TSTP Solution File: SEU281+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU281+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 : 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 18:32:59 EDT 2022
% Result : Theorem 2.16s 0.63s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of formulae : 173 ( 7 unt; 0 def)
% Number of atoms : 773 ( 283 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 865 ( 265 ~; 392 |; 177 &)
% ( 18 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 3 con; 0-3 aty)
% Number of variables : 344 ( 210 !; 134 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f838,plain,
$false,
inference(avatar_sat_refutation,[],[f204,f219,f642,f704,f724,f726,f735,f737,f814,f819,f831,f834]) ).
fof(f834,plain,
( spl26_6
| spl26_1
| ~ spl26_8 ),
inference(avatar_split_clause,[],[f833,f681,f165,f273]) ).
fof(f273,plain,
( spl26_6
<=> in(sK19(sK11(sK18,sK17)),sF23) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f165,plain,
( spl26_1
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
fof(f681,plain,
( spl26_8
<=> sK19(sK11(sK18,sK17)) = sK12(sK18,sK17,sK19(sK11(sK18,sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
fof(f833,plain,
( in(sK19(sK11(sK18,sK17)),sF23)
| spl26_1
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f832,f111]) ).
fof(f111,plain,
! [X2] :
( in(sK19(X2),sF23)
| in(sK19(X2),X2) ),
inference(definition_folding,[],[f95,f105]) ).
fof(f105,plain,
sF23 = cartesian_product2(sK18,sK17),
introduced(function_definition,[]) ).
fof(f95,plain,
! [X2] :
( in(sK19(X2),cartesian_product2(sK18,sK17))
| in(sK19(X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X2] :
( ( ! [X4,X5] :
( ~ in(X5,sK18)
| singleton(X5) != X4
| sK19(X2) != ordered_pair(X5,X4) )
| ~ in(sK19(X2),cartesian_product2(sK18,sK17))
| ~ in(sK19(X2),X2) )
& ( ( in(sK21(X2),sK18)
& sK20(X2) = singleton(sK21(X2))
& sK19(X2) = ordered_pair(sK21(X2),sK20(X2))
& in(sK19(X2),cartesian_product2(sK18,sK17)) )
| in(sK19(X2),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21])],[f57,f60,f59,f58]) ).
fof(f58,plain,
( ? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( ~ in(X5,X1)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(X1,X0))
| ~ in(X3,X2) )
& ( ( ? [X6,X7] :
( in(X7,X1)
& singleton(X7) = X6
& ordered_pair(X7,X6) = X3 )
& in(X3,cartesian_product2(X1,X0)) )
| in(X3,X2) ) )
=> ! [X2] :
? [X3] :
( ( ! [X5,X4] :
( ~ in(X5,sK18)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(sK18,sK17))
| ~ in(X3,X2) )
& ( ( ? [X7,X6] :
( in(X7,sK18)
& singleton(X7) = X6
& ordered_pair(X7,X6) = X3 )
& in(X3,cartesian_product2(sK18,sK17)) )
| in(X3,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X2] :
( ? [X3] :
( ( ! [X5,X4] :
( ~ in(X5,sK18)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(sK18,sK17))
| ~ in(X3,X2) )
& ( ( ? [X7,X6] :
( in(X7,sK18)
& singleton(X7) = X6
& ordered_pair(X7,X6) = X3 )
& in(X3,cartesian_product2(sK18,sK17)) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ~ in(X5,sK18)
| singleton(X5) != X4
| sK19(X2) != ordered_pair(X5,X4) )
| ~ in(sK19(X2),cartesian_product2(sK18,sK17))
| ~ in(sK19(X2),X2) )
& ( ( ? [X7,X6] :
( in(X7,sK18)
& singleton(X7) = X6
& sK19(X2) = ordered_pair(X7,X6) )
& in(sK19(X2),cartesian_product2(sK18,sK17)) )
| in(sK19(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X2] :
( ? [X7,X6] :
( in(X7,sK18)
& singleton(X7) = X6
& sK19(X2) = ordered_pair(X7,X6) )
=> ( in(sK21(X2),sK18)
& sK20(X2) = singleton(sK21(X2))
& sK19(X2) = ordered_pair(sK21(X2),sK20(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( ~ in(X5,X1)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(X1,X0))
| ~ in(X3,X2) )
& ( ( ? [X6,X7] :
( in(X7,X1)
& singleton(X7) = X6
& ordered_pair(X7,X6) = X3 )
& in(X3,cartesian_product2(X1,X0)) )
| in(X3,X2) ) ),
inference(rectify,[],[f56]) ).
