TSTP Solution File: SEU210+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n008.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 18:32:31 EDT 2022
% Result : Theorem 2.47s 0.66s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 110 ( 27 unt; 0 def)
% Number of atoms : 355 ( 55 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 412 ( 167 ~; 150 |; 68 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 226 ( 197 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1644,plain,
$false,
inference(avatar_sat_refutation,[],[f264,f267,f1637]) ).
fof(f1637,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[],[f1636]) ).
fof(f1636,plain,
( $false
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f1635,f139]) ).
fof(f139,plain,
empty_set != sK5,
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( relation(sK4)
& empty_set = relation_inverse_image(sK4,sK5)
& empty_set != sK5
& subset(sK5,relation_rng(sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f56,f87]) ).
fof(f87,plain,
( ? [X0,X1] :
( relation(X0)
& empty_set = relation_inverse_image(X0,X1)
& empty_set != X1
& subset(X1,relation_rng(X0)) )
=> ( relation(sK4)
& empty_set = relation_inverse_image(sK4,sK5)
& empty_set != sK5
& subset(sK5,relation_rng(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
? [X0,X1] :
( relation(X0)
& empty_set = relation_inverse_image(X0,X1)
& empty_set != X1
& subset(X1,relation_rng(X0)) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
? [X0,X1] :
( empty_set = relation_inverse_image(X0,X1)
& subset(X1,relation_rng(X0))
& empty_set != X1
& relation(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
~ ! [X0,X1] :
( relation(X0)
=> ~ ( empty_set = relation_inverse_image(X0,X1)
& subset(X1,relation_rng(X0))
& empty_set != X1 ) ),
inference(rectify,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X1,X0] :
( relation(X1)
=> ~ ( empty_set != X0
& subset(X0,relation_rng(X1))
& empty_set = relation_inverse_image(X1,X0) ) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X1,X0] :
( relation(X1)
=> ~ ( empty_set != X0
& subset(X0,relation_rng(X1))
& empty_set = relation_inverse_image(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f1635,plain,
( empty_set = sK5
| ~ spl16_4 ),
inference(resolution,[],[f1621,f357]) ).
fof(f357,plain,
( ! [X6] :
( in(sK12(empty_set,X6),X6)
| empty_set = X6 )
| ~ spl16_4 ),
inference(forward_demodulation,[],[f356,f213]) ).
fof(f213,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[],[f199,f137]) ).
fof(f137,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f199,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(resolution,[],[f126,f114]) ).
fof(f114,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f126,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f356,plain,
( ! [X6] :
( in(sK12(empty_set,X6),X6)
| relation_rng(empty_set) = X6 )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f352,f111]) ).
fof(f111,plain,
relation(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f352,plain,
( ! [X6] :
( ~ relation(empty_set)
| relation_rng(empty_set) = X6
| in(sK12(empty_set,X6),X6) )
| ~ spl16_4 ),
inference(resolution,[],[f183,f263]) ).
fof(f263,plain,
( ! [X3] : ~ in(X3,empty_set)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f262,plain,
( spl16_4
<=> ! [X3] : ~ in(X3,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f183,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK13(X0,X1)),unordered_pair(sK12(X0,X1),sK13(X0,X1))),X0)
| in(sK12(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 ),
inference(forward_demodulation,[],[f182,f148]) ).
fof(f148,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f182,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = X1
| in(sK12(X0,X1),X1)
| in(unordered_pair(singleton(sK13(X0,X1)),unordered_pair(sK13(X0,X1),sK12(X0,X1))),X0) ),
inference(forward_demodulation,[],[f167,f148]) ).
fof(f167,plain,
! [X0,X1] :
( in(sK12(X0,X1),X1)
| relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK13(X0,X1),sK12(X0,X1)),singleton(sK13(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f155,f142]) ).
fof(f142,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X1,X0] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f155,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK13(X0,X1),sK12(X0,X1)),X0)
| in(sK12(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK11(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK12(X0,X1)),X0)
| ~ in(sK12(X0,X1),X1) )
& ( in(ordered_pair(sK13(X0,X1),sK12(X0,X1)),X0)
| in(sK12(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f105,f108,f107,f106]) ).
