TSTP Solution File: SEU310+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU310+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 : n017.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 18:33:09 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 14 unt; 0 def)
% Number of atoms : 478 ( 74 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 568 ( 190 ~; 242 |; 114 &)
% ( 7 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 204 ( 149 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f418,plain,
$false,
inference(subsumption_resolution,[],[f416,f394]) ).
fof(f394,plain,
~ sP0(sK7,sK6),
inference(subsumption_resolution,[],[f393,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK2(X0,X1) = sK1(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( in(set_difference(cast_as_carrier_subset(X1),sK1(X0,X1)),X0)
& sK3(X0,X1) != sK1(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK3(X0,X1)),X0)
& sK2(X0,X1) = sK3(X0,X1)
& sK2(X0,X1) = sK1(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 != X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X3 = X4
& X2 = X3 )
=> ( in(set_difference(cast_as_carrier_subset(X1),sK1(X0,X1)),X0)
& sK3(X0,X1) != sK1(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK3(X0,X1)),X0)
& sK2(X0,X1) = sK3(X0,X1)
& sK2(X0,X1) = sK1(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 != X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X3 = X4
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X2,X4,X3] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 != X3
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X3 = X4
& X2 = X4 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2,X4,X3] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 != X3
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X3 = X4
& X2 = X4 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f393,plain,
( ~ sP0(sK7,sK6)
| sK2(sK7,sK6) != sK1(sK7,sK6) ),
inference(superposition,[],[f113,f391]) ).
fof(f391,plain,
sK3(sK7,sK6) = sK2(sK7,sK6),
inference(subsumption_resolution,[],[f389,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK2(X0,X1) = sK3(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f389,plain,
( sP0(sK7,sK6)
| sK3(sK7,sK6) = sK2(sK7,sK6) ),
inference(resolution,[],[f387,f362]) ).
fof(f362,plain,
( ~ in(sK8(sK4(sK6,sK7)),sF14)
| sP0(sK7,sK6) ),
inference(subsumption_resolution,[],[f358,f344]) ).
fof(f344,plain,
( in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| sP0(sK7,sK6) ),
inference(factoring,[],[f337]) ).
fof(f337,plain,
! [X0] :
( in(sK8(X0),X0)
| in(sK8(X0),sK4(sK6,sK7))
| sP0(sK7,sK6) ),
inference(subsumption_resolution,[],[f336,f187]) ).
fof(f187,plain,
! [X2] :
( in(sK8(X2),sF14)
| in(sK8(X2),X2) ),
inference(definition_folding,[],[f134,f181,f180]) ).
fof(f180,plain,
sF13 = the_carrier(sK6),
introduced(function_definition,[]) ).
fof(f181,plain,
sF14 = powerset(sF13),
introduced(function_definition,[]) ).
fof(f134,plain,
! [X2] :
( in(sK8(X2),powerset(the_carrier(sK6)))
| in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
( top_str(sK6)
& element(sK7,powerset(powerset(the_carrier(sK6))))
& ! [X2] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
| ~ in(sK8(X2),powerset(the_carrier(sK6)))
| ~ in(sK8(X2),X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
& in(sK8(X2),powerset(the_carrier(sK6))) )
| in(sK8(X2),X2) ) )
& topological_space(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f97,f99,f98]) ).
fof(f98,plain,
( ? [X0,X1] :
( top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0))))
& ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& topological_space(X0) )
=> ( top_str(sK6)
& element(sK7,powerset(powerset(the_carrier(sK6))))
& ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK6),X3),sK7)
| ~ in(X3,powerset(the_carrier(sK6)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK6),X3),sK7)
& in(X3,powerset(the_carrier(sK6))) )
| in(X3,X2) ) )
& topological_space(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK6),X3),sK7)
| ~ in(X3,powerset(the_carrier(sK6)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK6),X3),sK7)
& in(X3,powerset(the_carrier(sK6))) )
| in(X3,X2) ) )
=> ( ( ~ in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
| ~ in(sK8(X2),powerset(the_carrier(sK6)))
| ~ in(sK8(X2),X2) )
& ( ( in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
& in(sK8(X2),powerset(the_carrier(sK6))) )
| in(sK8(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
? [X0,X1] :
( top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0))))
& ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& topological_space(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
? [X0,X1] :
( top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0))))
& ! [X2] :
? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| ~ in(X3,X2) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| in(X3,X2) ) )
& topological_space(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
? [X0,X1] :
( top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0))))
& ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
? [X1,X0] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X1,X0] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
<=> in(X3,X2) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X1,X0] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f336,plain,
! [X0] :
( ~ in(sK8(X0),sF14)
| in(sK8(X0),sK4(sK6,sK7))
| sP0(sK7,sK6)
| in(sK8(X0),X0) ),
inference(subsumption_resolution,[],[f332,f183]) ).
