TSTP Solution File: SEU212+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n025.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 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 101 ( 14 unt; 0 def)
% Number of atoms : 371 ( 76 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 : 135 ( 104 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f784,plain,
$false,
inference(avatar_sat_refutation,[],[f195,f198,f200,f503,f699,f769,f777]) ).
fof(f777,plain,
( ~ spl20_1
| spl20_3
| ~ spl20_10 ),
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f776,plain,
( $false
| ~ spl20_1
| spl20_3
| ~ spl20_10 ),
inference(subsumption_resolution,[],[f775,f194]) ).
fof(f194,plain,
( ~ in(sF17,sK14)
| spl20_3 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f192,plain,
( spl20_3
<=> in(sF17,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
fof(f775,plain,
( in(sF17,sK14)
| ~ spl20_1
| ~ spl20_10 ),
inference(forward_demodulation,[],[f774,f177]) ).
fof(f177,plain,
unordered_pair(sF15,sF16) = sF17,
introduced(function_definition,[]) ).
fof(f774,plain,
( in(unordered_pair(sF15,sF16),sK14)
| ~ spl20_1
| ~ spl20_10 ),
inference(forward_demodulation,[],[f773,f158]) ).
fof(f158,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(f773,plain,
( in(unordered_pair(sF16,sF15),sK14)
| ~ spl20_1
| ~ spl20_10 ),
inference(forward_demodulation,[],[f772,f175]) ).
fof(f175,plain,
sF15 = unordered_pair(sK12,sK13),
introduced(function_definition,[]) ).
fof(f772,plain,
( in(unordered_pair(sF16,unordered_pair(sK12,sK13)),sK14)
| ~ spl20_1
| ~ spl20_10 ),
inference(superposition,[],[f502,f185]) ).
fof(f185,plain,
( sK13 = sF18
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f184,plain,
( spl20_1
<=> sK13 = sF18 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f502,plain,
( in(unordered_pair(sF16,unordered_pair(sK12,sF18)),sK14)
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f500,plain,
( spl20_10
<=> in(unordered_pair(sF16,unordered_pair(sK12,sF18)),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
fof(f769,plain,
( spl20_1
| ~ spl20_3 ),
inference(avatar_contradiction_clause,[],[f768]) ).
fof(f768,plain,
( $false
| spl20_1
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f755,f186]) ).
fof(f186,plain,
( sK13 != sF18
| spl20_1 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f755,plain,
( sK13 = sF18
| ~ spl20_3 ),
inference(superposition,[],[f754,f178]) ).
fof(f178,plain,
apply(sK14,sK12) = sF18,
introduced(function_definition,[]) ).
fof(f754,plain,
( sK13 = apply(sK14,sK12)
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f753,f154]) ).
fof(f154,plain,
function(sK14),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( ( ~ in(ordered_pair(sK12,sK13),sK14)
| sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14)) )
& ( in(ordered_pair(sK12,sK13),sK14)
| ( sK13 = apply(sK14,sK12)
& in(sK12,relation_dom(sK14)) ) )
& function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f104,f105]) ).
fof(f105,plain,
( ? [X0,X1,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(X2) )
=> ( ( ~ in(ordered_pair(sK12,sK13),sK14)
| sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14)) )
& ( in(ordered_pair(sK12,sK13),sK14)
| ( sK13 = apply(sK14,sK12)
& in(sK12,relation_dom(sK14)) ) )
& function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
? [X0,X1,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(X2) ),
inference(rectify,[],[f103]) ).
fof(f103,plain,
? [X1,X0,X2] :
( ( ~ in(ordered_pair(X1,X0),X2)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& ( in(ordered_pair(X1,X0),X2)
| ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
? [X1,X0,X2] :
( ( ~ in(ordered_pair(X1,X0),X2)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& ( in(ordered_pair(X1,X0),X2)
| ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
? [X1,X0,X2] :
( ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
<~> in(ordered_pair(X1,X0),X2) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
? [X1,X0,X2] :
( ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
<~> in(ordered_pair(X1,X0),X2) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
~ ! [X1,X0,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X1,X0),X2)
<=> ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) ) ) ),
inference(rectify,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X1,X0,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
<=> in(ordered_pair(X0,X1),X2) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X1,X0,X2] :
( ( relation(X2)
& function(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(f753,plain,
( sK13 = apply(sK14,sK12)
| ~ function(sK14)
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f749,f153]) ).
fof(f153,plain,
relation(sK14),
inference(cnf_transformation,[],[f106]) ).
fof(f749,plain,
( ~ relation(sK14)
| sK13 = apply(sK14,sK12)
| ~ function(sK14)
| ~ spl20_3 ),
inference(resolution,[],[f546,f193]) ).
fof(f193,plain,
( in(sF17,sK14)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f546,plain,
! [X0] :
( ~ in(sF17,X0)
| ~ relation(X0)
| ~ function(X0)
| sK13 = apply(X0,sK12) ),
inference(subsumption_resolution,[],[f545,f357]) ).
