TSTP Solution File: SEU212+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU212+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 : n003.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 18:32:32 EDT 2022
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 100 ( 13 unt; 0 def)
% Number of atoms : 370 ( 75 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 446 ( 176 ~; 186 |; 54 &)
% ( 17 <=>; 11 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 133 ( 102 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f440,plain,
$false,
inference(avatar_sat_refutation,[],[f168,f169,f173,f251,f360,f398,f422]) ).
fof(f422,plain,
( spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f421]) ).
fof(f421,plain,
( $false
| spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f420,f163]) ).
fof(f163,plain,
( ~ in(sF15,sK7)
| spl18_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl18_2
<=> in(sF15,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f420,plain,
( in(sF15,sK7)
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f419,f150]) ).
fof(f150,plain,
unordered_pair(sF13,sF14) = sF15,
introduced(function_definition,[]) ).
fof(f419,plain,
( in(unordered_pair(sF13,sF14),sK7)
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f418,f104]) ).
fof(f104,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f418,plain,
( in(unordered_pair(sF14,sF13),sK7)
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f417,f148]) ).
fof(f148,plain,
unordered_pair(sK5,sK6) = sF13,
introduced(function_definition,[]) ).
fof(f417,plain,
( in(unordered_pair(sF14,unordered_pair(sK5,sK6)),sK7)
| ~ spl18_3
| ~ spl18_4 ),
inference(backward_demodulation,[],[f250,f166]) ).
fof(f166,plain,
( sF16 = sK6
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f165,plain,
( spl18_3
<=> sF16 = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f250,plain,
( in(unordered_pair(sF14,unordered_pair(sK5,sF16)),sK7)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f248,plain,
( spl18_4
<=> in(unordered_pair(sF14,unordered_pair(sK5,sF16)),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f398,plain,
( ~ spl18_2
| spl18_3 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f397,plain,
( $false
| ~ spl18_2
| spl18_3 ),
inference(subsumption_resolution,[],[f396,f167]) ).
fof(f167,plain,
( sF16 != sK6
| spl18_3 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f396,plain,
( sF16 = sK6
| ~ spl18_2 ),
inference(backward_demodulation,[],[f151,f395]) ).
fof(f395,plain,
( sK6 = apply(sK7,sK5)
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f394,f113]) ).
fof(f113,plain,
relation(sK7),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( relation(sK7)
& ( ~ in(ordered_pair(sK5,sK6),sK7)
| sK6 != apply(sK7,sK5)
| ~ in(sK5,relation_dom(sK7)) )
& ( in(ordered_pair(sK5,sK6),sK7)
| ( sK6 = apply(sK7,sK5)
& in(sK5,relation_dom(sK7)) ) )
& function(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f75,f76]) ).
fof(f76,plain,
( ? [X0,X1,X2] :
( relation(X2)
& ( ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( in(ordered_pair(X0,X1),X2)
| ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2) )
=> ( relation(sK7)
& ( ~ in(ordered_pair(sK5,sK6),sK7)
| sK6 != apply(sK7,sK5)
| ~ in(sK5,relation_dom(sK7)) )
& ( in(ordered_pair(sK5,sK6),sK7)
| ( sK6 = apply(sK7,sK5)
& in(sK5,relation_dom(sK7)) ) )
& function(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
? [X0,X1,X2] :
( relation(X2)
& ( ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( in(ordered_pair(X0,X1),X2)
| ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
? [X2,X0,X1] :
( relation(X1)
& ( ~ in(ordered_pair(X2,X0),X1)
| apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) )
& ( in(ordered_pair(X2,X0),X1)
| ( apply(X1,X2) = X0
& in(X2,relation_dom(X1)) ) )
& function(X1) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
? [X2,X0,X1] :
( relation(X1)
& ( ~ in(ordered_pair(X2,X0),X1)
| apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) )
& ( in(ordered_pair(X2,X0),X1)
| ( apply(X1,X2) = X0
& in(X2,relation_dom(X1)) ) )
& function(X1) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
? [X2,X0,X1] :
( relation(X1)
& ( ( apply(X1,X2) = X0
& in(X2,relation_dom(X1)) )
<~> in(ordered_pair(X2,X0),X1) )
& function(X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X1,X2,X0] :
( ( ( apply(X1,X2) = X0
& in(X2,relation_dom(X1)) )
<~> in(ordered_pair(X2,X0),X1) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
~ ! [X1,X2,X0] :
( ( function(X1)
& relation(X1) )
=> ( ( apply(X1,X2) = X0
& in(X2,relation_dom(X1)) )
<=> in(ordered_pair(X2,X0),X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X1,X2,X0] :
( ( function(X2)
& relation(X2) )
=> ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
<=> in(ordered_pair(X0,X1),X2) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X1,X2,X0] :
( ( function(X2)
& relation(X2) )
=> ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
<=> in(ordered_pair(X0,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f394,plain,
( ~ relation(sK7)
| sK6 = apply(sK7,sK5)
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f391,f109]) ).