fof(f183,plain,
element(sK7,sF15),
inference(definition_folding,[],[f137,f182,f181,f180]) ).
fof(f182,plain,
powerset(sF14) = sF15,
introduced(function_definition,[]) ).
fof(f137,plain,
element(sK7,powerset(powerset(the_carrier(sK6)))),
inference(cnf_transformation,[],[f100]) ).
fof(f332,plain,
! [X0] :
( ~ in(sK8(X0),sF14)
| in(sK8(X0),sK4(sK6,sK7))
| in(sK8(X0),X0)
| sP0(sK7,sK6)
| ~ element(sK7,sF15) ),
inference(resolution,[],[f328,f186]) ).
fof(f186,plain,
! [X2] :
( in(sK8(X2),X2)
| in(set_difference(sF16,sK8(X2)),sK7) ),
inference(definition_folding,[],[f135,f184]) ).
fof(f184,plain,
cast_as_carrier_subset(sK6) = sF16,
introduced(function_definition,[]) ).
fof(f135,plain,
! [X2] :
( in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
| in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f328,plain,
! [X0,X1] :
( ~ in(set_difference(sF16,X0),X1)
| in(X0,sK4(sK6,X1))
| ~ element(X1,sF15)
| ~ in(X0,sF14)
| sP0(X1,sK6) ),
inference(forward_demodulation,[],[f327,f181]) ).
fof(f327,plain,
! [X0,X1] :
( in(X0,sK4(sK6,X1))
| ~ in(X0,powerset(sF13))
| sP0(X1,sK6)
| ~ element(X1,sF15)
| ~ in(set_difference(sF16,X0),X1) ),
inference(forward_demodulation,[],[f326,f180]) ).
fof(f326,plain,
! [X0,X1] :
( in(X0,sK4(sK6,X1))
| sP0(X1,sK6)
| ~ element(X1,sF15)
| ~ in(X0,powerset(the_carrier(sK6)))
| ~ in(set_difference(sF16,X0),X1) ),
inference(forward_demodulation,[],[f325,f182]) ).
fof(f325,plain,
! [X0,X1] :
( ~ element(X1,powerset(sF14))
| ~ in(X0,powerset(the_carrier(sK6)))
| ~ in(set_difference(sF16,X0),X1)
| in(X0,sK4(sK6,X1))
| sP0(X1,sK6) ),
inference(forward_demodulation,[],[f324,f184]) ).
fof(f324,plain,
! [X0,X1] :
( sP0(X1,sK6)
| ~ in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| ~ element(X1,powerset(sF14))
| in(X0,sK4(sK6,X1))
| ~ in(X0,powerset(the_carrier(sK6))) ),
inference(forward_demodulation,[],[f323,f181]) ).
fof(f323,plain,
! [X0,X1] :
( sP0(X1,sK6)
| ~ element(X1,powerset(powerset(sF13)))
| in(X0,sK4(sK6,X1))
| ~ in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| ~ in(X0,powerset(the_carrier(sK6))) ),
inference(forward_demodulation,[],[f322,f180]) ).
fof(f322,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(sK6))))
| ~ in(X0,powerset(the_carrier(sK6)))
| in(X0,sK4(sK6,X1))
| ~ in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| sP0(X1,sK6) ),
inference(subsumption_resolution,[],[f321,f133]) ).
fof(f133,plain,
topological_space(sK6),
inference(cnf_transformation,[],[f100]) ).