fof(f357,plain,
! [X0] :
( in(sK12,relation_dom(X0))
| ~ relation(X0)
| ~ in(sF17,X0) ),
inference(forward_demodulation,[],[f356,f177]) ).
fof(f356,plain,
! [X0] :
( in(sK12,relation_dom(X0))
| ~ in(unordered_pair(sF15,sF16),X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f355,f176]) ).
fof(f176,plain,
singleton(sK12) = sF16,
introduced(function_definition,[]) ).
fof(f355,plain,
! [X0] :
( in(sK12,relation_dom(X0))
| ~ relation(X0)
| ~ in(unordered_pair(sF15,singleton(sK12)),X0) ),
inference(forward_demodulation,[],[f351,f158]) ).
fof(f351,plain,
! [X0] :
( ~ relation(X0)
| in(sK12,relation_dom(X0))
| ~ in(unordered_pair(singleton(sK12),sF15),X0) ),
inference(superposition,[],[f202,f175]) ).
fof(f202,plain,
! [X2,X0,X4] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X4)),X0)
| in(X2,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f171,f158]) ).
fof(f171,plain,
! [X2,X0,X4] :
( ~ relation(X0)
| in(X2,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f161,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X0)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f115,f125]) ).
fof(f125,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f7]) ).
fof(f7,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(f115,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| in(X2,X1)
| ~ in(ordered_pair(X2,X4),X0)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( in(ordered_pair(X2,sK2(X0,X2)),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X4] : ~ in(ordered_pair(X2,X4),X0) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ( ( ~ in(sK3(X0,X1),X1)
| ! [X6] : ~ in(ordered_pair(sK3(X0,X1),X6),X0) )
& ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f76,f79,f78,f77]) ).
fof(f77,plain,
! [X0,X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,sK2(X0,X2)),X0) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X5] :
( ( ~ in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) ) )
=> ( ( ~ in(sK3(X0,X1),X1)
| ! [X6] : ~ in(ordered_pair(sK3(X0,X1),X6),X0) )
& ( in(sK3(X0,X1),X1)
| ? [X7] : in(ordered_pair(sK3(X0,X1),X7),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(sK3(X0,X1),X7),X0)
=> in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X4] : ~ in(ordered_pair(X2,X4),X0) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X5] :
( ( ~ in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) ) ) ) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) )
<=> relation_dom(X0) = X1 ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) )
<=> relation_dom(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f545,plain,
! [X0] :
( sK13 = apply(X0,sK12)
| ~ in(sF17,X0)
| ~ in(sK12,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f544,f177]) ).
fof(f544,plain,
! [X0] :
( sK13 = apply(X0,sK12)
| ~ in(sK12,relation_dom(X0))
| ~ relation(X0)
| ~ in(unordered_pair(sF15,sF16),X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f543,f176]) ).
fof(f543,plain,
! [X0] :
( ~ in(sK12,relation_dom(X0))
| sK13 = apply(X0,sK12)
| ~ function(X0)
| ~ in(unordered_pair(sF15,singleton(sK12)),X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f534,f158]) ).
fof(f534,plain,
! [X0] :
( sK13 = apply(X0,sK12)
| ~ function(X0)
| ~ in(unordered_pair(singleton(sK12),sF15),X0)
| ~ relation(X0)
| ~ in(sK12,relation_dom(X0)) ),
inference(superposition,[],[f201,f175]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f166,f158]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f149,f125]) ).
fof(f149,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( empty_set = X2
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| empty_set != X2 ) ) )
& ( ( ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( empty_set = X2
<=> apply(X0,X1) = X2 ) )
& ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( empty_set = X2
<=> apply(X0,X1) = X2 ) )
& ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X2,X1] :
( ( ~ 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(f699,plain,
( spl20_2
| ~ spl20_3 ),
inference(avatar_contradiction_clause,[],[f698]) ).
fof(f698,plain,
( $false
| spl20_2
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f697,f153]) ).
fof(f697,plain,
( ~ relation(sK14)
| spl20_2
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f696,f190]) ).
fof(f190,plain,
( ~ in(sK12,sF19)
| spl20_2 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f188,plain,
( spl20_2
<=> in(sK12,sF19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f696,plain,
( in(sK12,sF19)
| ~ relation(sK14)
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f694,f193]) ).
fof(f694,plain,
( ~ in(sF17,sK14)
| ~ relation(sK14)
| in(sK12,sF19) ),
inference(superposition,[],[f357,f179]) ).
fof(f179,plain,
relation_dom(sK14) = sF19,
introduced(function_definition,[]) ).
fof(f503,plain,
( ~ spl20_2
| spl20_10 ),
inference(avatar_split_clause,[],[f498,f500,f188]) ).
fof(f498,plain,
( in(unordered_pair(sF16,unordered_pair(sK12,sF18)),sK14)
| ~ in(sK12,sF19) ),
inference(forward_demodulation,[],[f497,f179]) ).