fof(f109,plain,
function(sK7),
inference(cnf_transformation,[],[f77]) ).
fof(f391,plain,
( sK6 = apply(sK7,sK5)
| ~ function(sK7)
| ~ relation(sK7)
| ~ spl18_2 ),
inference(resolution,[],[f266,f162]) ).
fof(f162,plain,
( in(sF15,sK7)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f266,plain,
! [X0] :
( ~ in(sF15,X0)
| apply(X0,sK5) = sK6
| ~ function(X0)
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f265,f228]) ).
fof(f228,plain,
! [X0] :
( in(sK5,relation_dom(X0))
| ~ relation(X0)
| ~ in(sF15,X0) ),
inference(forward_demodulation,[],[f227,f150]) ).
fof(f227,plain,
! [X0] :
( ~ relation(X0)
| in(sK5,relation_dom(X0))
| ~ in(unordered_pair(sF13,sF14),X0) ),
inference(forward_demodulation,[],[f226,f149]) ).
fof(f149,plain,
sF14 = singleton(sK5),
introduced(function_definition,[]) ).
fof(f226,plain,
! [X0] :
( ~ relation(X0)
| in(sK5,relation_dom(X0))
| ~ in(unordered_pair(sF13,singleton(sK5)),X0) ),
inference(forward_demodulation,[],[f221,f104]) ).
fof(f221,plain,
! [X0] :
( in(sK5,relation_dom(X0))
| ~ in(unordered_pair(singleton(sK5),sF13),X0)
| ~ relation(X0) ),
inference(superposition,[],[f176,f148]) ).
fof(f176,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
| in(X2,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f143,f104]) ).
fof(f143,plain,
! [X2,X3,X0] :
( in(X2,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f95,f117]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,sK0(X0,X2)),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(sK1(X0,X1),X6),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f62,f65,f64,f63]) ).
fof(f63,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X2,X4),X0)
=> in(ordered_pair(X2,sK0(X0,X2)),X0) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(sK1(X0,X1),X6),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(sK1(X0,X1),X7),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(sK1(X0,X1),X7),X0)
=> in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| in(X5,X1) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) )
<=> relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) )
<=> relation_dom(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f265,plain,
! [X0] :
( ~ relation(X0)
| ~ in(sF15,X0)
| apply(X0,sK5) = sK6
| ~ in(sK5,relation_dom(X0))
| ~ function(X0) ),
inference(forward_demodulation,[],[f264,f150]) ).
fof(f264,plain,
! [X0] :
( ~ relation(X0)
| ~ in(sK5,relation_dom(X0))
| apply(X0,sK5) = sK6
| ~ function(X0)
| ~ in(unordered_pair(sF13,sF14),X0) ),
inference(forward_demodulation,[],[f263,f149]) ).
