TSTP Solution File: SEU061+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU061+1 : 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 : n027.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 18:31:51 EDT 2022
% Result : Theorem 1.76s 0.58s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 102 ( 15 unt; 0 def)
% Number of atoms : 380 ( 97 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 445 ( 167 ~; 181 |; 63 &)
% ( 16 <=>; 17 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 223 ( 179 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f514,plain,
$false,
inference(subsumption_resolution,[],[f513,f211]) ).
fof(f211,plain,
in(sK11,sF21),
inference(superposition,[],[f201,f206]) ).
fof(f206,plain,
singleton(sK11) = sF21,
introduced(function_definition,[]) ).
fof(f201,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f200]) ).
fof(f200,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( sK9(X0,X1) != X1
| ~ in(sK9(X0,X1),X0) )
& ( sK9(X0,X1) = X1
| in(sK9(X0,X1),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) )
=> ( ( sK9(X0,X1) != X1
| ~ in(sK9(X0,X1),X0) )
& ( sK9(X0,X1) = X1
| in(sK9(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) ) ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> X1 = X2 )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f513,plain,
~ in(sK11,sF21),
inference(resolution,[],[f509,f461]) ).
fof(f461,plain,
in(sK11,sF23),
inference(trivial_inequality_removal,[],[f428]) ).
fof(f428,plain,
( in(sK11,sF23)
| empty_set != empty_set ),
inference(backward_demodulation,[],[f210,f426]) ).
fof(f426,plain,
empty_set = sF22,
inference(subsumption_resolution,[],[f424,f133]) ).
fof(f133,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f424,plain,
( empty_set = sF22
| empty(sF22) ),
inference(resolution,[],[f412,f209]) ).
fof(f209,plain,
( ~ in(sK11,sF23)
| empty_set = sF22 ),
inference(definition_folding,[],[f171,f208,f207,f206]) ).
fof(f207,plain,
relation_inverse_image(sK12,sF21) = sF22,
introduced(function_definition,[]) ).
fof(f208,plain,
sF23 = relation_rng(sK12),
introduced(function_definition,[]) ).
fof(f171,plain,
( empty_set = relation_inverse_image(sK12,singleton(sK11))
| ~ in(sK11,relation_rng(sK12)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( relation(sK12)
& ( empty_set = relation_inverse_image(sK12,singleton(sK11))
| ~ in(sK11,relation_rng(sK12)) )
& ( empty_set != relation_inverse_image(sK12,singleton(sK11))
| in(sK11,relation_rng(sK12)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f111,f112]) ).
fof(f112,plain,
( ? [X0,X1] :
( relation(X1)
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) )
=> ( relation(sK12)
& ( empty_set = relation_inverse_image(sK12,singleton(sK11))
| ~ in(sK11,relation_rng(sK12)) )
& ( empty_set != relation_inverse_image(sK12,singleton(sK11))
| in(sK11,relation_rng(sK12)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
? [X0,X1] :
( relation(X1)
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
? [X1,X0] :
( relation(X0)
& ( empty_set = relation_inverse_image(X0,singleton(X1))
| ~ in(X1,relation_rng(X0)) )
& ( empty_set != relation_inverse_image(X0,singleton(X1))
| in(X1,relation_rng(X0)) ) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
? [X1,X0] :
( relation(X0)
& ( empty_set = relation_inverse_image(X0,singleton(X1))
| ~ in(X1,relation_rng(X0)) )
& ( empty_set != relation_inverse_image(X0,singleton(X1))
| in(X1,relation_rng(X0)) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
? [X1,X0] :
( relation(X0)
& ( in(X1,relation_rng(X0))
<~> empty_set != relation_inverse_image(X0,singleton(X1)) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
~ ! [X1,X0] :
( relation(X0)
=> ( empty_set != relation_inverse_image(X0,singleton(X1))
<=> in(X1,relation_rng(X0)) ) ),
inference(rectify,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X1,X0] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X1,X0] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f412,plain,
( in(sK11,sF23)
| empty(sF22) ),
inference(subsumption_resolution,[],[f411,f210]) ).
fof(f411,plain,
( empty_set = sF22
| in(sK11,sF23)
| empty(sF22) ),
inference(superposition,[],[f408,f341]) ).
fof(f341,plain,
( sK11 = sK15(sK12,sF21,sK1(sF22))
| empty_set = sF22 ),
inference(resolution,[],[f334,f133]) ).
fof(f334,plain,
( empty(sF22)
| sK11 = sK15(sK12,sF21,sK1(sF22)) ),
inference(resolution,[],[f326,f254]) ).
