TSTP Solution File: SET919+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET919+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 : n008.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 18:26:05 EDT 2022
% Result : Theorem 1.94s 0.62s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 113 ( 27 unt; 0 def)
% Number of atoms : 402 ( 174 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 460 ( 171 ~; 195 |; 75 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 176 ( 153 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1696,plain,
$false,
inference(avatar_sat_refutation,[],[f90,f1584,f1615,f1681,f1686]) ).
fof(f1686,plain,
( spl11_1
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[],[f1685]) ).
fof(f1685,plain,
( $false
| spl11_1
| ~ spl11_12 ),
inference(subsumption_resolution,[],[f1622,f85]) ).
fof(f85,plain,
( ~ in(sK5,sK4)
| spl11_1 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f83,plain,
( spl11_1
<=> in(sK5,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f1622,plain,
( in(sK5,sK4)
| ~ spl11_12 ),
inference(superposition,[],[f1567,f1583]) ).
fof(f1583,plain,
( sK3(sF10,sF8,sK4) = sK5
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f1581]) ).
fof(f1581,plain,
( spl11_12
<=> sK3(sF10,sF8,sK4) = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f1567,plain,
in(sK3(sF10,sF8,sK4),sK4),
inference(resolution,[],[f1565,f130]) ).
fof(f130,plain,
! [X8] :
( ~ in(X8,sF10)
| in(X8,sK4) ),
inference(superposition,[],[f75,f80]) ).
fof(f80,plain,
set_intersection2(sF9,sK4) = sF10,
introduced(function_definition,[]) ).
fof(f75,plain,
! [X2,X3,X0] :
( ~ in(X3,set_intersection2(X2,X0))
| in(X3,X0) ),
inference(equality_resolution,[],[f60]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X1)
| set_intersection2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 )
& ( set_intersection2(X2,X0) = X1
| ( ( ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( in(sK3(X0,X1,X2),X1)
| ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X2) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X0)
| ~ in(X4,X2) )
& ( in(X4,X1)
| ( in(X4,X0)
& in(X4,X2) ) ) )
=> ( ( ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2) )
& ( in(sK3(X0,X1,X2),X1)
| ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 )
& ( set_intersection2(X2,X0) = X1
| ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X0)
| ~ in(X4,X2) )
& ( in(X4,X1)
| ( in(X4,X0)
& in(X4,X2) ) ) ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) ) ) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X0] :
( ! [X3] :
( ( in(X3,X1)
& in(X3,X0) )
<=> in(X3,X2) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f1565,plain,
in(sK3(sF10,sF8,sK4),sF10),
inference(subsumption_resolution,[],[f1564,f81]) ).
fof(f81,plain,
sF8 != sF10,
inference(definition_folding,[],[f63,f80,f79,f78]) ).
fof(f78,plain,
singleton(sK6) = sF8,
introduced(function_definition,[]) ).
fof(f79,plain,
unordered_pair(sK6,sK5) = sF9,
introduced(function_definition,[]) ).
fof(f63,plain,
singleton(sK6) != set_intersection2(unordered_pair(sK6,sK5),sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( singleton(sK6) != set_intersection2(unordered_pair(sK6,sK5),sK4)
& ( sK5 = sK6
| ~ in(sK5,sK4) )
& in(sK6,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f36,f37]) ).
