
subset: ( set * set ) > $o ).
tff(f130,plain,
$false,
inference(avatar_sat_refutation,[],[f103,f108,f110,f112,f129]) ).
tff(f129,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f128]) ).
tff(f128,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f127,f101]) ).
tff(f101,plain,
( ( empty_set != sK1 )
| spl4_2 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f100,plain,
( spl4_2
<=> ( empty_set = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f127,plain,
( ( empty_set = sK1 )
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f125,f98]) ).
tff(f98,plain,
( ( 0 = sK2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f96,plain,
( spl4_1
<=> ( 0 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f125,plain,
( ( 0 != sK2 )
| ( empty_set = sK1 ) ),
inference(superposition,[],[f65,f62]) ).
tff(f62,plain,
sK2 = cardinality(sK1),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
( ( ( empty_set != sK1 )
| ( 0 != sK2 ) )
& ( ( empty_set = sK1 )
| ( 0 = sK2 ) )
& ( sK2 = cardinality(sK1) )
& ~ member(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f42]) ).
tff(f42,plain,
( ? [X0: element,X1: set,X2: $int] :
( ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( empty_set = X1 )
| ( 0 = X2 ) )
& ( cardinality(X1) = X2 )
& ~ member(X0,X1) )
=> ( ( ( empty_set != sK1 )
| ( 0 != sK2 ) )
& ( ( empty_set = sK1 )
| ( 0 = sK2 ) )
& ( sK2 = cardinality(sK1) )
& ~ member(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( empty_set = X1 )
| ( 0 = X2 ) )
& ( cardinality(X1) = X2 )
& ~ member(X0,X1) ),
inference(flattening,[],[f40]) ).
tff(f40,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( empty_set = X1 )
| ( 0 = X2 ) )
& ( cardinality(X1) = X2 )
& ~ member(X0,X1) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( 0 = X2 )
<~> ( empty_set = X1 ) )
& ( cardinality(X1) = X2 )
& ~ member(X0,X1) ),
inference(flattening,[],[f38]) ).
tff(f38,plain,
? [X0: element,X1: set,X2: $int] :
( ( ( 0 = X2 )
<~> ( empty_set = X1 ) )
& ( cardinality(X1) = X2 )
& ~ member(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
tff(f27,plain,
~ ! [X0: element,X1: set,X2: $int] :
( ( ( cardinality(X1) = X2 )
& ~ member(X0,X1) )
=> ( ( 0 = X2 )
<=> ( empty_set = X1 ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X1: element,X6: set,X7: $int] :
( ( ( cardinality(X6) = X7 )
& ~ member(X1,X6) )
=> ( ( 0 = X7 )
<=> ( empty_set = X6 ) ) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X1: element,X6: set,X7: $int] :
( ( ( cardinality(X6) = X7 )
& ~ member(X1,X6) )
=> ( ( 0 = X7 )
<=> ( empty_set = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vc1) ).
tff(f65,plain,
! [X0: set] :
( ( cardinality(X0) != 0 )
| ( empty_set = X0 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: set] :
( ( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) )
& ( ( empty_set = X0 )
| ( cardinality(X0) != 0 ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: set] :
( ( cardinality(X0) = 0 )
<=> ( empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_empty_set) ).
tff(f112,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f111]) ).
tff(f111,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(global_subsumption,[],[f98,f26,f25,f24,f23,f22,f21,f19,f18,f17,f16,f15,f64,f65,f67,f70,f69,f71,f74,f73,f76,f93,f94,f75,f78,f77,f80,f79,f83,f82,f81,f86,f85,f84,f89,f88,f87,f61,f20,f91,f62,f90,f92,f63,f102,f106]) ).
tff(f106,plain,
( ( 0 = sK2 )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f104,f90]) ).
tff(f104,plain,
( ( sK2 = cardinality(empty_set) )
| ~ spl4_2 ),
inference(superposition,[],[f62,f102]) ).