fof(f254,plain,
! [X5] :
( in(sK1(X5),X5)
| empty(X5) ),
inference(resolution,[],[f143,f132]) ).
fof(f132,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f143,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( in(X1,X0)
| empty(X0)
| ~ element(X1,X0) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
! [X1,X0] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f326,plain,
! [X0] :
( ~ in(X0,sF22)
| sK15(sK12,sF21,X0) = sK11 ),
inference(resolution,[],[f325,f248]) ).
fof(f248,plain,
! [X0] :
( ~ in(X0,sF21)
| sK11 = X0 ),
inference(superposition,[],[f202,f206]) ).
fof(f202,plain,
! [X2,X1] :
( ~ in(X2,singleton(X1))
| X1 = X2 ),
inference(equality_resolution,[],[f155]) ).
fof(f155,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f325,plain,
! [X0] :
( in(sK15(sK12,sF21,X0),sF21)
| ~ in(X0,sF22) ),
inference(subsumption_resolution,[],[f324,f172]) ).
fof(f172,plain,
relation(sK12),
inference(cnf_transformation,[],[f113]) ).
fof(f324,plain,
! [X0] :
( ~ relation(sK12)
| in(sK15(sK12,sF21,X0),sF21)
| ~ in(X0,sF22) ),
inference(superposition,[],[f204,f207]) ).
fof(f204,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_inverse_image(X0,X1))
| in(sK15(X0,X1,X6),X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f174]) ).
fof(f174,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| in(sK15(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(sK13(X0,X1,X2),X2)
| ! [X4] :
( ~ in(ordered_pair(sK13(X0,X1,X2),X4),X0)
| ~ in(X4,X1) ) )
& ( in(sK13(X0,X1,X2),X2)
| ( in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X0)
& in(sK14(X0,X1,X2),X1) ) ) ) )
& ( ! [X6] :
( ( ( in(ordered_pair(X6,sK15(X0,X1,X6)),X0)
& in(sK15(X0,X1,X6),X1) )
| ~ in(X6,X2) )
& ( in(X6,X2)
| ! [X8] :
( ~ in(ordered_pair(X6,X8),X0)
| ~ in(X8,X1) ) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f115,f118,f117,f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) ) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X2)
| ! [X4] :
( ~ in(ordered_pair(sK13(X0,X1,X2),X4),X0)
| ~ in(X4,X1) ) )
& ( in(sK13(X0,X1,X2),X2)
| ? [X5] :
( in(ordered_pair(sK13(X0,X1,X2),X5),X0)
& in(X5,X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(ordered_pair(sK13(X0,X1,X2),X5),X0)
& in(X5,X1) )
=> ( in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X0)
& in(sK14(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0,X1,X6] :
( ? [X7] :
( in(ordered_pair(X6,X7),X0)
& in(X7,X1) )
=> ( in(ordered_pair(X6,sK15(X0,X1,X6)),X0)
& in(sK15(X0,X1,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) ) ) ) )
& ( ! [X6] :
( ( ? [X7] :
( in(ordered_pair(X6,X7),X0)
& in(X7,X1) )
| ~ in(X6,X2) )
& ( in(X6,X2)
| ! [X8] :
( ~ in(ordered_pair(X6,X8),X0)
| ~ in(X8,X1) ) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(rectify,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) )
& ( ! [X3] :
( ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) ) )
| relation_inverse_image(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
<=> in(X3,X2) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
<=> in(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f408,plain,
( in(sK15(sK12,sF21,sK1(sF22)),sF23)
| empty(sF22) ),
inference(forward_demodulation,[],[f407,f208]) ).
fof(f407,plain,
( empty(sF22)
| in(sK15(sK12,sF21,sK1(sF22)),relation_rng(sK12)) ),
inference(subsumption_resolution,[],[f401,f172]) ).
fof(f401,plain,
( ~ relation(sK12)
| empty(sF22)
| in(sK15(sK12,sF21,sK1(sF22)),relation_rng(sK12)) ),
inference(resolution,[],[f364,f198]) ).