fof(f56,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( ~ in(X5,X1)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(X1,X0))
| ~ in(X3,X2) )
& ( ( ? [X4,X5] :
( in(X5,X1)
& singleton(X5) = X4
& ordered_pair(X5,X4) = X3 )
& in(X3,cartesian_product2(X1,X0)) )
| in(X3,X2) ) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( ~ in(X5,X1)
| singleton(X5) != X4
| ordered_pair(X5,X4) != X3 )
| ~ in(X3,cartesian_product2(X1,X0))
| ~ in(X3,X2) )
& ( ( ? [X4,X5] :
( in(X5,X1)
& singleton(X5) = X4
& ordered_pair(X5,X4) = X3 )
& in(X3,cartesian_product2(X1,X0)) )
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4,X5] :
( in(X5,X1)
& singleton(X5) = X4
& ordered_pair(X5,X4) = X3 )
& in(X3,cartesian_product2(X1,X0)) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X1,X0] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( in(X5,X1)
& singleton(X5) = X4
& ordered_pair(X5,X4) = X3 )
& in(X3,cartesian_product2(X1,X0)) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X1,X0] :
? [X2] :
! [X3] :
( ( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& singleton(X4) = X5 )
& in(X3,cartesian_product2(X0,X1)) )
<=> in(X3,X2) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X1,X0] :
? [X2] :
! [X3] :
( ( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& singleton(X4) = X5 )
& in(X3,cartesian_product2(X0,X1)) )
<=> in(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f832,plain,
( in(sK19(sK11(sK18,sK17)),sF23)
| ~ in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| spl26_1
| ~ spl26_8 ),
inference(forward_demodulation,[],[f815,f105]) ).
fof(f815,plain,
( ~ in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| in(sK19(sK11(sK18,sK17)),cartesian_product2(sK18,sK17))
| spl26_1
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f782,f166]) ).
fof(f166,plain,
( ~ sP1(sK18)
| spl26_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f782,plain,
( sP1(sK18)
| in(sK19(sK11(sK18,sK17)),cartesian_product2(sK18,sK17))
| ~ in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| ~ spl26_8 ),
inference(superposition,[],[f87,f683]) ).
fof(f683,plain,
( sK19(sK11(sK18,sK17)) = sK12(sK18,sK17,sK19(sK11(sK18,sK17)))
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f87,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),cartesian_product2(X0,X1))
| sP1(X0)
| ~ in(X3,sK11(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( sP1(X0)
| ! [X3] :
( ( ( in(sK12(X0,X1,X3),cartesian_product2(X0,X1))
& sK12(X0,X1,X3) = X3
& in(sK14(X0,X3),X0)
& ordered_pair(sK14(X0,X3),sK13(X0,X3)) = X3
& sK13(X0,X3) = singleton(sK14(X0,X3)) )
| ~ in(X3,sK11(X0,X1)) )
& ( in(X3,sK11(X0,X1))
| ! [X7] :
( ~ in(X7,cartesian_product2(X0,X1))
| X3 != X7
| ! [X8,X9] :
( ~ in(X9,X0)
| ordered_pair(X9,X8) != X3
| singleton(X9) != X8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f46,f49,f48,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X3 = X4
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 ) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X7] :
( ~ in(X7,cartesian_product2(X0,X1))
| X3 != X7
| ! [X8,X9] :
( ~ in(X9,X0)
| ordered_pair(X9,X8) != X3
| singleton(X9) != X8 ) ) ) )
=> ! [X3] :
( ( ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X3 = X4
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 ) )
| ~ in(X3,sK11(X0,X1)) )
& ( in(X3,sK11(X0,X1))
| ! [X7] :
( ~ in(X7,cartesian_product2(X0,X1))
| X3 != X7
| ! [X8,X9] :
( ~ in(X9,X0)
| ordered_pair(X9,X8) != X3
| singleton(X9) != X8 ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1,X3] :
( ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X3 = X4
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 ) )
=> ( in(sK12(X0,X1,X3),cartesian_product2(X0,X1))
& sK12(X0,X1,X3) = X3
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 ) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X3] :
( ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 )
=> ( in(sK14(X0,X3),X0)
