TSTP Solution File: SEU266+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU266+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 : n029.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 18:32:54 EDT 2022
% Result : Theorem 1.99s 0.61s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of formulae : 132 ( 21 unt; 0 def)
% Number of atoms : 384 ( 78 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 404 ( 152 ~; 159 |; 52 &)
% ( 11 <=>; 28 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 287 ( 241 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f653,plain,
$false,
inference(subsumption_resolution,[],[f651,f580]) ).
fof(f580,plain,
empty_set != sF14,
inference(subsumption_resolution,[],[f579,f157]) ).
fof(f157,plain,
! [X1] : ~ in(X1,empty_set),
inference(resolution,[],[f115,f137]) ).
fof(f137,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f115,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X1,X0] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f579,plain,
( empty_set != sF14
| in(sK3,empty_set) ),
inference(forward_demodulation,[],[f459,f455]) ).
fof(f455,plain,
empty_set = sK0,
inference(subsumption_resolution,[],[f454,f400]) ).
fof(f400,plain,
( sF14 = sK0
| empty_set = sK0 ),
inference(resolution,[],[f397,f120]) ).
fof(f120,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f397,plain,
( empty(sK0)
| sF14 = sK0 ),
inference(subsumption_resolution,[],[f396,f365]) ).
fof(f365,plain,
( ~ in(sK7(sK0,sF14),sK0)
| sF14 = sK0 ),
inference(duplicate_literal_removal,[],[f362]) ).
fof(f362,plain,
( sF14 = sK0
| sF14 = sK0
| ~ in(sK7(sK0,sF14),sK0) ),
inference(resolution,[],[f360,f126]) ).
fof(f126,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| X0 = X1
| ~ in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( ~ in(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f90,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ in(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X1)
<~> in(X2,X0) )
| X0 = X1 ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
<=> in(X2,X0) )
=> X0 = X1 ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f360,plain,
( in(sK7(sK0,sF14),sF14)
| sF14 = sK0 ),
inference(duplicate_literal_removal,[],[f357]) ).
fof(f357,plain,
( sF14 = sK0
| in(sK7(sK0,sF14),sF14)
| sF14 = sK0 ),
inference(factoring,[],[f246]) ).
fof(f246,plain,
! [X0] :
( in(sK7(sK0,X0),X0)
| in(sK7(sK0,X0),sF14)
| sK0 = X0
| sF14 = sK0 ),
inference(resolution,[],[f226,f125]) ).
fof(f125,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f226,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sF14)
| sF14 = sK0 ),
inference(backward_demodulation,[],[f216,f225]) ).
fof(f225,plain,
relation_rng(sK2) = sF14,
inference(forward_demodulation,[],[f223,f152]) ).
fof(f152,plain,
sF14 = relation_rng_as_subset(sK1,sK0,sK2),
introduced(function_definition,[]) ).
fof(f223,plain,
relation_rng(sK2) = relation_rng_as_subset(sK1,sK0,sK2),
inference(resolution,[],[f146,f165]) ).
fof(f165,plain,
relation_of2(sK2,sK1,sK0),
inference(resolution,[],[f113,f119]) ).
fof(f119,plain,
relation_of2_as_subset(sK2,sK1,sK0),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( relation_of2_as_subset(sK2,sK1,sK0)
& ( ( ! [X4] : ~ in(ordered_pair(X4,sK3),sK2)
& in(sK3,sK0) )
| sK0 != relation_rng_as_subset(sK1,sK0,sK2) )
& ( ! [X5] :
( in(ordered_pair(sK4(X5),X5),sK2)
| ~ in(X5,sK0) )
| sK0 = relation_rng_as_subset(sK1,sK0,sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f79,f82,f81,f80]) ).