fof(f321,plain,
! [X0,X1] :
( ~ in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| ~ topological_space(sK6)
| sP0(X1,sK6)
| ~ element(X1,powerset(powerset(the_carrier(sK6))))
| ~ in(X0,powerset(the_carrier(sK6)))
| in(X0,sK4(sK6,X1)) ),
inference(resolution,[],[f179,f138]) ).
fof(f138,plain,
top_str(sK6),
inference(cnf_transformation,[],[f100]) ).
fof(f179,plain,
! [X0,X1,X5] :
( ~ top_str(X0)
| in(X5,sK4(X0,X1))
| ~ in(X5,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X5),X1)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f115]) ).
fof(f115,plain,
! [X3,X0,X1,X5] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP0(X1,X0)
| in(X3,sK4(X0,X1))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X5,powerset(the_carrier(X0)))
| X3 != X5
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP0(X1,X0)
| ! [X3] :
( ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(sK5(X0,X1,X3),powerset(the_carrier(X0)))
& sK5(X0,X1,X3) = X3 )
| ~ in(X3,sK4(X0,X1)) )
& ( in(X3,sK4(X0,X1))
| ! [X5] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X5,powerset(the_carrier(X0)))
| X3 != X5 ) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f91,f93,f92]) ).
fof(f92,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X4,powerset(the_carrier(X0)))
& X3 = X4 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X5] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X5,powerset(the_carrier(X0)))
| X3 != X5 ) ) )
=> ! [X3] :
( ( ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X4,powerset(the_carrier(X0)))
& X3 = X4 )
| ~ in(X3,sK4(X0,X1)) )
& ( in(X3,sK4(X0,X1))
| ! [X5] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X5,powerset(the_carrier(X0)))
| X3 != X5 ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1,X3] :
( ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X4,powerset(the_carrier(X0)))
& X3 = X4 )
=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(sK5(X0,X1,X3),powerset(the_carrier(X0)))
& sK5(X0,X1,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP0(X1,X0)
| ? [X2] :
! [X3] :
( ( ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X4,powerset(the_carrier(X0)))
& X3 = X4 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X5] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X5,powerset(the_carrier(X0)))
| X3 != X5 ) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f90]) ).
fof(f90,plain,
! [X1,X0] :
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| sP0(X0,X1)
| ? [X5] :
! [X6] :
( ( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X1),X6),X0)
& in(X7,powerset(the_carrier(X1)))
& X6 = X7 )
| ~ in(X6,X5) )
& ( in(X6,X5)
| ! [X7] :
( ~ in(set_difference(cast_as_carrier_subset(X1),X6),X0)
| ~ in(X7,powerset(the_carrier(X1)))
| X6 != X7 ) ) )
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(nnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X1,X0] :
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| sP0(X0,X1)
| ? [X5] :
! [X6] :
( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X1),X6),X0)
& in(X7,powerset(the_carrier(X1)))
& X6 = X7 )
<=> in(X6,X5) )
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(definition_folding,[],[f78,f84]) ).
fof(f78,plain,
! [X1,X0] :
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ? [X2,X4,X3] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 != X3
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X3 = X4
& X2 = X4 )
| ? [X5] :
! [X6] :
( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X1),X6),X0)
& in(X7,powerset(the_carrier(X1)))
& X6 = X7 )
<=> in(X6,X5) )
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X1),X6),X0)
& in(X7,powerset(the_carrier(X1)))
& X6 = X7 )
<=> in(X6,X5) )
| ? [X3,X2,X4] :
( X2 != X3
& in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 = X4
& X3 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0) )
| ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( element(X0,powerset(powerset(the_carrier(X1))))
& topological_space(X1)
& top_str(X1) )
=> ( ! [X3,X2,X4] :
( ( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
& X2 = X4
& X3 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0) )
=> X2 = X3 )
=> ? [X5] :
! [X6] :
( ? [X7] :
( in(set_difference(cast_as_carrier_subset(X1),X6),X0)
& in(X7,powerset(the_carrier(X1)))
& X6 = X7 )
<=> in(X6,X5) ) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X1,X0] :
( ( top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0))))
& topological_space(X0) )
=> ( ! [X4,X3,X2] :
( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = X4
& in(X4,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(f358,plain,
( ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| ~ in(sK8(sK4(sK6,sK7)),sF14)
| sP0(sK7,sK6) ),
inference(resolution,[],[f355,f185]) ).