fof(f37,plain,
( ? [X0,X1,X2] :
( singleton(X2) != set_intersection2(unordered_pair(X2,X1),X0)
& ( X1 = X2
| ~ in(X1,X0) )
& in(X2,X0) )
=> ( singleton(sK6) != set_intersection2(unordered_pair(sK6,sK5),sK4)
& ( sK5 = sK6
| ~ in(sK5,sK4) )
& in(sK6,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0,X1,X2] :
( singleton(X2) != set_intersection2(unordered_pair(X2,X1),X0)
& ( X1 = X2
| ~ in(X1,X0) )
& in(X2,X0) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
? [X0,X2,X1] :
( set_intersection2(unordered_pair(X1,X2),X0) != singleton(X1)
& ( X1 = X2
| ~ in(X2,X0) )
& in(X1,X0) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1,X2] :
( set_intersection2(unordered_pair(X1,X2),X0) != singleton(X1)
& ( X1 = X2
| ~ in(X2,X0) )
& in(X1,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X0,X1,X2] :
( in(X1,X0)
=> ( set_intersection2(unordered_pair(X1,X2),X0) = singleton(X1)
| ( X1 != X2
& in(X2,X0) ) ) ),
inference(rectify,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X1,X0,X2] :
( in(X0,X1)
=> ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
| ( X0 != X2
& in(X2,X1) ) ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X1,X0,X2] :
( in(X0,X1)
=> ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
| ( X0 != X2
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
fof(f1564,plain,
( sF8 = sF10
| in(sK3(sF10,sF8,sK4),sF10) ),
inference(forward_demodulation,[],[f1562,f682]) ).
fof(f682,plain,
set_intersection2(sK4,sF10) = sF10,
inference(subsumption_resolution,[],[f664,f343]) ).
fof(f343,plain,
! [X0,X1] :
( in(sK3(X0,X0,X1),X0)
| set_intersection2(X1,X0) = X0 ),
inference(factoring,[],[f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X0)
| set_intersection2(X2,X0) = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f664,plain,
( ~ in(sK3(sF10,sF10,sK4),sF10)
| set_intersection2(sK4,sF10) = sF10 ),
inference(duplicate_literal_removal,[],[f645]) ).
fof(f645,plain,
( set_intersection2(sK4,sF10) = sF10
| ~ in(sK3(sF10,sF10,sK4),sF10)
| set_intersection2(sK4,sF10) = sF10
| ~ in(sK3(sF10,sF10,sK4),sF10) ),
inference(resolution,[],[f57,f362]) ).
fof(f362,plain,
! [X18] :
( in(sK3(sF10,sF10,X18),sK4)
| set_intersection2(X18,sF10) = sF10 ),
inference(resolution,[],[f343,f130]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ in(sK3(X0,X1,X2),X2)
| set_intersection2(X2,X0) = X1
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f1562,plain,
( in(sK3(sF10,sF8,sK4),sF10)
| set_intersection2(sK4,sF10) = sF8 ),
inference(resolution,[],[f1516,f56]) ).
fof(f1516,plain,
~ in(sK3(sF10,sF8,sK4),sF8),
inference(subsumption_resolution,[],[f1515,f81]) ).
fof(f1515,plain,
( sF8 = sF10
| ~ in(sK3(sF10,sF8,sK4),sF8) ),
inference(forward_demodulation,[],[f1514,f682]) ).
fof(f1514,plain,
( ~ in(sK3(sF10,sF8,sK4),sF8)
| set_intersection2(sK4,sF10) = sF8 ),
inference(subsumption_resolution,[],[f1513,f725]) ).
fof(f725,plain,
! [X0] :
( ~ in(X0,sF8)
| in(X0,sF10) ),
inference(superposition,[],[f75,f707]) ).
fof(f707,plain,
set_intersection2(sF8,sF10) = sF8,
inference(resolution,[],[f679,f159]) ).
fof(f159,plain,
in(sK6,sF10),
inference(subsumption_resolution,[],[f157,f61]) ).
fof(f61,plain,
in(sK6,sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f157,plain,
( ~ in(sK6,sK4)
| in(sK6,sF10) ),
inference(resolution,[],[f155,f93]) ).
fof(f93,plain,
in(sK6,sF9),
inference(superposition,[],[f68,f79]) ).
fof(f68,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f67]) ).