fof(f263,plain,
! [X0] :
( ~ function(X0)
| apply(X0,sK5) = sK6
| ~ in(unordered_pair(sF13,singleton(sK5)),X0)
| ~ in(sK5,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f256,f104]) ).
fof(f256,plain,
! [X0] :
( ~ relation(X0)
| ~ in(sK5,relation_dom(X0))
| ~ function(X0)
| ~ in(unordered_pair(singleton(sK5),sF13),X0)
| apply(X0,sK5) = sK6 ),
inference(superposition,[],[f172,f148]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ relation(X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0) ),
inference(forward_demodulation,[],[f139,f104]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ relation(X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f100,f117]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ function(X0)
| ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
| ( ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) ) ) )
& ( ( ( empty_set = X2
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| empty_set != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
| ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 ) )
& ( ( empty_set = X2
<=> apply(X0,X1) = X2 )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
| ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 ) )
& ( ( empty_set = X2
<=> apply(X0,X1) = X2 )
| in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( empty_set = X2
<=> apply(X0,X1) = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f151,plain,
sF16 = apply(sK7,sK5),
introduced(function_definition,[]) ).
fof(f360,plain,
( spl18_1
| ~ spl18_2 ),
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f359,plain,
( $false
| spl18_1
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f358,f113]) ).
fof(f358,plain,
( ~ relation(sK7)
| spl18_1
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f357,f162]) ).
fof(f357,plain,
( ~ in(sF15,sK7)
| ~ relation(sK7)
| spl18_1 ),
inference(subsumption_resolution,[],[f355,f159]) ).
fof(f159,plain,
( ~ in(sK5,sF17)
| spl18_1 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f157,plain,
( spl18_1
<=> in(sK5,sF17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f355,plain,
( ~ in(sF15,sK7)
| ~ relation(sK7)
| in(sK5,sF17) ),
inference(superposition,[],[f228,f152]) ).
fof(f152,plain,
sF17 = relation_dom(sK7),
introduced(function_definition,[]) ).
fof(f251,plain,
( ~ spl18_1
| spl18_4 ),
inference(avatar_split_clause,[],[f246,f248,f157]) ).
fof(f246,plain,
( in(unordered_pair(sF14,unordered_pair(sK5,sF16)),sK7)
| ~ in(sK5,sF17) ),
inference(forward_demodulation,[],[f245,f152]) ).
fof(f245,plain,
( in(unordered_pair(sF14,unordered_pair(sK5,sF16)),sK7)
| ~ in(sK5,relation_dom(sK7)) ),
inference(forward_demodulation,[],[f244,f149]) ).
fof(f244,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sF16)),sK7)
| ~ in(sK5,relation_dom(sK7)) ),
inference(subsumption_resolution,[],[f243,f109]) ).
fof(f243,plain,
( ~ function(sK7)
| ~ in(sK5,relation_dom(sK7))
| in(unordered_pair(singleton(sK5),unordered_pair(sK5,sF16)),sK7) ),
inference(subsumption_resolution,[],[f241,f113]) ).
fof(f241,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sF16)),sK7)
| ~ in(sK5,relation_dom(sK7))
| ~ relation(sK7)
| ~ function(sK7) ),
inference(superposition,[],[f171,f151]) ).
fof(f171,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f145,f104]) ).
fof(f145,plain,
! [X0,X1] :
( ~ function(X0)
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0)) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f101,f117]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f173,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f155,f161,f157]) ).
fof(f155,plain,
( in(sF15,sK7)
| in(sK5,sF17) ),
inference(definition_folding,[],[f142,f152,f150,f149,f148]) ).
fof(f142,plain,
( in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK7)
| in(sK5,relation_dom(sK7)) ),
inference(definition_unfolding,[],[f110,f117]) ).
fof(f110,plain,
( in(ordered_pair(sK5,sK6),sK7)
| in(sK5,relation_dom(sK7)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f169,plain,
( spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f154,f165,f161]) ).