fof(f198,plain,
! [X0,X7,X5] :
( ~ in(ordered_pair(X7,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X7,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X7,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ~ in(sK2(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK2(X0,X1)),X0) )
& ( in(sK2(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0) ) ) )
& ( ! [X5] :
( ( in(ordered_pair(sK4(X0,X5),X5),X0)
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] : ~ in(ordered_pair(X7,X5),X0) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f83,f86,f85,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) ) )
=> ( ( ~ in(sK2(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK2(X0,X1)),X0) )
& ( in(sK2(X0,X1),X1)
| ? [X4] : in(ordered_pair(X4,sK2(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK2(X0,X1)),X0)
=> in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X5] :
( ? [X6] : in(ordered_pair(X6,X5),X0)
=> in(ordered_pair(sK4(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) ) ) )
& ( ! [X5] :
( ( ? [X6] : in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] : ~ in(ordered_pair(X7,X5),X0) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [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) ) ) )
& ( ! [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(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( ? [X3] : in(ordered_pair(X3,X2),X0)
<=> in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( ? [X3] : in(ordered_pair(X3,X2),X0)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f364,plain,
( in(ordered_pair(sK1(sF22),sK15(sK12,sF21,sK1(sF22))),sK12)
| empty(sF22) ),
inference(resolution,[],[f357,f254]) ).
fof(f357,plain,
! [X0] :
( ~ in(X0,sF22)
| in(ordered_pair(X0,sK15(sK12,sF21,X0)),sK12) ),
inference(subsumption_resolution,[],[f356,f172]) ).
fof(f356,plain,
! [X0] :
( ~ relation(sK12)
| ~ in(X0,sF22)
| in(ordered_pair(X0,sK15(sK12,sF21,X0)),sK12) ),
inference(superposition,[],[f203,f207]) ).
fof(f203,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_inverse_image(X0,X1))
| in(ordered_pair(X6,sK15(X0,X1,X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| in(ordered_pair(X6,sK15(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f119]) ).
fof(f210,plain,
( empty_set != sF22
| in(sK11,sF23) ),
inference(definition_folding,[],[f170,f208,f207,f206]) ).
fof(f170,plain,
( empty_set != relation_inverse_image(sK12,singleton(sK11))
| in(sK11,relation_rng(sK12)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f509,plain,
! [X0] :
( ~ in(X0,sF23)
| ~ in(X0,sF21) ),
inference(subsumption_resolution,[],[f506,f199]) ).
fof(f199,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f138]) ).
fof(f138,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( empty_set = X0
| in(sK5(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f89,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f506,plain,
! [X0] :
( in(sK4(sK12,X0),empty_set)
| ~ in(X0,sF21)
| ~ in(X0,sF23) ),
inference(superposition,[],[f361,f427]) ).
fof(f427,plain,
empty_set = relation_inverse_image(sK12,sF21),
inference(backward_demodulation,[],[f207,f426]) ).
fof(f361,plain,
! [X0,X1] :
( in(sK4(sK12,X0),relation_inverse_image(sK12,X1))
| ~ in(X0,sF23)
| ~ in(X0,X1) ),
inference(subsumption_resolution,[],[f358,f172]) ).
fof(f358,plain,
! [X0,X1] :
( ~ relation(sK12)
| ~ in(X0,X1)
| in(sK4(sK12,X0),relation_inverse_image(sK12,X1))
| ~ in(X0,sF23) ),
inference(resolution,[],[f205,f317]) ).
fof(f317,plain,
! [X0] :
( in(ordered_pair(sK4(sK12,X0),X0),sK12)
| ~ in(X0,sF23) ),
inference(subsumption_resolution,[],[f315,f172]) ).
fof(f315,plain,
! [X0] :
( ~ in(X0,sF23)
| in(ordered_pair(sK4(sK12,X0),X0),sK12)
| ~ relation(sK12) ),
inference(superposition,[],[f197,f208]) ).
fof(f197,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| in(ordered_pair(sK4(X0,X5),X5),X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK4(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f205,plain,
! [X0,X1,X8,X6] :
( ~ in(ordered_pair(X6,X8),X0)
| ~ in(X8,X1)
| ~ relation(X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,plain,
! [X2,X0,X1,X8,X6] :
( ~ relation(X0)
| in(X6,X2)
| ~ in(ordered_pair(X6,X8),X0)
| ~ in(X8,X1)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:51:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % (2193)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)
% 0.19/0.50 % (2184)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)
% 0.19/0.50 % (2173)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (2175)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)
% 0.19/0.51 % (2174)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 TRYING [1]
% 0.19/0.51 TRYING [2]
% 0.19/0.51 % (2170)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 % (2190)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 % (2171)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)
% 0.19/0.52 % (2169)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 % (2179)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 % (2197)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 % (2170)Refutation not found, incomplete strategy% (2170)------------------------------
% 0.19/0.52 % (2170)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (2170)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (2170)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52
% 0.19/0.52 % (2170)Memory used [KB]: 5628
% 0.19/0.52 % (2170)Time elapsed: 0.129 s
% 0.19/0.52 % (2170)Instructions burned: 9 (million)
% 0.19/0.52 % (2170)------------------------------
% 0.19/0.52 % (2170)------------------------------
% 0.19/0.52 % (2189)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)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 % (2196)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52 TRYING [2]
% 0.19/0.52 TRYING [3]
% 0.19/0.52 % (2181)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 % (2200)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)
% 0.19/0.52 % (2172)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)
% 0.19/0.53 % (2198)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)
% 0.19/0.53 % (2186)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)
% 0.19/0.53 % (2194)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)
% 0.19/0.53 % (2191)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 % (2188)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 % (2195)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.53 % (2185)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)
% 0.19/0.53 % (2187)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.53 % (2183)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54 % (2177)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54 % (2199)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.54 % (2180)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)
% 0.19/0.54 TRYING [1]
% 0.19/0.54 % (2177)Instruction limit reached!