fof(f80,plain,
( ? [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X0) )
| relation_rng_as_subset(X1,X0,X2) != X0 )
& ( ! [X5] :
( ? [X6] : in(ordered_pair(X6,X5),X2)
| ~ in(X5,X0) )
| relation_rng_as_subset(X1,X0,X2) = X0 ) )
=> ( relation_of2_as_subset(sK2,sK1,sK0)
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),sK2)
& in(X3,sK0) )
| sK0 != relation_rng_as_subset(sK1,sK0,sK2) )
& ( ! [X5] :
( ? [X6] : in(ordered_pair(X6,X5),sK2)
| ~ in(X5,sK0) )
| sK0 = relation_rng_as_subset(sK1,sK0,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),sK2)
& in(X3,sK0) )
=> ( ! [X4] : ~ in(ordered_pair(X4,sK3),sK2)
& in(sK3,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X5] :
( ? [X6] : in(ordered_pair(X6,X5),sK2)
=> in(ordered_pair(sK4(X5),X5),sK2) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X0) )
| relation_rng_as_subset(X1,X0,X2) != X0 )
& ( ! [X5] :
( ? [X6] : in(ordered_pair(X6,X5),X2)
| ~ in(X5,X0) )
| relation_rng_as_subset(X1,X0,X2) = X0 ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X0,X1,X2)
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X0)
& in(X3,X2) )
| relation_rng_as_subset(X1,X2,X0) != X2 )
& ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X0)
| ~ in(X3,X2) )
| relation_rng_as_subset(X1,X2,X0) = X2 ) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X0,X1,X2)
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X0)
& in(X3,X2) )
| relation_rng_as_subset(X1,X2,X0) != X2 )
& ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X0)
| ~ in(X3,X2) )
| relation_rng_as_subset(X1,X2,X0) = X2 ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X0,X1,X2)
& ( relation_rng_as_subset(X1,X2,X0) = X2
<~> ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X0)
| ~ in(X3,X2) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
~ ! [X1,X2,X0] :
( relation_of2_as_subset(X0,X1,X2)
=> ( relation_rng_as_subset(X1,X2,X0) = X2
<=> ! [X3] :
~ ( in(X3,X2)
& ! [X4] : ~ in(ordered_pair(X4,X3),X0) ) ) ),
inference(rectify,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
=> ( relation_rng_as_subset(X0,X1,X2) = X1
<=> ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
=> ( relation_rng_as_subset(X0,X1,X2) = X1
<=> ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X2,X1)
| relation_of2(X0,X2,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X0,X2,X1)
| ~ relation_of2(X0,X2,X1) )
& ( relation_of2(X0,X2,X1)
| ~ relation_of2_as_subset(X0,X2,X1) ) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X0,X2,X1] :
( ( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) )
& ( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X2,X1] :
( relation_of2_as_subset(X0,X1,X2)
<=> relation_of2(X0,X1,X2) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
<=> relation_of2_as_subset(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( relation_rng_as_subset(X0,X1,X2) = relation_rng(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X2,X1,X0] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f216,plain,
! [X0] :
( sF14 = sK0
| ~ in(X0,sK0)
| in(X0,relation_rng(sK2)) ),
inference(subsumption_resolution,[],[f215,f198]) ).
fof(f198,plain,
relation(sK2),
inference(resolution,[],[f182,f119]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f128,f130]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
! [X1,X2,X0] :
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X1,X2,X0] :
( element(X1,powerset(cartesian_product2(X2,X0)))
=> relation(X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f128,plain,
! [X2,X0,X1] :
( element(X1,powerset(cartesian_product2(X2,X0)))
| ~ relation_of2_as_subset(X1,X2,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X1,X2,X0)
| element(X1,powerset(cartesian_product2(X2,X0))) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X1,X2,X0] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X2,X1,X0] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f215,plain,
! [X0] :
( ~ in(X0,sK0)
| sF14 = sK0
| in(X0,relation_rng(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f141,f155]) ).
fof(f155,plain,
! [X5] :
( in(ordered_pair(sK4(X5),X5),sK2)
| ~ in(X5,sK0)
| sF14 = sK0 ),
inference(definition_folding,[],[f116,f152]) ).