tff(f102,plain,
( ( empty_set = sK1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f63,plain,
( ( empty_set = sK1 )
| ( 0 = sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f92,plain,
! [X1: element] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f72]) ).
tff(f72,plain,
! [X0: element,X1: element] :
( member(X0,singleton(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: element,X1: element] :
( ( member(X0,singleton(X1))
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: element,X1: element] :
( member(X0,singleton(X1))
<=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: element,X2: element] :
( member(X1,singleton(X2))
<=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
tff(f90,plain,
0 = cardinality(empty_set),
inference(equality_resolution,[],[f66]) ).
tff(f66,plain,
! [X0: set] :
( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f91,plain,
! [X1: element] : ~ member(X1,empty_set),
inference(equality_resolution,[],[f68]) ).
tff(f68,plain,
! [X0: set,X1: element] :
( ~ member(X1,X0)
| ( empty_set != X0 ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: set] :
( ( ! [X1: element] : ~ member(X1,X0)
| ( empty_set != X0 ) )
& ( ( empty_set = X0 )
| member(sK3(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f46,f47]) ).
tff(f47,plain,
! [X0: set] :
( ? [X2: element] : member(X2,X0)
=> member(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f46,plain,
! [X0: set] :
( ( ! [X1: element] : ~ member(X1,X0)
| ( empty_set != X0 ) )
& ( ( empty_set = X0 )
| ? [X2: element] : member(X2,X0) ) ),
inference(rectify,[],[f45]) ).
tff(f45,plain,
! [X0: set] :
( ( ! [X1: element] : ~ member(X1,X0)
| ( empty_set != X0 ) )
& ( ( empty_set = X0 )
| ? [X1: element] : member(X1,X0) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: set] :
( ! [X1: element] : ~ member(X1,X0)
<=> ( empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
tff(f20,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f61,plain,
~ member(sK0,sK1),
inference(cnf_transformation,[],[f43]) ).
tff(f87,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tff(f60,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f59]) ).
tff(f59,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: element,X1: set,X2: set] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X1: element,X2: set,X3: set] :
( member(X1,intersection(X2,X3))
<=> ( member(X1,X3)
& member(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
tff(f88,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tff(f89,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tff(f84,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f57]) ).
tff(f57,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: element,X1: set,X2: set] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X1: element,X2: set,X3: set] :
( member(X1,union(X2,X3))
<=> ( member(X1,X3)
| member(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
tff(f85,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f86,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
tff(f81,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f55]) ).
tff(f55,plain,
! [X0: element,X1: set,X2: set] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: element,X1: set,X2: set] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X3: element,X2: set,X4: set] :
( member(X3,difference(X4,X2))
<=> ( ~ member(X3,X2)
& member(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
tff(f82,plain,
! [X2: set,X0: element,X1: set] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f56]) ).
tff(f83,plain,
! [X2: set,X0: element,X1: set] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f56]) ).
tff(f79,plain,
! [X0: element,X1: set] :
( ( cardinality(X1) = cardinality(union(singleton(X0),X1)) )
| ( singleton(X0) != intersection(singleton(X0),X1) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: element,X1: set] :
( ( ( singleton(X0) = intersection(singleton(X0),X1) )
| ( cardinality(X1) != cardinality(union(singleton(X0),X1)) ) )
& ( ( cardinality(X1) = cardinality(union(singleton(X0),X1)) )
| ( singleton(X0) != intersection(singleton(X0),X1) ) ) ),
inference(nnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: element,X1: set] :
( ( singleton(X0) = intersection(singleton(X0),X1) )
<=> ( cardinality(X1) = cardinality(union(singleton(X0),X1)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X1: element,X0: set] :
( ( singleton(X1) = intersection(singleton(X1),X0) )
<=> ( cardinality(X0) = cardinality(union(singleton(X1),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_1) ).