fof(f106,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK11(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(X6,sK12(X0,X1)),X0)
| ~ in(sK12(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK12(X0,X1)),X0)
| in(sK12(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK12(X0,X1)),X0)
=> in(ordered_pair(sK13(X0,X1),sK12(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f1621,plain,
( ! [X0] : ~ in(X0,sK5)
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f1620,f251]) ).
fof(f251,plain,
! [X7] :
( ~ in(X7,sK5)
| in(X7,sF15) ),
inference(resolution,[],[f122,f173]) ).
fof(f173,plain,
subset(sK5,sF15),
inference(definition_folding,[],[f138,f172]) ).
fof(f172,plain,
relation_rng(sK4) = sF15,
introduced(function_definition,[]) ).
fof(f138,plain,
subset(sK5,relation_rng(sK4)),
inference(cnf_transformation,[],[f88]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f79,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) ) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X1,X0] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X1,X0)
<=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1620,plain,
( ! [X0] :
( ~ in(X0,sF15)
| ~ in(X0,sK5) )
| ~ spl16_4 ),
inference(forward_demodulation,[],[f1619,f172]) ).
fof(f1619,plain,
( ! [X0] :
( ~ in(X0,sK5)
| ~ in(X0,relation_rng(sK4)) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f1618,f141]) ).
fof(f141,plain,
relation(sK4),
inference(cnf_transformation,[],[f88]) ).
fof(f1618,plain,
( ! [X0] :
( ~ in(X0,sK5)
| ~ relation(sK4)
| ~ in(X0,relation_rng(sK4)) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f1599,f263]) ).
fof(f1599,plain,
! [X0] :
( in(sK11(sK4,X0),empty_set)
| ~ relation(sK4)
| ~ in(X0,sK5)
| ~ in(X0,relation_rng(sK4)) ),
inference(superposition,[],[f636,f181]) ).
fof(f181,plain,
empty_set = relation_inverse_image(sK4,sK5),
inference(forward_demodulation,[],[f170,f171]) ).
fof(f171,plain,
empty_set = sF14,
inference(definition_folding,[],[f140,f170]) ).
fof(f140,plain,
empty_set = relation_inverse_image(sK4,sK5),
inference(cnf_transformation,[],[f88]) ).
fof(f170,plain,
sF14 = relation_inverse_image(sK4,sK5),
introduced(function_definition,[]) ).
fof(f636,plain,
! [X2,X0,X1] :
( in(sK11(X2,X0),relation_inverse_image(X2,X1))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(duplicate_literal_removal,[],[f630]) ).
fof(f630,plain,
! [X2,X0,X1] :
( in(sK11(X2,X0),relation_inverse_image(X2,X1))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation(X2) ),
inference(resolution,[],[f300,f180]) ).
fof(f180,plain,
! [X2,X0] :
( in(unordered_pair(singleton(sK11(X0,X2)),unordered_pair(X2,sK11(X0,X2))),X0)
| ~ in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f178,f148]) ).
fof(f178,plain,
! [X2,X0] :
( in(unordered_pair(singleton(sK11(X0,X2)),unordered_pair(sK11(X0,X2),X2)),X0)
| ~ relation(X0)
| ~ in(X2,relation_rng(X0)) ),
inference(backward_demodulation,[],[f169,f148]) ).
fof(f169,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(sK11(X0,X2),X2),singleton(sK11(X0,X2))),X0)
| ~ in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK11(X0,X2),X2),singleton(sK11(X0,X2))),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f157,f142]) ).
fof(f157,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK11(X0,X2),X2),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f300,plain,
! [X6,X7,X4,X5] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X5,X4)),X6)
| ~ in(X5,X7)
| in(X4,relation_inverse_image(X6,X7))
| ~ relation(X6) ),
inference(superposition,[],[f179,f148]) ).
fof(f179,plain,
! [X2,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X4)),X1)
| ~ relation(X1)
| in(X2,relation_inverse_image(X1,X0))
| ~ in(X4,X0) ),
inference(subsumption_resolution,[],[f175,f174]) ).
fof(f174,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),X0)
| in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(backward_demodulation,[],[f168,f148]) ).
fof(f168,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f164]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f158,f142]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f175,plain,
! [X2,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X4)),X1)
| ~ relation(X1)
| in(X2,relation_inverse_image(X1,X0))
| ~ in(X4,X0)
| ~ in(X4,relation_rng(X1)) ),
inference(backward_demodulation,[],[f163,f148]) ).