fof(f116,plain,
! [X5] :
( in(ordered_pair(sK4(X5),X5),sK2)
| ~ in(X5,sK0)
| sK0 = relation_rng_as_subset(sK1,sK0,sK2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X2),X1)
| in(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X1))
& in(X2,relation_rng(X1)) )
| ~ in(ordered_pair(X0,X2),X1)
| ~ relation(X1) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X2,X1,X0] :
( ( in(X0,relation_dom(X1))
& in(X2,relation_rng(X1)) )
| ~ in(ordered_pair(X0,X2),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X2,X1,X0] :
( relation(X1)
=> ( in(ordered_pair(X0,X2),X1)
=> ( in(X0,relation_dom(X1))
& in(X2,relation_rng(X1)) ) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X2,X1] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f396,plain,
( sF14 = sK0
| in(sK7(sK0,sF14),sK0)
| empty(sK0) ),
inference(resolution,[],[f392,f143]) ).
fof(f143,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X1,X0] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X1,X0] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f392,plain,
( element(sK7(sK0,sF14),sK0)
| sF14 = sK0 ),
inference(resolution,[],[f363,f214]) ).
fof(f214,plain,
element(sF14,powerset(sK0)),
inference(forward_demodulation,[],[f212,f152]) ).
fof(f212,plain,
element(relation_rng_as_subset(sK1,sK0,sK2),powerset(sK0)),
inference(resolution,[],[f136,f165]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ relation_of2(X0,X2,X1)
| element(relation_rng_as_subset(X2,X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( element(relation_rng_as_subset(X2,X1,X0),powerset(X1))
| ~ relation_of2(X0,X2,X1) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X2,X0,X1] :
( element(relation_rng_as_subset(X1,X0,X2),powerset(X0))
| ~ relation_of2(X2,X1,X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X2,X1,X0] :
( relation_of2(X2,X1,X0)
=> element(relation_rng_as_subset(X1,X0,X2),powerset(X0)) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X1,X0,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f363,plain,
! [X0] :
( ~ element(sF14,powerset(X0))
| element(sK7(sK0,sF14),X0)
| sF14 = sK0 ),
inference(resolution,[],[f360,f144]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X0,X2,X1] :
( ~ in(X1,X0)
| element(X1,X2)
| ~ element(X0,powerset(X2)) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X1,X0,X2] :
( element(X1,X2)
| ~ element(X0,powerset(X2))
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X1,X0,X2] :
( ( element(X0,powerset(X2))
& in(X1,X0) )
=> element(X1,X2) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X1,X0,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f454,plain,
( sF14 != sK0
| empty_set = sK0 ),
inference(resolution,[],[f453,f154]) ).
fof(f154,plain,
( in(sK3,sK0)
| sF14 != sK0 ),
inference(definition_folding,[],[f117,f152]) ).
fof(f117,plain,
( in(sK3,sK0)
| sK0 != relation_rng_as_subset(sK1,sK0,sK2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f453,plain,
( ~ in(sK3,sK0)
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f452]) ).
fof(f452,plain,
( ~ in(sK3,sK0)
| empty_set = sK0
| empty_set = sK0 ),
inference(superposition,[],[f451,f400]) ).
fof(f451,plain,
( ~ in(sK3,sF14)
| empty_set = sK0 ),
inference(resolution,[],[f427,f243]) ).
fof(f243,plain,
! [X6] :
( in(ordered_pair(sK9(sK2,X6),X6),sK2)
| ~ in(X6,sF14) ),
inference(forward_demodulation,[],[f242,f225]) ).
fof(f242,plain,
! [X6] :
( in(ordered_pair(sK9(sK2,X6),X6),sK2)
| ~ in(X6,relation_rng(sK2)) ),
inference(resolution,[],[f151,f198]) ).
fof(f151,plain,
! [X2,X0] :
( ~ relation(X0)
| in(ordered_pair(sK9(X0,X2),X2),X0)
| ~ in(X2,relation_rng(X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK9(X0,X2),X2),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK9(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f99,f102,f101,f100]) ).
fof(f100,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK9(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f101,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,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK10(X0,X1)),X0)
=> in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0] :
( ~ relation(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) ) ) ) ) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ~ relation(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) ) ) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,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(f427,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK3),sK2)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f402]) ).
fof(f402,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK3),sK2)
| sK0 != sK0
| empty_set = sK0 ),
inference(superposition,[],[f153,f400]) ).