& ordered_pair(sK14(X0,X3),sK13(X0,X3)) = X3
& sK13(X0,X3) = singleton(sK14(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( sP1(X0)
| ? [X2] :
! [X3] :
( ( ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X3 = X4
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X3
& singleton(X6) = X5 ) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X7] :
( ~ in(X7,cartesian_product2(X0,X1))
| X3 != X7
| ! [X8,X9] :
( ~ in(X9,X0)
| ordered_pair(X9,X8) != X3
| singleton(X9) != X8 ) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( sP1(X0)
| ? [X9] :
! [X10] :
( ( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( in(X13,X0)
& ordered_pair(X13,X12) = X10
& singleton(X13) = X12 ) )
| ~ in(X10,X9) )
& ( in(X10,X9)
| ! [X11] :
( ~ in(X11,cartesian_product2(X0,X1))
| X10 != X11
| ! [X12,X13] :
( ~ in(X13,X0)
| ordered_pair(X13,X12) != X10
| singleton(X13) != X12 ) ) ) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( sP1(X0)
| ? [X9] :
! [X10] :
( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( in(X13,X0)
& ordered_pair(X13,X12) = X10
& singleton(X13) = X12 ) )
<=> in(X10,X9) ) ),
inference(definition_folding,[],[f28,f30,f29]) ).
fof(f29,plain,
! [X0,X2] :
( ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X2
& singleton(X6) = X5 )
| ~ sP0(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f30,plain,
! [X0] :
( ? [X4,X3,X2] :
( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(X8,X0)
& singleton(X8) = X7 )
& X2 = X3
& sP0(X0,X2)
& X2 != X4
& X3 = X4 )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X4,X3,X2] :
( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(X8,X0)
& singleton(X8) = X7 )
& X2 = X3
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X2
& singleton(X6) = X5 )
& X2 != X4
& X3 = X4 )
| ? [X9] :
! [X10] :
( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( in(X13,X0)
& ordered_pair(X13,X12) = X10
& singleton(X13) = X12 ) )
<=> in(X10,X9) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( in(X13,X0)
& ordered_pair(X13,X12) = X10
& singleton(X13) = X12 ) )
<=> in(X10,X9) )
| ? [X4,X3,X2] :
( X2 != X4
& ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(X8,X0)
& singleton(X8) = X7 )
& X2 = X3
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X2
& singleton(X6) = X5 )
& X3 = X4 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ! [X4,X3,X2] :
( ( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(X8,X0)
& singleton(X8) = X7 )
& X2 = X3
& ? [X5,X6] :
( in(X6,X0)
& ordered_pair(X6,X5) = X2
& singleton(X6) = X5 )
& X3 = X4 )
=> X2 = X4 )
=> ? [X9] :
! [X10] :
( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( in(X13,X0)
& ordered_pair(X13,X12) = X10
& singleton(X13) = X12 ) )
<=> in(X10,X9) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X4,X2,X3] :
( ( X2 = X4
& ? [X8,X7] :
( singleton(X7) = X8
& ordered_pair(X7,X8) = X4
& in(X7,X0) )
& ? [X6,X5] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( ? [X4] :
( X3 = X4
& ? [X10,X9] :
( ordered_pair(X9,X10) = X3
& singleton(X9) = X10
& in(X9,X0) )
& in(X4,cartesian_product2(X0,X1)) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f831,plain,
( spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6
| spl26_12 ),
inference(avatar_contradiction_clause,[],[f830]) ).
fof(f830,plain,
( $false
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6
| spl26_12 ),
inference(subsumption_resolution,[],[f829,f166]) ).
fof(f829,plain,
( sP1(sK18)
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6
| spl26_12 ),
inference(subsumption_resolution,[],[f827,f708]) ).
fof(f708,plain,
( ~ in(sK14(sK18,sK19(sK11(sK18,sK17))),sK18)
| spl26_12 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f707,plain,
( spl26_12
<=> in(sK14(sK18,sK19(sK11(sK18,sK17))),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f827,plain,
( in(sK14(sK18,sK19(sK11(sK18,sK17))),sK18)
| sP1(sK18)
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6 ),
inference(resolution,[],[f808,f85]) ).