fof(f163,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| in(X2,relation_inverse_image(X1,X0))
| ~ in(X4,relation_rng(X1))
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X1) ),
inference(definition_unfolding,[],[f150,f142]) ).
fof(f150,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| in(X2,relation_inverse_image(X1,X0))
| ~ in(X4,relation_rng(X1))
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ relation(X1)
| ( ( ( in(sK10(X0,X1,X2),relation_rng(X1))
& in(ordered_pair(X2,sK10(X0,X1,X2)),X1)
& in(sK10(X0,X1,X2),X0) )
| ~ in(X2,relation_inverse_image(X1,X0)) )
& ( in(X2,relation_inverse_image(X1,X0))
| ! [X4] :
( ~ in(X4,relation_rng(X1))
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ? [X3] :
( in(X3,relation_rng(X1))
& in(ordered_pair(X2,X3),X1)
& in(X3,X0) )
=> ( in(sK10(X0,X1,X2),relation_rng(X1))
& in(ordered_pair(X2,sK10(X0,X1,X2)),X1)
& in(sK10(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ relation(X1)
| ( ( ? [X3] :
( in(X3,relation_rng(X1))
& in(ordered_pair(X2,X3),X1)
& in(X3,X0) )
| ~ in(X2,relation_inverse_image(X1,X0)) )
& ( in(X2,relation_inverse_image(X1,X0))
| ! [X4] :
( ~ in(X4,relation_rng(X1))
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,X0) ) ) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X1,X2,X0] :
( ~ relation(X2)
| ( ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X1,X2,X0] :
( ~ relation(X2)
| ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
<=> in(X0,relation_inverse_image(X2,X1)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X2,X0,X1] :
( relation(X2)
=> ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
<=> in(X0,relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f267,plain,
~ spl16_3,
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f266,plain,
( $false
| ~ spl16_3 ),
inference(resolution,[],[f260,f137]) ).
fof(f260,plain,
( ! [X4] : ~ empty(X4)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f259,plain,
( spl16_3
<=> ! [X4] : ~ empty(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f264,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f255,f262,f259]) ).
fof(f255,plain,
! [X3,X4] :
( ~ in(X3,empty_set)
| ~ empty(X4) ),
inference(resolution,[],[f133,f195]) ).
fof(f195,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(backward_demodulation,[],[f123,f190]) ).
fof(f190,plain,
! [X0] : empty_set = sK2(X0),
inference(resolution,[],[f114,f124]) ).
fof(f124,plain,
! [X0] : empty(sK2(X0)),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f82]) ).
fof(f82,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f123,plain,
! [X0] : element(sK2(X0),powerset(X0)),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X1))
| ~ in(X0,X2)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ element(X2,powerset(X1)) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
! [X1,X2,X0] :
( ~ empty(X2)
| ~ in(X1,X0)
| ~ element(X0,powerset(X2)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X1,X2,X0] :
~ ( in(X1,X0)
& empty(X2)
& element(X0,powerset(X2)) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X1,X0,X2] :
~ ( empty(X2)
& in(X0,X1)
& element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 30 14:59:25 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.15/0.45 % (25650)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.45 % (25650)Instruction limit reached!
% 0.15/0.45 % (25650)------------------------------
% 0.15/0.45 % (25650)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.45 % (25657)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.15/0.46 % (25650)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.46 % (25650)Termination reason: Unknown
% 0.15/0.46 % (25650)Termination phase: Preprocessing 3
% 0.15/0.46
% 0.15/0.46 % (25650)Memory used [KB]: 895
% 0.15/0.46 % (25650)Time elapsed: 0.003 s
% 0.15/0.46 % (25650)Instructions burned: 2 (million)
% 0.15/0.46 % (25650)------------------------------
% 0.15/0.46 % (25650)------------------------------
% 0.15/0.46 % (25648)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.46 % (25665)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.15/0.46 % (25656)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.15/0.46 % (25659)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.15/0.47 % (25649)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.47 % (25666)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.15/0.47 TRYING [1]
% 0.15/0.47 TRYING [2]
% 0.15/0.47 TRYING [1]
% 0.15/0.47 % (25649)Instruction limit reached!