fof(f185,plain,
! [X2] :
( ~ in(set_difference(sF16,sK8(X2)),sK7)
| ~ in(sK8(X2),sF14)
| ~ in(sK8(X2),X2) ),
inference(definition_folding,[],[f136,f181,f180,f184]) ).
fof(f136,plain,
! [X2] :
( ~ in(set_difference(cast_as_carrier_subset(sK6),sK8(X2)),sK7)
| ~ in(sK8(X2),powerset(the_carrier(sK6)))
| ~ in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f355,plain,
( in(set_difference(sF16,sK8(sK4(sK6,sK7))),sK7)
| sP0(sK7,sK6) ),
inference(subsumption_resolution,[],[f352,f183]) ).
fof(f352,plain,
( sP0(sK7,sK6)
| in(set_difference(sF16,sK8(sK4(sK6,sK7))),sK7)
| ~ element(sK7,sF15) ),
inference(duplicate_literal_removal,[],[f349]) ).
fof(f349,plain,
( sP0(sK7,sK6)
| ~ element(sK7,sF15)
| sP0(sK7,sK6)
| in(set_difference(sF16,sK8(sK4(sK6,sK7))),sK7) ),
inference(resolution,[],[f344,f313]) ).
fof(f313,plain,
! [X0,X1] :
( ~ in(X0,sK4(sK6,X1))
| ~ element(X1,sF15)
| sP0(X1,sK6)
| in(set_difference(sF16,X0),X1) ),
inference(forward_demodulation,[],[f312,f182]) ).
fof(f312,plain,
! [X0,X1] :
( sP0(X1,sK6)
| ~ element(X1,powerset(sF14))
| ~ in(X0,sK4(sK6,X1))
| in(set_difference(sF16,X0),X1) ),
inference(forward_demodulation,[],[f311,f181]) ).
fof(f311,plain,
! [X0,X1] :
( ~ in(X0,sK4(sK6,X1))
| ~ element(X1,powerset(powerset(sF13)))
| in(set_difference(sF16,X0),X1)
| sP0(X1,sK6) ),
inference(forward_demodulation,[],[f310,f180]) ).
fof(f310,plain,
! [X0,X1] :
( in(set_difference(sF16,X0),X1)
| ~ in(X0,sK4(sK6,X1))
| sP0(X1,sK6)
| ~ element(X1,powerset(powerset(the_carrier(sK6)))) ),
inference(forward_demodulation,[],[f309,f184]) ).
fof(f309,plain,
! [X0,X1] :
( in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(sK6))))
| ~ in(X0,sK4(sK6,X1))
| sP0(X1,sK6) ),
inference(subsumption_resolution,[],[f308,f133]) ).
fof(f308,plain,
! [X0,X1] :
( ~ topological_space(sK6)
| ~ element(X1,powerset(powerset(the_carrier(sK6))))
| in(set_difference(cast_as_carrier_subset(sK6),X0),X1)
| ~ in(X0,sK4(sK6,X1))
| sP0(X1,sK6) ),
inference(resolution,[],[f118,f138]) ).
fof(f118,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(X3,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f387,plain,
( in(sK8(sK4(sK6,sK7)),sF14)
| sK3(sK7,sK6) = sK2(sK7,sK6) ),
inference(subsumption_resolution,[],[f386,f187]) ).
fof(f386,plain,
( ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| in(sK8(sK4(sK6,sK7)),sF14)
| sK3(sK7,sK6) = sK2(sK7,sK6) ),
inference(subsumption_resolution,[],[f385,f111]) ).
fof(f385,plain,
( sK3(sK7,sK6) = sK2(sK7,sK6)
| in(sK8(sK4(sK6,sK7)),sF14)
| ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| sP0(sK7,sK6) ),
inference(subsumption_resolution,[],[f381,f183]) ).