fof(f154,plain,
( sF16 = sK6
| in(sF15,sK7) ),
inference(definition_folding,[],[f141,f151,f150,f149,f148]) ).
fof(f141,plain,
( in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK7)
| sK6 = apply(sK7,sK5) ),
inference(definition_unfolding,[],[f111,f117]) ).
fof(f111,plain,
( in(ordered_pair(sK5,sK6),sK7)
| sK6 = apply(sK7,sK5) ),
inference(cnf_transformation,[],[f77]) ).
fof(f168,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f153,f165,f161,f157]) ).
fof(f153,plain,
( sF16 != sK6
| ~ in(sF15,sK7)
| ~ in(sK5,sF17) ),
inference(definition_folding,[],[f140,f152,f151,f150,f149,f148]) ).
fof(f140,plain,
( ~ in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK7)
| sK6 != apply(sK7,sK5)
| ~ in(sK5,relation_dom(sK7)) ),
inference(definition_unfolding,[],[f112,f117]) ).
fof(f112,plain,
( ~ in(ordered_pair(sK5,sK6),sK7)
| sK6 != apply(sK7,sK5)
| ~ in(sK5,relation_dom(sK7)) ),
inference(cnf_transformation,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:49:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.50 % (22647)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (22661)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.51 % (22665)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)
% 0.21/0.51 % (22657)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)
% 0.21/0.51 % (22654)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)
% 0.21/0.51 % (22650)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.52 % (22644)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)
% 0.21/0.53 % (22645)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)
% 0.21/0.53 % (22661)First to succeed.
% 0.21/0.53 % (22643)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)
% 0.21/0.53 % (22650)Instruction limit reached!
% 0.21/0.53 % (22650)------------------------------
% 0.21/0.53 % (22650)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (22650)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (22650)Termination reason: Unknown
% 0.21/0.53 % (22650)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (22650)Memory used [KB]: 5500
% 0.21/0.53 % (22650)Time elapsed: 0.075 s
% 0.21/0.53 % (22650)Instructions burned: 8 (million)
% 0.21/0.53 % (22650)------------------------------
% 0.21/0.53 % (22650)------------------------------
% 0.21/0.53 % (22651)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.53 % (22651)Instruction limit reached!
% 0.21/0.53 % (22651)------------------------------
% 0.21/0.53 % (22651)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (22651)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (22651)Termination reason: Unknown
% 0.21/0.53 % (22651)Termination phase: Blocked clause elimination
% 0.21/0.53
% 0.21/0.53 % (22651)Memory used [KB]: 895
% 0.21/0.53 % (22651)Time elapsed: 0.004 s
% 0.21/0.53 % (22651)Instructions burned: 3 (million)
% 0.21/0.53 % (22651)------------------------------
% 0.21/0.53 % (22651)------------------------------
% 0.21/0.53 % (22667)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.53 % (22648)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)
% 0.21/0.54 % (22666)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)
% 0.21/0.54 % (22663)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)
% 0.21/0.54 % (22660)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.54 % (22658)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)
% 0.21/0.54 TRYING [1]
% 0.21/0.54 % (22649)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)
% 0.21/0.54 % (22665)Also succeeded, but the first one will report.
% 0.21/0.54 TRYING [2]
% 0.21/0.54 % (22661)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 % (22661)------------------------------
% 0.21/0.54 % (22661)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (22661)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (22661)Termination reason: Refutation
% 0.21/0.54
% 0.21/0.54 % (22661)Memory used [KB]: 5628
% 0.21/0.54 % (22661)Time elapsed: 0.125 s
% 0.21/0.54 % (22661)Instructions burned: 14 (million)
% 0.21/0.54 % (22661)------------------------------
% 0.21/0.54 % (22661)------------------------------
% 0.21/0.54 % (22642)Success in time 0.184 s
%------------------------------------------------------------------------------