% 0.15/0.47 % (25649)------------------------------
% 0.15/0.47 % (25649)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48 % (25649)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48 % (25649)Termination reason: Unknown
% 0.15/0.48 % (25649)Termination phase: Saturation
% 0.15/0.48
% 0.15/0.48 % (25649)Memory used [KB]: 5500
% 0.15/0.48 % (25649)Time elapsed: 0.117 s
% 0.15/0.48 % (25649)Instructions burned: 7 (million)
% 0.15/0.48 % (25649)------------------------------
% 0.15/0.48 % (25649)------------------------------
% 0.15/0.48 % (25664)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.15/0.48 TRYING [2]
% 0.15/0.48 TRYING [3]
% 0.15/0.49 TRYING [3]
% 0.15/0.50 % (25667)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.15/0.50 % (25653)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.15/0.51 % (25647)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.15/0.51 % (25646)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.51 % (25655)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.15/0.51 % (25645)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.51 % (25654)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.15/0.51 % (25658)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.15/0.52 % (25671)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.15/0.52 % (25669)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.15/0.52 TRYING [4]
% 0.15/0.52 % (25662)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.15/0.53 % (25663)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.15/0.53 % (25651)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.54 % (25659)Instruction limit reached!
% 0.15/0.54 % (25659)------------------------------
% 0.15/0.54 % (25659)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.54 % (25661)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.15/0.54 % (25643)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.15/0.54 % (25670)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.15/0.54 TRYING [4]
% 0.15/0.55 % (25642)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.15/0.55 % (25659)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.55 % (25659)Termination reason: Unknown
% 0.15/0.55 % (25659)Termination phase: Finite model building constraint generation
% 0.15/0.55
% 0.15/0.55 % (25659)Memory used [KB]: 7803
% 0.15/0.55 % (25659)Time elapsed: 0.171 s
% 0.15/0.55 % (25659)Instructions burned: 59 (million)
% 0.15/0.55 % (25659)------------------------------
% 0.15/0.55 % (25659)------------------------------
% 1.86/0.56 % (25648)Instruction limit reached!
% 1.86/0.56 % (25648)------------------------------
% 1.86/0.56 % (25648)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.86/0.56 % (25648)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.86/0.56 % (25648)Termination reason: Unknown
% 1.86/0.56 % (25648)Termination phase: Finite model building constraint generation
% 1.86/0.56
% 1.86/0.56 % (25648)Memory used [KB]: 7547
% 1.86/0.56 % (25648)Time elapsed: 0.183 s
% 1.86/0.56 % (25648)Instructions burned: 51 (million)
% 1.86/0.56 % (25643)Refutation not found, incomplete strategy% (25643)------------------------------
% 1.86/0.56 % (25643)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.86/0.56 % (25643)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.86/0.56 % (25643)Termination reason: Refutation not found, incomplete strategy
% 1.86/0.56
% 1.86/0.56 % (25643)Memory used [KB]: 5500
% 1.86/0.56 % (25643)Time elapsed: 0.172 s
% 1.86/0.56 % (25643)Instructions burned: 6 (million)
% 1.86/0.56 % (25643)------------------------------
% 1.86/0.56 % (25643)------------------------------
% 1.86/0.56 % (25648)------------------------------
% 1.86/0.56 % (25648)------------------------------
% 1.86/0.57 % (25668)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 2.00/0.57 TRYING [1]
% 2.00/0.57 TRYING [2]
% 2.00/0.58 TRYING [3]
% 2.00/0.58 % (25644)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 2.00/0.58 % (25652)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 2.00/0.59 % (25660)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 2.00/0.61 % (25656)Instruction limit reached!
% 2.00/0.61 % (25656)------------------------------
% 2.00/0.61 % (25656)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.00/0.61 % (25656)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.00/0.61 % (25656)Termination reason: Unknown
% 2.00/0.61 % (25656)Termination phase: Saturation
% 2.00/0.61
% 2.00/0.61 % (25656)Memory used [KB]: 6652
% 2.00/0.61 % (25656)Time elapsed: 0.061 s
% 2.00/0.61 % (25656)Instructions burned: 68 (million)
% 2.00/0.61 % (25656)------------------------------
% 2.00/0.61 % (25656)------------------------------
% 2.00/0.62 % (25657)Instruction limit reached!
