TSTP Solution File: SEV421_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEV421_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:35:21 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 51 ( 3 unt; 15 typ; 0 def)
% Number of atoms : 110 ( 73 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 121 ( 47 ~; 36 |; 26 &)
% ( 6 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 41 ( 0 atm; 0 fun; 32 num; 9 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 13 !; 18 ?; 31 :)
% 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: $int ).
tff(func_def_13,type,
sK2: set ).
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(f120,plain,
$false,
inference(avatar_sat_refutation,[],[f105,f106,f114,f119]) ).
tff(f119,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f118]) ).
tff(f118,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f117,f103]) ).
tff(f103,plain,
( ( 0 != sK1 )
| spl4_2 ),
inference(avatar_component_clause,[],[f102]) ).
tff(f102,plain,
( spl4_2
<=> ( 0 = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f117,plain,
( ( 0 = sK1 )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f116,f94]) ).
tff(f94,plain,
0 = cardinality(empty_set),
inference(equality_resolution,[],[f70]) ).
tff(f70,plain,
! [X0: set] :
( ( cardinality(X0) = 0 )
| ( empty_set != X0 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,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(f116,plain,
( ( cardinality(empty_set) = sK1 )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f65,f100]) ).
tff(f100,plain,
( ( empty_set = sK2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f98]) ).
tff(f98,plain,
( spl4_1
<=> ( empty_set = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f65,plain,
cardinality(sK2) = sK1,
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
( ~ member(sK0,sK2)
& ( ( empty_set != sK2 )
| ( 0 != sK1 ) )
& ( ( empty_set = sK2 )
| ( 0 = sK1 ) )
& ( cardinality(sK2) = sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f40,f41]) ).
tff(f41,plain,
( ? [X0: element,X1: $int,X2: set] :
( ~ member(X0,X2)
& ( ( empty_set != X2 )
| ( 0 != X1 ) )
& ( ( empty_set = X2 )
| ( 0 = X1 ) )
& ( cardinality(X2) = X1 ) )
=> ( ~ member(sK0,sK2)
& ( ( empty_set != sK2 )
| ( 0 != sK1 ) )
& ( ( empty_set = sK2 )
| ( 0 = sK1 ) )
& ( cardinality(sK2) = sK1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
? [X0: element,X1: $int,X2: set] :
( ~ member(X0,X2)
& ( ( empty_set != X2 )
| ( 0 != X1 ) )
& ( ( empty_set = X2 )
| ( 0 = X1 ) )
& ( cardinality(X2) = X1 ) ),
inference(rectify,[],[f39]) ).
tff(f39,plain,
? [X0: element,X2: $int,X1: set] :
( ~ member(X0,X1)
& ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( empty_set = X1 )
| ( 0 = X2 ) )
& ( cardinality(X1) = X2 ) ),
inference(flattening,[],[f38]) ).
tff(f38,plain,
? [X0: element,X2: $int,X1: set] :
( ~ member(X0,X1)
& ( ( empty_set != X1 )
| ( 0 != X2 ) )
& ( ( empty_set = X1 )
| ( 0 = X2 ) )
& ( cardinality(X1) = X2 ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
? [X0: element,X2: $int,X1: set] :
( ~ member(X0,X1)
& ( ( 0 = X2 )
<~> ( empty_set = X1 ) )
& ( cardinality(X1) = X2 ) ),
inference(flattening,[],[f36]) ).
tff(f36,plain,
? [X0: element,X2: $int,X1: set] :
( ( ( 0 = X2 )
<~> ( empty_set = X1 ) )
& ~ member(X0,X1)
& ( cardinality(X1) = X2 ) ),
inference(ennf_transformation,[],[f30]) ).
tff(f30,plain,
~ ! [X0: element,X2: $int,X1: set] :
( ( ~ member(X0,X1)
& ( cardinality(X1) = X2 ) )
=> ( ( 0 = X2 )
<=> ( empty_set = X1 ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X1: element,X6: set,X7: $int] :
( ( ~ member(X1,X6)
& ( cardinality(X6) = X7 ) )
=> ( ( 0 = X7 )
<=> ( empty_set = X6 ) ) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X1: element,X6: set,X7: $int] :
( ( ~ member(X1,X6)
& ( cardinality(X6) = X7 ) )
=> ( ( 0 = X7 )
<=> ( empty_set = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vc1) ).
tff(f114,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f113]) ).
tff(f113,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f111,f99]) ).
tff(f99,plain,
( ( empty_set != sK2 )
| spl4_1 ),
inference(avatar_component_clause,[],[f98]) ).
tff(f111,plain,
( ( empty_set = sK2 )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f110]) ).
tff(f110,plain,
( ( 0 != 0 )
| ( empty_set = sK2 )
| ~ spl4_2 ),
inference(superposition,[],[f69,f107]) ).
tff(f107,plain,
( ( 0 = cardinality(sK2) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f65,f104]) ).
tff(f104,plain,
( ( 0 = sK1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f102]) ).
tff(f69,plain,
! [X0: set] :
( ( cardinality(X0) != 0 )
| ( empty_set = X0 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f106,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f67,f102,f98]) ).
tff(f67,plain,
( ( 0 != sK1 )
| ( empty_set != sK2 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f105,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f66,f102,f98]) ).
tff(f66,plain,
( ( 0 = sK1 )
| ( empty_set = sK2 ) ),
inference(cnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV421=1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 17:13:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47 % (3120)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.47 % (3111)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.19/0.48 % (3120)First to succeed.
% 0.19/0.48 % (3111)Instruction limit reached!
% 0.19/0.48 % (3111)------------------------------
% 0.19/0.48 % (3111)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (3111)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (3111)Termination reason: Unknown
% 0.19/0.48 % (3111)Termination phase: Preprocessing 3
% 0.19/0.48
% 0.19/0.48 % (3111)Memory used [KB]: 1023
% 0.19/0.48 % (3111)Time elapsed: 0.007 s
% 0.19/0.48 % (3111)Instructions burned: 2 (million)
% 0.19/0.48 % (3111)------------------------------
% 0.19/0.48 % (3111)------------------------------
% 0.19/0.49 % (3120)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (3120)------------------------------
% 0.19/0.49 % (3120)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (3120)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (3120)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (3120)Memory used [KB]: 5500
% 0.19/0.49 % (3120)Time elapsed: 0.076 s
% 0.19/0.49 % (3120)Instructions burned: 4 (million)
% 0.19/0.49 % (3120)------------------------------
% 0.19/0.49 % (3120)------------------------------
% 0.19/0.49 % (3093)Success in time 0.143 s
%------------------------------------------------------------------------------