fof(f153,plain,
! [X4] :
( sF14 != sK0
| ~ in(ordered_pair(X4,sK3),sK2) ),
inference(definition_folding,[],[f118,f152]) ).
fof(f118,plain,
! [X4] :
( ~ in(ordered_pair(X4,sK3),sK2)
| sK0 != relation_rng_as_subset(sK1,sK0,sK2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f459,plain,
( in(sK3,sK0)
| empty_set != sF14 ),
inference(backward_demodulation,[],[f154,f455]) ).
fof(f651,plain,
empty_set = sF14,
inference(resolution,[],[f646,f120]) ).
fof(f646,plain,
empty(sF14),
inference(resolution,[],[f642,f171]) ).
fof(f171,plain,
! [X0] :
( in(sK6(X0),X0)
| empty(X0) ),
inference(resolution,[],[f143,f124]) ).
fof(f124,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f642,plain,
! [X0] : ~ in(X0,sF14),
inference(resolution,[],[f466,f177]) ).
fof(f177,plain,
! [X0,X1] :
( ~ element(X0,powerset(empty_set))
| ~ in(X1,X0) ),
inference(resolution,[],[f129,f137]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ empty(X0)
| ~ element(X1,powerset(X0))
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ element(X1,powerset(X0))
| ~ empty(X0) ),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X1,X0,X2] :
( ~ in(X2,X0)
| ~ element(X0,powerset(X1))
| ~ empty(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X2,X1,X0] :
~ ( element(X0,powerset(X1))
& empty(X1)
& in(X2,X0) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X1,X2,X0] :
~ ( in(X0,X1)
& empty(X2)
& element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f466,plain,
element(sF14,powerset(empty_set)),
inference(backward_demodulation,[],[f214,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU266+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:10:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (17620)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)
% 0.20/0.51 % (17631)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (17627)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)
% 0.20/0.52 % (17618)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)
% 0.20/0.52 % (17621)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)
% 0.20/0.52 % (17624)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)
% 0.20/0.52 % (17639)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53 TRYING [1]
% 0.20/0.53 % (17629)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)
% 0.20/0.53 % (17622)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (17619)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)
% 0.20/0.53 % (17626)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53 % (17623)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)
% 0.20/0.53 % (17630)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.53 % (17640)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)
% 0.20/0.53 % (17641)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)
% 0.20/0.53 TRYING [1]
% 0.20/0.54 % (17635)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (17633)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)
% 0.20/0.54 % (17626)Instruction limit reached!
% 0.20/0.54 % (17626)------------------------------
% 0.20/0.54 % (17626)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (17645)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)
% 0.20/0.54 % (17647)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)
% 0.20/0.54 % (17626)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (17626)Termination reason: Unknown
% 0.20/0.54 % (17626)Termination phase: Preprocessing 3
% 0.20/0.54
% 0.20/0.54 % (17626)Memory used [KB]: 895
% 0.20/0.54 % (17626)Time elapsed: 0.004 s
% 0.20/0.54 % (17626)Instructions burned: 2 (million)
% 0.20/0.54 % (17626)------------------------------
% 0.20/0.54 % (17626)------------------------------
% 0.20/0.54 % (17637)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)
% 0.20/0.54 % (17628)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (17632)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)
% 0.20/0.54 % (17646)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (17619)Refutation not found, incomplete strategy% (17619)------------------------------
% 0.20/0.54 % (17619)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 TRYING [3]
% 0.20/0.54 TRYING [1]
% 0.20/0.54 % (17643)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.54 TRYING [2]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 % (17634)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)
% 0.20/0.55 % (17619)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (17619)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.55
% 0.20/0.55 % (17619)Memory used [KB]: 5628
% 0.20/0.55 % (17619)Time elapsed: 0.136 s
% 0.20/0.55 % (17619)Instructions burned: 7 (million)
% 0.20/0.55 % (17619)------------------------------
% 0.20/0.55 % (17619)------------------------------
% 0.20/0.55 % (17642)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55 % (17638)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)
% 0.20/0.55 TRYING [3]
% 0.20/0.55 % (17636)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (17644)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)
% 0.20/0.55 % (17625)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.56 % (17625)Instruction limit reached!