fof(f67,plain,
! [X3,X0,X1] :
( in(X3,X0)
| unordered_pair(X3,X1) != X0 ),
inference(equality_resolution,[],[f47]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| X2 != X3
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ( ( ( sK0(X0,X1,X2) != X2
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X0) )
& ( sK0(X0,X1,X2) = X2
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) )
=> ( ( ( sK0(X0,X1,X2) != X2
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X0) )
& ( sK0(X0,X1,X2) = X2
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X3] :
( ( ( X2 != X3
& X1 != X3 )
| ~ in(X3,X0) )
& ( X2 = X3
| X1 = X3
| in(X3,X0) ) ) ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X3] :
( ( ( X2 != X3
& X1 != X3 )
| ~ in(X3,X0) )
& ( X2 = X3
| X1 = X3
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ! [X3] :
( in(X3,X0)
<=> ( X2 = X3
| X1 = X3 ) )
<=> unordered_pair(X2,X1) = X0 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X1,X0] :
( ! [X3] :
( in(X3,X2)
<=> ( X0 = X3
| X1 = X3 ) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f155,plain,
! [X9] :
( ~ in(X9,sF9)
| ~ in(X9,sK4)
| in(X9,sF10) ),
inference(superposition,[],[f77,f123]) ).
fof(f123,plain,
set_intersection2(sK4,sF9) = sF10,
inference(superposition,[],[f80,f66]) ).
fof(f66,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f77,plain,
! [X2,X3,X0] :
( in(X3,set_intersection2(X2,X0))
| ~ in(X3,X2)
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2)
| set_intersection2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f679,plain,
! [X0] :
( ~ in(sK6,X0)
| sF8 = set_intersection2(sF8,X0) ),
inference(subsumption_resolution,[],[f677,f91]) ).
fof(f91,plain,
in(sK6,sF8),
inference(superposition,[],[f74,f78]) ).
fof(f74,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( ~ in(sK1(X0,X1),X0)
| sK1(X0,X1) != X1 )
& ( in(sK1(X0,X1),X0)
| sK1(X0,X1) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) )
=> ( ( ~ in(sK1(X0,X1),X0)
| sK1(X0,X1) != X1 )
& ( in(sK1(X0,X1),X0)
| sK1(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( X0 = X2
<=> in(X2,X1) )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f677,plain,
! [X0] :
( ~ in(sK6,X0)
| ~ in(sK6,sF8)
| sF8 = set_intersection2(sF8,X0) ),
inference(duplicate_literal_removal,[],[f650]) ).
fof(f650,plain,
! [X0] :
( ~ in(sK6,sF8)
| ~ in(sK6,X0)
| sF8 = set_intersection2(sF8,X0)
| ~ in(sK6,sF8)
| sF8 = set_intersection2(sF8,X0) ),
inference(superposition,[],[f57,f295]) ).
fof(f295,plain,
! [X14] :
( sK3(X14,sF8,sF8) = sK6
| set_intersection2(sF8,X14) = sF8 ),
inference(resolution,[],[f288,f125]) ).
fof(f125,plain,
! [X0] :
( ~ in(X0,sF8)
| sK6 = X0 ),
inference(superposition,[],[f72,f78]) ).
fof(f72,plain,
! [X2,X1] :
( ~ in(X2,singleton(X1))
| X1 = X2 ),
inference(equality_resolution,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f288,plain,
! [X0,X1] :
( in(sK3(X0,X1,X1),X1)
| set_intersection2(X1,X0) = X1 ),
inference(factoring,[],[f55]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| set_intersection2(X2,X0) = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f1513,plain,
( ~ in(sK3(sF10,sF8,sK4),sF8)
| set_intersection2(sK4,sF10) = sF8
| ~ in(sK3(sF10,sF8,sK4),sF10) ),
inference(duplicate_literal_removal,[],[f1507]) ).
fof(f1507,plain,
( ~ in(sK3(sF10,sF8,sK4),sF10)
| ~ in(sK3(sF10,sF8,sK4),sF8)
| set_intersection2(sK4,sF10) = sF8
| set_intersection2(sK4,sF10) = sF8 ),
inference(resolution,[],[f769,f57]) ).