% 0.19/0.54 % (2177)------------------------------
% 0.19/0.54 % (2177)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (2177)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (2177)Termination reason: Unknown
% 0.19/0.54 % (2177)Termination phase: Blocked clause elimination
% 0.19/0.54
% 0.19/0.54 % (2177)Memory used [KB]: 1023
% 0.19/0.54 % (2177)Time elapsed: 0.004 s
% 0.19/0.54 % (2177)Instructions burned: 3 (million)
% 0.19/0.54 % (2177)------------------------------
% 0.19/0.54 % (2177)------------------------------
% 0.19/0.54 % (2176)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54 % (2178)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)
% 0.19/0.54 % (2176)Instruction limit reached!
% 0.19/0.54 % (2176)------------------------------
% 0.19/0.54 % (2176)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (2176)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (2176)Termination reason: Unknown
% 0.19/0.54 % (2176)Termination phase: Saturation
% 0.19/0.54
% 0.19/0.54 % (2176)Memory used [KB]: 5500
% 0.19/0.54 % (2176)Time elapsed: 0.154 s
% 0.19/0.54 % (2176)Instructions burned: 8 (million)
% 0.19/0.54 % (2176)------------------------------
% 0.19/0.54 % (2176)------------------------------
% 0.19/0.54 TRYING [3]
% 1.61/0.56 TRYING [2]
% 1.61/0.56 % (2185)First to succeed.
% 1.61/0.56 TRYING [3]
% 1.61/0.57 % (2175)Instruction limit reached!
% 1.61/0.57 % (2175)------------------------------
% 1.61/0.57 % (2175)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.61/0.57 % (2175)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.61/0.57 % (2175)Termination reason: Unknown
% 1.61/0.57 % (2175)Termination phase: Finite model building SAT solving
% 1.61/0.57
% 1.61/0.57 % (2175)Memory used [KB]: 7675
% 1.61/0.57 % (2175)Time elapsed: 0.103 s
% 1.61/0.57 % (2175)Instructions burned: 51 (million)
% 1.61/0.57 % (2175)------------------------------
% 1.61/0.57 % (2175)------------------------------
% 1.61/0.57 % (2171)Instruction limit reached!
% 1.61/0.57 % (2171)------------------------------
% 1.61/0.57 % (2171)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.61/0.57 % (2171)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.61/0.57 % (2171)Termination reason: Unknown
% 1.61/0.57 % (2171)Termination phase: Saturation
% 1.61/0.57
% 1.61/0.57 % (2171)Memory used [KB]: 1407
% 1.61/0.57 % (2171)Time elapsed: 0.181 s
% 1.61/0.57 % (2171)Instructions burned: 37 (million)
% 1.61/0.57 % (2171)------------------------------
% 1.61/0.57 % (2171)------------------------------
% 1.76/0.58 % (2189)Also succeeded, but the first one will report.
% 1.76/0.58 % (2185)Refutation found. Thanks to Tanya!
% 1.76/0.58 % SZS status Theorem for theBenchmark
% 1.76/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.76/0.58 % (2185)------------------------------
% 1.76/0.58 % (2185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.76/0.58 % (2185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.76/0.58 % (2185)Termination reason: Refutation
% 1.76/0.58
% 1.76/0.58 % (2185)Memory used [KB]: 1279
% 1.76/0.58 % (2185)Time elapsed: 0.176 s
% 1.76/0.58 % (2185)Instructions burned: 19 (million)
% 1.76/0.58 % (2185)------------------------------
% 1.76/0.58 % (2185)------------------------------
% 1.76/0.58 % (2168)Success in time 0.225 s
%------------------------------------------------------------------------------