% 0.20/0.56 % (17625)------------------------------
% 0.20/0.56 % (17625)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (17625)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (17625)Termination reason: Unknown
% 0.20/0.56 % (17625)Termination phase: Saturation
% 0.20/0.56
% 0.20/0.56 % (17625)Memory used [KB]: 5628
% 0.20/0.56 % (17625)Time elapsed: 0.122 s
% 0.20/0.56 % (17625)Instructions burned: 7 (million)
% 0.20/0.56 % (17625)------------------------------
% 0.20/0.56 % (17625)------------------------------
% 0.20/0.56 TRYING [3]
% 0.20/0.56 % (17620)Instruction limit reached!
% 0.20/0.56 % (17620)------------------------------
% 0.20/0.56 % (17620)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (17620)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (17620)Termination reason: Unknown
% 0.20/0.56 % (17620)Termination phase: Saturation
% 0.20/0.56
% 0.20/0.56 % (17620)Memory used [KB]: 1407
% 0.20/0.56 % (17620)Time elapsed: 0.157 s
% 0.20/0.56 % (17620)Instructions burned: 38 (million)
% 0.20/0.56 % (17620)------------------------------
% 0.20/0.56 % (17620)------------------------------
% 1.81/0.59 % (17645)First to succeed.
% 1.81/0.59 % (17627)Instruction limit reached!
% 1.81/0.59 % (17627)------------------------------
% 1.81/0.59 % (17627)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.60 % (17621)Instruction limit reached!
% 1.81/0.60 % (17621)------------------------------
% 1.81/0.60 % (17621)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.60 % (17621)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.60 % (17621)Termination reason: Unknown
% 1.81/0.60 % (17621)Termination phase: Saturation
% 1.81/0.60
% 1.81/0.60 % (17621)Memory used [KB]: 6396
% 1.81/0.60 % (17621)Time elapsed: 0.192 s
% 1.81/0.60 % (17621)Instructions burned: 51 (million)
% 1.81/0.60 % (17621)------------------------------
% 1.81/0.60 % (17621)------------------------------
% 1.81/0.60 % (17627)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.60 % (17627)Termination reason: Unknown
% 1.81/0.60 % (17627)Termination phase: Saturation
% 1.81/0.60
% 1.81/0.60 % (17627)Memory used [KB]: 1407
% 1.81/0.60 % (17627)Time elapsed: 0.200 s
% 1.81/0.60 % (17627)Instructions burned: 51 (million)
% 1.81/0.60 % (17627)------------------------------
% 1.81/0.60 % (17627)------------------------------
% 1.81/0.60 % (17624)Instruction limit reached!
% 1.81/0.60 % (17624)------------------------------
% 1.81/0.60 % (17624)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.60 % (17624)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.60 % (17624)Termination reason: Unknown
% 1.81/0.60 % (17624)Termination phase: Finite model building SAT solving
% 1.81/0.60
% 1.81/0.60 % (17624)Memory used [KB]: 6780
% 1.81/0.60 % (17624)Time elapsed: 0.141 s
% 1.81/0.60 % (17624)Instructions burned: 51 (million)
% 1.81/0.60 % (17624)------------------------------
% 1.81/0.60 % (17624)------------------------------
% 1.99/0.61 % (17645)Refutation found. Thanks to Tanya!
% 1.99/0.61 % SZS status Theorem for theBenchmark
% 1.99/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.62 % (17645)------------------------------
% 1.99/0.62 % (17645)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.99/0.62 % (17645)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.99/0.62 % (17645)Termination reason: Refutation
% 1.99/0.62
% 1.99/0.62 % (17645)Memory used [KB]: 1279
% 1.99/0.62 % (17645)Time elapsed: 0.184 s
% 1.99/0.62 % (17645)Instructions burned: 28 (million)
% 1.99/0.62 % (17645)------------------------------
% 1.99/0.62 % (17645)------------------------------
% 1.99/0.62 % (17617)Success in time 0.258 s
%------------------------------------------------------------------------------