TSTP Solution File: SEU177+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU177+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 : n015.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 18:32:21 EDT 2022
% Result : Theorem 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 12 unt; 0 def)
% Number of atoms : 200 ( 24 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 235 ( 88 ~; 85 |; 37 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 141 ( 103 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[f123,f149,f158]) ).
fof(f158,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f157,plain,
( $false
| spl13_1 ),
inference(subsumption_resolution,[],[f156,f97]) ).
fof(f97,plain,
relation(sK10),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( in(ordered_pair(sK11,sK12),sK10)
& relation(sK10)
& ( ~ in(sK12,relation_rng(sK10))
| ~ in(sK11,relation_dom(sK10)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f69,f70]) ).
fof(f70,plain,
( ? [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
& relation(X0)
& ( ~ in(X2,relation_rng(X0))
| ~ in(X1,relation_dom(X0)) ) )
=> ( in(ordered_pair(sK11,sK12),sK10)
& relation(sK10)
& ( ~ in(sK12,relation_rng(sK10))
| ~ in(sK11,relation_dom(sK10)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
? [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
& relation(X0)
& ( ~ in(X2,relation_rng(X0))
| ~ in(X1,relation_dom(X0)) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
? [X0,X2,X1] :
( in(ordered_pair(X2,X1),X0)
& relation(X0)
& ( ~ in(X1,relation_rng(X0))
| ~ in(X2,relation_dom(X0)) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
? [X1,X2,X0] :
( ( ~ in(X1,relation_rng(X0))
| ~ in(X2,relation_dom(X0)) )
& in(ordered_pair(X2,X1),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
~ ! [X1,X2,X0] :
( relation(X0)
=> ( in(ordered_pair(X2,X1),X0)
=> ( in(X1,relation_rng(X0))
& in(X2,relation_dom(X0)) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,negated_conjecture,
~ ! [X2,X1,X0] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f24]) ).
fof(f24,conjecture,
! [X2,X1,X0] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f156,plain,
( ~ relation(sK10)
| spl13_1 ),
inference(subsumption_resolution,[],[f153,f118]) ).
fof(f118,plain,
( ~ in(sK12,relation_rng(sK10))
| spl13_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f116,plain,
( spl13_1
<=> in(sK12,relation_rng(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f153,plain,
( in(sK12,relation_rng(sK10))
| ~ relation(sK10) ),
inference(resolution,[],[f144,f134]) ).
fof(f134,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK10),
inference(forward_demodulation,[],[f110,f95]) ).
fof(f95,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f110,plain,
in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK10),
inference(definition_unfolding,[],[f98,f82]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,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(f98,plain,
in(ordered_pair(sK11,sK12),sK10),
inference(cnf_transformation,[],[f71]) ).
fof(f144,plain,
! [X2,X0,X4] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),X0)
| ~ relation(X0)
| in(X2,relation_rng(X0)) ),
inference(forward_demodulation,[],[f114,f95]) ).
fof(f114,plain,
! [X2,X0,X4] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X4,X2),singleton(X4)),X0)
| in(X2,relation_rng(X0)) ),
inference(equality_resolution,[],[f107]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X4,X2),singleton(X4)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f93,f82]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( in(X2,X1)
| ~ in(ordered_pair(X4,X2),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(ordered_pair(sK7(X0,X2),X2),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X4] : ~ in(ordered_pair(X4,X2),X0) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ~ in(sK8(X0,X1),X1)
| ! [X6] : ~ in(ordered_pair(X6,sK8(X0,X1)),X0) )
& ( in(sK8(X0,X1),X1)
| in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f64,f67,f66,f65]) ).
fof(f65,plain,
! [X0,X2] :
( ? [X3] : in(ordered_pair(X3,X2),X0)
=> in(ordered_pair(sK7(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1] :
( ? [X5] :
( ( ~ in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) ) )
=> ( ( ~ in(sK8(X0,X1),X1)
| ! [X6] : ~ in(ordered_pair(X6,sK8(X0,X1)),X0) )
& ( in(sK8(X0,X1),X1)
| ? [X7] : in(ordered_pair(X7,sK8(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK8(X0,X1)),X0)
=> in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X4] : ~ in(ordered_pair(X4,X2),X0) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X5] :
( ( ~ in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X3,X2),X0)
<=> in(X2,X1) )
<=> relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X3,X2),X0)
<=> in(X2,X1) )
<=> relation_rng(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f149,plain,
spl13_2,
inference(avatar_split_clause,[],[f148,f120]) ).
fof(f120,plain,
( spl13_2
<=> in(sK11,relation_dom(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f148,plain,
in(sK11,relation_dom(sK10)),
inference(subsumption_resolution,[],[f145,f97]) ).
fof(f145,plain,
( in(sK11,relation_dom(sK10))
| ~ relation(sK10) ),
inference(resolution,[],[f143,f134]) ).
fof(f143,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
| in(X2,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f111,f95]) ).
fof(f111,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| ~ relation(X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f102]) ).
fof(f102,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,[],[f90,f82]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,sK4(X0,X2)),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(sK5(X0,X1),X6),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f58,f61,f60,f59]) ).
fof(f59,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X2,X4),X0)
=> in(ordered_pair(X2,sK4(X0,X2)),X0) ),
introduced(choice_axiom,[]) ).
fof(f60,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(sK5(X0,X1),X6),X0)
| ~ in(sK5(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(sK5(X0,X1),X7),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(sK5(X0,X1),X7),X0)
=> in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f58,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,[],[f57]) ).
fof(f57,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,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) )
<=> relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,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(f123,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f96,f120,f116]) ).
fof(f96,plain,
( ~ in(sK11,relation_dom(sK10))
| ~ in(sK12,relation_rng(sK10)) ),
inference(cnf_transformation,[],[f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % 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 : n015.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 14:58:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.53 % (5601)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)
% 0.21/0.55 % (5601)First to succeed.
% 0.21/0.56 % (5617)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.56 % (5601)Refutation found. Thanks to Tanya!
% 0.21/0.56 % SZS status Theorem for theBenchmark
% 0.21/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56 % (5601)------------------------------
% 0.21/0.56 % (5601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56 % (5601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.56 % (5601)Termination reason: Refutation
% 0.21/0.56
% 0.21/0.56 % (5601)Memory used [KB]: 5500
% 0.21/0.56 % (5601)Time elapsed: 0.135 s
% 0.21/0.56 % (5601)Instructions burned: 4 (million)
% 0.21/0.56 % (5601)------------------------------
% 0.21/0.56 % (5601)------------------------------
% 0.21/0.56 % (5595)Success in time 0.208 s
%------------------------------------------------------------------------------