fof(f381,plain,
( sP0(sK7,sK6)
| in(sK8(sK4(sK6,sK7)),sF14)
| sK3(sK7,sK6) = sK2(sK7,sK6)
| ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| ~ element(sK7,sF15) ),
inference(superposition,[],[f320,f373]) ).
fof(f373,plain,
( sK8(sK4(sK6,sK7)) = sK5(sK6,sK7,sK8(sK4(sK6,sK7)))
| sK3(sK7,sK6) = sK2(sK7,sK6) ),
inference(resolution,[],[f354,f111]) ).
fof(f354,plain,
( sP0(sK7,sK6)
| sK8(sK4(sK6,sK7)) = sK5(sK6,sK7,sK8(sK4(sK6,sK7))) ),
inference(subsumption_resolution,[],[f353,f183]) ).
fof(f353,plain,
( sP0(sK7,sK6)
| ~ element(sK7,sF15)
| sK8(sK4(sK6,sK7)) = sK5(sK6,sK7,sK8(sK4(sK6,sK7))) ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f350,plain,
( sP0(sK7,sK6)
| sP0(sK7,sK6)
| ~ element(sK7,sF15)
| sK8(sK4(sK6,sK7)) = sK5(sK6,sK7,sK8(sK4(sK6,sK7))) ),
inference(resolution,[],[f344,f299]) ).
fof(f299,plain,
! [X0,X1] :
( ~ in(X1,sK4(sK6,X0))
| sP0(X0,sK6)
| ~ element(X0,sF15)
| sK5(sK6,X0,X1) = X1 ),
inference(forward_demodulation,[],[f298,f182]) ).
fof(f298,plain,
! [X0,X1] :
( sP0(X0,sK6)
| sK5(sK6,X0,X1) = X1
| ~ element(X0,powerset(sF14))
| ~ in(X1,sK4(sK6,X0)) ),
inference(forward_demodulation,[],[f297,f181]) ).
fof(f297,plain,
! [X0,X1] :
( ~ in(X1,sK4(sK6,X0))
| sK5(sK6,X0,X1) = X1
| ~ element(X0,powerset(powerset(sF13)))
| sP0(X0,sK6) ),
inference(forward_demodulation,[],[f296,f180]) ).
fof(f296,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(the_carrier(sK6))))
| sK5(sK6,X0,X1) = X1
| ~ in(X1,sK4(sK6,X0))
| sP0(X0,sK6) ),
inference(subsumption_resolution,[],[f295,f133]) ).
fof(f295,plain,
! [X0,X1] :
( sP0(X0,sK6)
| ~ topological_space(sK6)
| ~ element(X0,powerset(powerset(the_carrier(sK6))))
| ~ in(X1,sK4(sK6,X0))
| sK5(sK6,X0,X1) = X1 ),
inference(resolution,[],[f116,f138]) ).
fof(f116,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| sK5(X0,X1,X3) = X3
| sP0(X1,X0)
| ~ in(X3,sK4(X0,X1))
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f94]) ).
fof(f320,plain,
! [X0,X1] :
( in(sK5(sK6,X0,X1),sF14)
| sP0(X0,sK6)
| ~ in(X1,sK4(sK6,X0))
| ~ element(X0,sF15) ),
inference(forward_demodulation,[],[f319,f181]) ).
fof(f319,plain,
! [X0,X1] :
( ~ in(X1,sK4(sK6,X0))
| sP0(X0,sK6)
| in(sK5(sK6,X0,X1),powerset(sF13))
| ~ element(X0,sF15) ),
inference(forward_demodulation,[],[f318,f182]) ).
fof(f318,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF14))
| in(sK5(sK6,X0,X1),powerset(sF13))
| ~ in(X1,sK4(sK6,X0))
| sP0(X0,sK6) ),
inference(forward_demodulation,[],[f317,f180]) ).
fof(f317,plain,
! [X0,X1] :
( sP0(X0,sK6)
| in(sK5(sK6,X0,X1),powerset(the_carrier(sK6)))
| ~ element(X0,powerset(sF14))
| ~ in(X1,sK4(sK6,X0)) ),
inference(forward_demodulation,[],[f316,f181]) ).