fof(f769,plain,
! [X20] :
( in(sK3(sF10,sF8,X20),sK4)
| set_intersection2(X20,sF10) = sF8 ),
inference(duplicate_literal_removal,[],[f764]) ).
fof(f764,plain,
! [X20] :
( in(sK3(sF10,sF8,X20),sK4)
| in(sK3(sF10,sF8,X20),sK4)
| set_intersection2(X20,sF10) = sF8 ),
inference(resolution,[],[f717,f342]) ).
fof(f342,plain,
! [X28,X29] :
( in(sK3(sF10,X28,X29),sK4)
| in(sK3(sF10,X28,X29),X28)
| set_intersection2(X29,sF10) = X28 ),
inference(resolution,[],[f56,f130]) ).
fof(f717,plain,
! [X0] :
( ~ in(X0,sF8)
| in(X0,sK4) ),
inference(superposition,[],[f75,f704]) ).
fof(f704,plain,
set_intersection2(sF8,sK4) = sF8,
inference(resolution,[],[f679,f61]) ).
fof(f1681,plain,
( ~ spl11_2
| spl11_11
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f1625,f1581,f1577,f87]) ).
fof(f87,plain,
( spl11_2
<=> sK5 = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f1577,plain,
( spl11_11
<=> sK3(sF10,sF8,sK4) = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f1625,plain,
( sK5 != sK6
| spl11_11
| ~ spl11_12 ),
inference(superposition,[],[f1578,f1583]) ).
fof(f1578,plain,
( sK3(sF10,sF8,sK4) != sK6
| spl11_11 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1615,plain,
~ spl11_11,
inference(avatar_contradiction_clause,[],[f1614]) ).
fof(f1614,plain,
( $false
| ~ spl11_11 ),
inference(subsumption_resolution,[],[f1594,f91]) ).
fof(f1594,plain,
( ~ in(sK6,sF8)
| ~ spl11_11 ),
inference(superposition,[],[f1516,f1579]) ).
fof(f1579,plain,
( sK3(sF10,sF8,sK4) = sK6
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1584,plain,
( spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f1572,f1581,f1577]) ).
fof(f1572,plain,
( sK3(sF10,sF8,sK4) = sK5
| sK3(sF10,sF8,sK4) = sK6 ),
inference(resolution,[],[f1566,f142]) ).
fof(f142,plain,
! [X7] :
( ~ in(X7,sF9)
| sK6 = X7
| sK5 = X7 ),
inference(superposition,[],[f71,f105]) ).
fof(f105,plain,
unordered_pair(sK5,sK6) = sF9,
inference(superposition,[],[f52,f79]) ).
fof(f52,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f71,plain,
! [X2,X3,X1] :
( ~ in(X3,unordered_pair(X2,X1))
| X2 = X3
| X1 = X3 ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X3
| ~ in(X3,X0)
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f1566,plain,
in(sK3(sF10,sF8,sK4),sF9),
inference(resolution,[],[f1565,f131]) ).
fof(f131,plain,
! [X9] :
( ~ in(X9,sF10)
| in(X9,sF9) ),
inference(superposition,[],[f75,f123]) ).
fof(f90,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f62,f87,f83]) ).