% 2.00/0.62 % (25657)------------------------------
% 2.00/0.62 % (25657)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.00/0.62 % (25657)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.00/0.62 % (25657)Termination reason: Unknown
% 2.00/0.62 % (25657)Termination phase: Saturation
% 2.00/0.62
% 2.00/0.62 % (25657)Memory used [KB]: 2302
% 2.00/0.62 % (25657)Time elapsed: 0.253 s
% 2.00/0.62 % (25657)Instructions burned: 75 (million)
% 2.00/0.62 % (25657)------------------------------
% 2.00/0.62 % (25657)------------------------------
% 2.00/0.63 % (25666)First to succeed.
% 2.47/0.64 % (25672)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/388Mi)
% 2.47/0.64 % (25651)Instruction limit reached!
% 2.47/0.64 % (25651)------------------------------
% 2.47/0.64 % (25651)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.47/0.64 % (25651)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.47/0.64 % (25651)Termination reason: Unknown
% 2.47/0.64 % (25651)Termination phase: Saturation
% 2.47/0.64
% 2.47/0.64 % (25651)Memory used [KB]: 1791
% 2.47/0.64 % (25651)Time elapsed: 0.243 s
% 2.47/0.64 % (25651)Instructions burned: 51 (million)
% 2.47/0.64 % (25651)------------------------------
% 2.47/0.64 % (25651)------------------------------
% 2.47/0.64 % (25646)Instruction limit reached!
% 2.47/0.64 % (25646)------------------------------
% 2.47/0.64 % (25646)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.47/0.64 % (25646)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.47/0.64 % (25646)Termination reason: Unknown
% 2.47/0.64 % (25646)Termination phase: Saturation
% 2.47/0.64
% 2.47/0.64 % (25646)Memory used [KB]: 6396
% 2.47/0.64 % (25646)Time elapsed: 0.285 s
% 2.47/0.64 % (25646)Instructions burned: 51 (million)
% 2.47/0.64 % (25646)------------------------------
% 2.47/0.64 % (25646)------------------------------
% 2.47/0.64 % (25647)Instruction limit reached!
% 2.47/0.64 % (25647)------------------------------
% 2.47/0.64 % (25647)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.47/0.65 TRYING [4]
% 2.47/0.65 % (25647)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.47/0.65 % (25647)Termination reason: Unknown
% 2.47/0.65 % (25647)Termination phase: Saturation
% 2.47/0.65
% 2.47/0.65 % (25647)Memory used [KB]: 6012
% 2.47/0.65 % (25647)Time elapsed: 0.284 s
% 2.47/0.65 % (25647)Instructions burned: 49 (million)
% 2.47/0.65 % (25647)------------------------------
% 2.47/0.65 % (25647)------------------------------
% 2.47/0.65 % (25645)Instruction limit reached!
% 2.47/0.65 % (25645)------------------------------
% 2.47/0.65 % (25645)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.47/0.65 % (25645)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.47/0.65 % (25645)Termination reason: Unknown
% 2.47/0.65 % (25645)Termination phase: Saturation
% 2.47/0.65
% 2.47/0.65 % (25645)Memory used [KB]: 6012
% 2.47/0.65 % (25645)Time elapsed: 0.268 s
% 2.47/0.65 % (25645)Instructions burned: 51 (million)
% 2.47/0.65 % (25645)------------------------------
% 2.47/0.65 % (25645)------------------------------
% 2.47/0.66 % (25644)Also succeeded, but the first one will report.
% 2.47/0.66 % (25666)Refutation found. Thanks to Tanya!
% 2.47/0.66 % SZS status Theorem for theBenchmark
% 2.47/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/0.66 % (25666)------------------------------
% 2.47/0.66 % (25666)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.47/0.66 % (25666)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.47/0.66 % (25666)Termination reason: Refutation
% 2.47/0.66
% 2.47/0.66 % (25666)Memory used [KB]: 6652
% 2.47/0.66 % (25666)Time elapsed: 0.261 s
% 2.47/0.66 % (25666)Instructions burned: 84 (million)
% 2.47/0.66 % (25666)------------------------------
% 2.47/0.66 % (25666)------------------------------
% 2.47/0.66 % (25641)Success in time 0.344 s
%------------------------------------------------------------------------------