fof(f497,plain,
( in(unordered_pair(sF16,unordered_pair(sK12,sF18)),sK14)
| ~ in(sK12,relation_dom(sK14)) ),
inference(forward_demodulation,[],[f496,f176]) ).
fof(f496,plain,
( in(unordered_pair(singleton(sK12),unordered_pair(sK12,sF18)),sK14)
| ~ in(sK12,relation_dom(sK14)) ),
inference(subsumption_resolution,[],[f495,f153]) ).
fof(f495,plain,
( ~ relation(sK14)
| in(unordered_pair(singleton(sK12),unordered_pair(sK12,sF18)),sK14)
| ~ in(sK12,relation_dom(sK14)) ),
inference(subsumption_resolution,[],[f491,f154]) ).
fof(f491,plain,
( ~ function(sK14)
| ~ relation(sK14)
| ~ in(sK12,relation_dom(sK14))
| in(unordered_pair(singleton(sK12),unordered_pair(sK12,sF18)),sK14) ),
inference(superposition,[],[f196,f178]) ).
fof(f196,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f174,f158]) ).
fof(f174,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f150,f125]) ).
fof(f150,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f200,plain,
( spl20_3
| spl20_2 ),
inference(avatar_split_clause,[],[f182,f188,f192]) ).
fof(f182,plain,
( in(sK12,sF19)
| in(sF17,sK14) ),
inference(definition_folding,[],[f169,f179,f177,f176,f175]) ).
fof(f169,plain,
( in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14)
| in(sK12,relation_dom(sK14)) ),
inference(definition_unfolding,[],[f155,f125]) ).
fof(f155,plain,
( in(ordered_pair(sK12,sK13),sK14)
| in(sK12,relation_dom(sK14)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f198,plain,
( spl20_3
| spl20_1 ),
inference(avatar_split_clause,[],[f181,f184,f192]) ).
fof(f181,plain,
( sK13 = sF18
| in(sF17,sK14) ),
inference(definition_folding,[],[f168,f178,f177,f176,f175]) ).
fof(f168,plain,
( in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14)
| sK13 = apply(sK14,sK12) ),
inference(definition_unfolding,[],[f156,f125]) ).
fof(f156,plain,
( in(ordered_pair(sK12,sK13),sK14)
| sK13 = apply(sK14,sK12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f195,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_3 ),
inference(avatar_split_clause,[],[f180,f192,f188,f184]) ).
fof(f180,plain,
( ~ in(sF17,sK14)
| ~ in(sK12,sF19)
| sK13 != sF18 ),
inference(definition_folding,[],[f167,f179,f178,f177,f176,f175]) ).
fof(f167,plain,
( ~ in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14)
| sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14)) ),
inference(definition_unfolding,[],[f157,f125]) ).
fof(f157,plain,
( ~ in(ordered_pair(sK12,sK13),sK14)
| sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14)) ),
inference(cnf_transformation,[],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 14:58:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (14168)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)
% 0.19/0.49 % (14184)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.49 % (14171)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.50 % (14174)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)
% 0.19/0.50 % (14176)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.50 TRYING [1]
% 0.19/0.50 TRYING [2]
% 0.19/0.50 % (14172)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.50 TRYING [3]
% 0.19/0.51 % (14166)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (14182)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)
% 0.19/0.51 % (14170)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)
% 0.19/0.51 % (14161)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)
% 0.19/0.51 % (14160)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)
% 0.19/0.51 % (14164)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)
% 0.19/0.51 % (14179)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)
% 0.19/0.51 % (14159)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)
% 0.19/0.52 % (14163)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (14162)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)
% 0.19/0.52 % (14181)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)
% 0.19/0.52 % (14185)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)
% 0.19/0.52 % (14173)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)
% 0.19/0.52 % (14166)Instruction limit reached!
% 0.19/0.52 % (14166)------------------------------
% 0.19/0.52 % (14166)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (14183)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.52 % (14184)First to succeed.
% 0.19/0.53 % (14188)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)
% 0.19/0.53 % (14166)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (14166)Termination reason: Unknown
% 0.19/0.53 % (14166)Termination phase: Saturation
% 0.19/0.53
% 0.19/0.53 % (14166)Memory used [KB]: 5628
% 0.19/0.53 % (14166)Time elapsed: 0.126 s
% 0.19/0.53 % (14166)Instructions burned: 8 (million)
% 0.19/0.53 % (14166)------------------------------
% 0.19/0.53 % (14166)------------------------------
% 0.19/0.53 % (14177)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 % (14184)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (14184)------------------------------
% 0.19/0.53 % (14184)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (14184)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (14184)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (14184)Memory used [KB]: 5884
% 0.19/0.53 % (14184)Time elapsed: 0.125 s
% 0.19/0.53 % (14184)Instructions burned: 24 (million)
% 0.19/0.53 % (14184)------------------------------
% 0.19/0.53 % (14184)------------------------------
% 0.19/0.53 % (14158)Success in time 0.184 s
%------------------------------------------------------------------------------