tff(f80,plain,
! [X0: element,X1: set] :
( ( singleton(X0) = intersection(singleton(X0),X1) )
| ( cardinality(X1) != cardinality(union(singleton(X0),X1)) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f77,plain,
! [X0: element,X1: set] :
( ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) )
| ( empty_set != intersection(singleton(X0),X1) ) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: element,X1: set] :
( ( ( empty_set = intersection(singleton(X0),X1) )
| ( cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1) ) )
& ( ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) )
| ( empty_set != intersection(singleton(X0),X1) ) ) ),
inference(nnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: element,X1: set] :
( ( empty_set = intersection(singleton(X0),X1) )
<=> ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X1: element,X0: set] :
( ( empty_set = intersection(singleton(X1),X0) )
<=> ( cardinality(union(singleton(X1),X0)) = $sum(cardinality(X0),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_2) ).
tff(f78,plain,
! [X0: element,X1: set] :
( ( empty_set = intersection(singleton(X0),X1) )
| ( cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1) ) ),
inference(cnf_transformation,[],[f53]) ).
tff(f75,plain,
! [X0: set,X1: set] :
( ( empty_set = intersection(X0,X1) )
| ( 0 != cardinality(intersection(X0,X1)) ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: set,X1: set] :
( ( ( 0 = cardinality(intersection(X0,X1)) )
| ( empty_set != intersection(X0,X1) ) )
& ( ( empty_set = intersection(X0,X1) )
| ( 0 != cardinality(intersection(X0,X1)) ) ) ),
inference(nnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: set,X1: set] :
( ( 0 = cardinality(intersection(X0,X1)) )
<=> ( empty_set = intersection(X0,X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: set,X5: set] :
( ( 0 = cardinality(intersection(X0,X5)) )
<=> ( empty_set = intersection(X0,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_3) ).
tff(f94,plain,
0 = cardinality(empty_set),
inference(global_subsumption,[],[f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f64,f63,f62,f61,f90,f65,f91,f67,f70,f69,f92,f71,f74,f73,f76,f93]) ).
tff(f93,plain,
! [X0: set,X1: set] :
( ( 0 = cardinality(empty_set) )
| ( empty_set != intersection(X0,X1) ) ),
inference(inner_rewriting,[],[f76]) ).
tff(f76,plain,
! [X0: set,X1: set] :
( ( 0 = cardinality(intersection(X0,X1)) )
| ( empty_set != intersection(X0,X1) ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f73,plain,
! [X0: set,X1: set] :
( ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) )
| ( empty_set != intersection(X0,X1) ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: set,X1: set] :
( ( ( empty_set = intersection(X0,X1) )
| ( cardinality(union(X0,X1)) != $sum(cardinality(X0),cardinality(X1)) ) )
& ( ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) )
| ( empty_set != intersection(X0,X1) ) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: set,X1: set] :
( ( empty_set = intersection(X0,X1) )
<=> ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X2: set,X3: set] :
( ( empty_set = intersection(X2,X3) )
<=> ( cardinality(union(X2,X3)) = $sum(cardinality(X2),cardinality(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_union) ).
tff(f74,plain,
! [X0: set,X1: set] :
( ( empty_set = intersection(X0,X1) )
| ( cardinality(union(X0,X1)) != $sum(cardinality(X0),cardinality(X1)) ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f71,plain,
! [X0: element,X1: element] :
( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f50]) ).
tff(f69,plain,
! [X0: element,X1: set] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: element,X1: set] :
( ( member(X0,X1)
| member(X0,complement(X1)) )
& ( ~ member(X0,complement(X1))
| ~ member(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: element,X1: set] :
( member(X0,X1)
<=> ~ member(X0,complement(X1)) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X1: element,X0: set] :
( member(X1,X0)
<=> ~ member(X1,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
tff(f70,plain,
! [X0: element,X1: set] :
( member(X0,X1)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f67,plain,
! [X0: set] :
( ( empty_set = X0 )
| member(sK3(X0),X0) ),
inference(cnf_transformation,[],[f48]) ).