fof(f62,plain,
( sK5 = sK6
| ~ in(sK5,sK4) ),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 14:34:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.47 % (18389)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.48 % (18384)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.48 TRYING [1]
% 0.20/0.48 TRYING [2]
% 0.20/0.48 TRYING [3]
% 0.20/0.49 % (18394)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)
% 0.20/0.49 % (18386)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)
% 0.20/0.50 TRYING [4]
% 0.20/0.50 % (18397)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.50 % (18376)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (18378)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)
% 0.20/0.50 % (18377)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)
% 0.20/0.50 % (18379)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 TRYING [1]
% 0.20/0.50 TRYING [2]
% 0.20/0.51 TRYING [3]
% 0.20/0.51 % (18374)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 % (18372)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 TRYING [1]
% 0.20/0.52 TRYING [2]
% 0.20/0.52 % (18373)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)
% 0.20/0.52 % (18401)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)
% 0.20/0.52 % (18400)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.52 TRYING [4]
% 0.20/0.52 % (18373)Refutation not found, incomplete strategy% (18373)------------------------------
% 0.20/0.52 % (18373)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (18373)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (18373)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (18373)Memory used [KB]: 5500
% 0.20/0.52 % (18373)Time elapsed: 0.128 s
% 0.20/0.52 % (18373)Instructions burned: 4 (million)
% 0.20/0.52 % (18373)------------------------------
% 0.20/0.52 % (18373)------------------------------
% 0.20/0.52 % (18380)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (18380)Instruction limit reached!
% 0.20/0.52 % (18380)------------------------------
% 0.20/0.52 % (18380)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (18380)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (18380)Termination reason: Unknown
% 0.20/0.52 % (18380)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (18380)Memory used [KB]: 5373
% 0.20/0.52 % (18380)Time elapsed: 0.128 s
% 0.20/0.52 % (18380)Instructions burned: 3 (million)
% 0.20/0.52 % (18380)------------------------------
% 0.20/0.52 % (18380)------------------------------
% 0.20/0.52 % (18375)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 % (18396)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 % (18398)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)
% 0.20/0.52 % (18381)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 % (18383)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)
% 0.20/0.52 % (18388)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)
% 0.20/0.53 % (18379)Instruction limit reached!
% 0.20/0.53 % (18379)------------------------------
% 0.20/0.53 % (18379)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (18379)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (18379)Termination reason: Unknown
% 0.20/0.53 % (18379)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (18379)Memory used [KB]: 5500
% 0.20/0.53 % (18379)Time elapsed: 0.130 s
% 0.20/0.53 % (18379)Instructions burned: 8 (million)
% 0.20/0.53 % (18379)------------------------------
% 0.20/0.53 % (18379)------------------------------
% 0.20/0.53 % (18395)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 % (18399)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 % (18391)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)
% 0.20/0.53 % (18390)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (18392)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)
% 0.20/0.53 % (18385)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53 % (18393)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 % (18382)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 % (18387)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 TRYING [3]
% 0.20/0.54 TRYING [5]
% 0.20/0.54 TRYING [4]
% 0.20/0.55 % (18389)Instruction limit reached!
% 0.20/0.55 % (18389)------------------------------
% 0.20/0.55 % (18389)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (18378)Instruction limit reached!
% 0.20/0.55 % (18378)------------------------------
% 0.20/0.55 % (18378)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (18378)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (18378)Termination reason: Unknown
% 0.20/0.56 % (18378)Termination phase: Finite model building SAT solving
% 0.20/0.56
% 0.20/0.56 % (18378)Memory used [KB]: 7419
% 0.20/0.56 % (18378)Time elapsed: 0.098 s
% 0.20/0.56 % (18378)Instructions burned: 51 (million)
% 0.20/0.56 % (18378)------------------------------
% 0.20/0.56 % (18378)------------------------------
% 0.20/0.56 % (18389)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (18389)Termination reason: Unknown
% 0.20/0.56 % (18389)Termination phase: Finite model building constraint generation
% 0.20/0.56
% 0.20/0.56 % (18389)Memory used [KB]: 7547
% 0.20/0.56 % (18389)Time elapsed: 0.162 s
% 0.20/0.56 % (18389)Instructions burned: 59 (million)
% 0.20/0.56 % (18389)------------------------------
% 0.20/0.56 % (18389)------------------------------
% 1.84/0.58 % (18374)Instruction limit reached!