fof(f316,plain,
! [X0,X1] :
( ~ in(X1,sK4(sK6,X0))
| ~ element(X0,powerset(powerset(sF13)))
| in(sK5(sK6,X0,X1),powerset(the_carrier(sK6)))
| sP0(X0,sK6) ),
inference(forward_demodulation,[],[f315,f180]) ).
fof(f315,plain,
! [X0,X1] :
( sP0(X0,sK6)
| ~ element(X0,powerset(powerset(the_carrier(sK6))))
| in(sK5(sK6,X0,X1),powerset(the_carrier(sK6)))
| ~ in(X1,sK4(sK6,X0)) ),
inference(subsumption_resolution,[],[f314,f133]) ).
fof(f314,plain,
! [X0,X1] :
( in(sK5(sK6,X0,X1),powerset(the_carrier(sK6)))
| ~ topological_space(sK6)
| sP0(X0,sK6)
| ~ element(X0,powerset(powerset(the_carrier(sK6))))
| ~ in(X1,sK4(sK6,X0)) ),
inference(resolution,[],[f117,f138]) ).
fof(f117,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| in(sK5(X0,X1,X3),powerset(the_carrier(X0)))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK4(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f113,plain,
! [X0,X1] :
( sK3(X0,X1) != sK1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f416,plain,
sP0(sK7,sK6),
inference(resolution,[],[f411,f362]) ).
fof(f411,plain,
in(sK8(sK4(sK6,sK7)),sF14),
inference(subsumption_resolution,[],[f410,f187]) ).
fof(f410,plain,
( ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| in(sK8(sK4(sK6,sK7)),sF14) ),
inference(subsumption_resolution,[],[f409,f394]) ).
fof(f409,plain,
( sP0(sK7,sK6)
| in(sK8(sK4(sK6,sK7)),sF14)
| ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7)) ),
inference(subsumption_resolution,[],[f405,f183]) ).
fof(f405,plain,
( ~ element(sK7,sF15)
| ~ in(sK8(sK4(sK6,sK7)),sK4(sK6,sK7))
| sP0(sK7,sK6)
| in(sK8(sK4(sK6,sK7)),sF14) ),
inference(superposition,[],[f320,f395]) ).
fof(f395,plain,
sK8(sK4(sK6,sK7)) = sK5(sK6,sK7,sK8(sK4(sK6,sK7))),
inference(resolution,[],[f394,f354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU310+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % 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 : n017.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 14:33:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.49 % (20721)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)
% 0.20/0.50 % (20713)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50 % (20714)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (20729)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)
% 0.20/0.51 % (20719)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 % (20722)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)
% 0.20/0.51 % (20730)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.52 % (20713)Instruction limit reached!
% 0.20/0.52 % (20713)------------------------------
% 0.20/0.52 % (20713)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (20713)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (20713)Termination reason: Unknown
% 0.20/0.52 % (20713)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (20713)Memory used [KB]: 5500
% 0.20/0.52 % (20713)Time elapsed: 0.126 s
% 0.20/0.52 % (20713)Instructions burned: 7 (million)
% 0.20/0.52 % (20713)------------------------------
% 0.20/0.52 % (20713)------------------------------
% 0.20/0.52 % (20709)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 % (20711)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 % (20721)First to succeed.
% 0.20/0.53 % (20712)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)
% 0.20/0.53 % (20708)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)
% 0.20/0.53 % (20707)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 % (20728)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 % (20718)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 % (20733)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)
% 0.20/0.53 % (20721)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (20721)------------------------------
% 0.20/0.54 % (20721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (20721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (20721)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (20721)Memory used [KB]: 1151
% 0.20/0.54 % (20721)Time elapsed: 0.130 s
% 0.20/0.54 % (20721)Instructions burned: 17 (million)
% 0.20/0.54 % (20721)------------------------------
% 0.20/0.54 % (20721)------------------------------
% 0.20/0.54 % (20705)Success in time 0.186 s
%------------------------------------------------------------------------------