tff(f64,plain,
( ( empty_set != sK1 )
| ( 0 != sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f15,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f16,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f17,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f19,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f21,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f22,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f25,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f110,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f109]) ).
tff(f109,plain,
( $false
| ~ spl4_2 ),
inference(global_subsumption,[],[f26,f25,f24,f23,f22,f21,f19,f18,f17,f16,f15,f64,f65,f67,f70,f69,f71,f74,f73,f76,f93,f94,f75,f78,f77,f80,f79,f83,f82,f81,f86,f85,f84,f89,f88,f87,f61,f20,f91,f62,f90,f92,f63,f102,f106]) ).
tff(f108,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f107]) ).
tff(f107,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f106,f97]) ).
tff(f97,plain,
( ( 0 != sK2 )
| spl4_1 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f103,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f63,f100,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV421_1 : TPTP v8.2.0. Released v5.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n032.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sun May 19 19:08:22 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % (31025)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.34 % (31029)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.34 % (31029)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.34 % (31029)Terminated due to inappropriate strategy.
% 0.13/0.34 % (31029)------------------------------
% 0.13/0.34 % (31029)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34 % (31029)Termination reason: Inappropriate
% 0.13/0.34
% 0.13/0.34 % (31029)Memory used [KB]: 801
% 0.13/0.34 % (31029)Time elapsed: 0.002 s
% 0.13/0.34 % (31029)Instructions burned: 3 (million)
% 0.13/0.34 % (31029)------------------------------
% 0.13/0.34 % (31029)------------------------------
% 0.13/0.34 % (31027)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.34 % (31028)WARNING: value z3 for option sas not known
% 0.13/0.34 % (31030)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)
% 0.13/0.34 % (31027)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.34 % (31027)Terminated due to inappropriate strategy.
% 0.13/0.34 % (31027)------------------------------
% 0.13/0.34 % (31027)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34 % (31027)Termination reason: Inappropriate
% 0.13/0.34
% 0.13/0.34 % (31027)Memory used [KB]: 802
% 0.13/0.34 % (31027)Time elapsed: 0.002 s
% 0.13/0.34 % (31027)Instructions burned: 3 (million)
% 0.13/0.34 % (31027)------------------------------
% 0.13/0.34 % (31027)------------------------------
% 0.13/0.34 % (31028)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)
% 0.13/0.34 % (31026)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35 % (31032)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)
% 0.13/0.35 % (31031)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)
% 0.13/0.35 % (31026)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.35 % (31026)Terminated due to inappropriate strategy.
% 0.13/0.35 % (31026)------------------------------
% 0.13/0.35 % (31026)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35 % (31026)Termination reason: Inappropriate
% 0.13/0.35
% 0.13/0.35 % (31026)Memory used [KB]: 801
% 0.13/0.35 % (31026)Time elapsed: 0.002 s
% 0.13/0.35 % (31026)Instructions burned: 3 (million)
% 0.13/0.35 % (31026)------------------------------
% 0.13/0.35 % (31026)------------------------------
% 0.13/0.35 % (31028)First to succeed.
% 0.13/0.35 % (31030)Also succeeded, but the first one will report.
% 0.13/0.35 % (31032)Also succeeded, but the first one will report.
% 0.13/0.35 % (31031)Also succeeded, but the first one will report.
% 0.13/0.35 % (31028)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31025"
% 0.13/0.35 % (31028)Refutation found. Thanks to Tanya!
% 0.13/0.35 % SZS status Theorem for theBenchmark
% 0.13/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35 % (31028)------------------------------
% 0.13/0.35 % (31028)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35 % (31028)Termination reason: Refutation
% 0.13/0.35
% 0.13/0.35 % (31028)Memory used [KB]: 859
% 0.13/0.35 % (31028)Time elapsed: 0.007 s
% 0.13/0.35 % (31028)Instructions burned: 9 (million)
% 0.13/0.35 % (31025)Success in time 0.007 s
%------------------------------------------------------------------------------