% 1.84/0.58 % (18374)------------------------------
% 1.84/0.58 % (18374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.84/0.58 % (18374)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.84/0.58 % (18374)Termination reason: Unknown
% 1.84/0.58 % (18374)Termination phase: Saturation
% 1.84/0.58
% 1.84/0.58 % (18374)Memory used [KB]: 1407
% 1.84/0.58 % (18374)Time elapsed: 0.191 s
% 1.84/0.58 % (18374)Instructions burned: 39 (million)
% 1.84/0.58 % (18374)------------------------------
% 1.84/0.58 % (18374)------------------------------
% 1.94/0.60 TRYING [5]
% 1.94/0.60 % (18376)Instruction limit reached!
% 1.94/0.60 % (18376)------------------------------
% 1.94/0.60 % (18376)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.94/0.60 % (18376)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.94/0.60 % (18376)Termination reason: Unknown
% 1.94/0.60 % (18376)Termination phase: Saturation
% 1.94/0.60
% 1.94/0.60 % (18376)Memory used [KB]: 6140
% 1.94/0.60 % (18376)Time elapsed: 0.197 s
% 1.94/0.60 % (18376)Instructions burned: 53 (million)
% 1.94/0.60 % (18376)------------------------------
% 1.94/0.60 % (18376)------------------------------
% 1.94/0.61 % (18386)Instruction limit reached!
% 1.94/0.61 % (18386)------------------------------
% 1.94/0.61 % (18386)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.94/0.61 % (18386)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.94/0.61 % (18386)Termination reason: Unknown
% 1.94/0.61 % (18386)Termination phase: Saturation
% 1.94/0.61
% 1.94/0.61 % (18386)Memory used [KB]: 6396
% 1.94/0.61 % (18386)Time elapsed: 0.056 s
% 1.94/0.61 % (18386)Instructions burned: 68 (million)
% 1.94/0.61 % (18386)------------------------------
% 1.94/0.61 % (18386)------------------------------
% 1.94/0.61 % (18377)Instruction limit reached!
% 1.94/0.61 % (18377)------------------------------
% 1.94/0.61 % (18377)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.94/0.61 % (18377)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.94/0.61 % (18377)Termination reason: Unknown
% 1.94/0.61 % (18377)Termination phase: Saturation
% 1.94/0.61
% 1.94/0.61 % (18377)Memory used [KB]: 5884
% 1.94/0.61 % (18377)Time elapsed: 0.218 s
% 1.94/0.61 % (18377)Instructions burned: 49 (million)
% 1.94/0.61 % (18377)------------------------------
% 1.94/0.61 % (18377)------------------------------
% 1.94/0.61 % (18384)First to succeed.
% 1.94/0.61 % (18375)Instruction limit reached!
% 1.94/0.61 % (18375)------------------------------
% 1.94/0.61 % (18375)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.94/0.61 % (18375)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.94/0.61 % (18375)Termination reason: Unknown
% 1.94/0.61 % (18375)Termination phase: Saturation
% 1.94/0.61
% 1.94/0.61 % (18375)Memory used [KB]: 6140
% 1.94/0.61 % (18375)Time elapsed: 0.207 s
% 1.94/0.61 % (18375)Instructions burned: 51 (million)
% 1.94/0.61 % (18375)------------------------------
% 1.94/0.61 % (18375)------------------------------
% 1.94/0.62 % (18384)Refutation found. Thanks to Tanya!
% 1.94/0.62 % SZS status Theorem for theBenchmark
% 1.94/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.94/0.62 % (18384)------------------------------
% 1.94/0.62 % (18384)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.94/0.62 % (18384)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.94/0.62 % (18384)Termination reason: Refutation
% 1.94/0.62
% 1.94/0.62 % (18384)Memory used [KB]: 6780
% 1.94/0.62 % (18384)Time elapsed: 0.232 s
% 1.94/0.62 % (18384)Instructions burned: 89 (million)
% 1.94/0.62 % (18384)------------------------------
% 1.94/0.62 % (18384)------------------------------
% 1.94/0.62 % (18371)Success in time 0.274 s
%------------------------------------------------------------------------------