fof(f85,plain,
! [X3,X0,X1] :
( ~ in(X3,sK11(X0,X1))
| sP1(X0)
| in(sK14(X0,X3),X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f808,plain,
( in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f772,f98]) ).
fof(f98,plain,
! [X2] :
( in(sK21(X2),sK18)
| in(sK19(X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f772,plain,
( ~ in(sK21(sK11(sK18,sK17)),sK18)
| in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f763,f275]) ).
fof(f275,plain,
( in(sK19(sK11(sK18,sK17)),sF23)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f763,plain,
( ~ in(sK19(sK11(sK18,sK17)),sF23)
| ~ in(sK21(sK11(sK18,sK17)),sK18)
| in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| spl26_1
| ~ spl26_3
| ~ spl26_4 ),
inference(superposition,[],[f203,f759]) ).
fof(f759,plain,
( sK19(sK11(sK18,sK17)) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1
| ~ spl26_4 ),
inference(forward_demodulation,[],[f758,f263]) ).
fof(f263,plain,
( sK19(sK11(sK18,sK17)) = sF25(sK11(sK18,sK17))
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f261,plain,
( spl26_4
<=> sK19(sK11(sK18,sK17)) = sF25(sK11(sK18,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f758,plain,
( sF25(sK11(sK18,sK17)) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1 ),
inference(forward_demodulation,[],[f757,f109]) ).
fof(f109,plain,
! [X2] : ordered_pair(sK21(X2),sK20(X2)) = sF25(X2),
introduced(function_definition,[]) ).
fof(f757,plain,
( ordered_pair(sK21(sK11(sK18,sK17)),sK20(sK11(sK18,sK17))) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1 ),
inference(superposition,[],[f125,f738]) ).
fof(f738,plain,
( sK20(sK11(sK18,sK17)) = sF24(sK11(sK18,sK17))
| spl26_1 ),
inference(subsumption_resolution,[],[f303,f656]) ).
fof(f656,plain,
( ! [X0] :
( ~ in(sK19(sK11(sK18,X0)),sF23)
| sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0)) )
| spl26_1 ),
inference(subsumption_resolution,[],[f655,f166]) ).
fof(f655,plain,
( ! [X0] :
( ~ in(sK19(sK11(sK18,X0)),sF23)
| sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0))
| sP1(sK18) )
| spl26_1 ),
inference(duplicate_literal_removal,[],[f651]) ).
fof(f651,plain,
( ! [X0] :
( sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0))
| sP1(sK18)
| sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0))
| ~ in(sK19(sK11(sK18,X0)),sF23) )
| spl26_1 ),
inference(resolution,[],[f650,f143]) ).
fof(f143,plain,
! [X8,X7] :
( in(sK14(X7,sK19(sK11(X7,X8))),X7)
| sP1(X7)
| sF24(sK11(X7,X8)) = sK20(sK11(X7,X8)) ),
inference(resolution,[],[f85,f108]) ).
fof(f108,plain,
! [X2] :
( in(sK19(X2),X2)
| sK20(X2) = sF24(X2) ),
inference(definition_folding,[],[f97,f107]) ).
fof(f107,plain,
! [X2] : singleton(sK21(X2)) = sF24(X2),
introduced(function_definition,[]) ).
fof(f97,plain,
! [X2] :
( sK20(X2) = singleton(sK21(X2))
| in(sK19(X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f650,plain,
( ! [X0] :
( ~ in(sK14(sK18,sK19(sK11(sK18,X0))),sK18)
| sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0))
| ~ in(sK19(sK11(sK18,X0)),sF23) )
| spl26_1 ),
inference(subsumption_resolution,[],[f649,f108]) ).
fof(f649,plain,
( ! [X0] :
( ~ in(sK19(sK11(sK18,X0)),sK11(sK18,X0))
| ~ in(sK14(sK18,sK19(sK11(sK18,X0))),sK18)
| ~ in(sK19(sK11(sK18,X0)),sF23)
| sF24(sK11(sK18,X0)) = sK20(sK11(sK18,X0)) )
| spl26_1 ),
inference(equality_resolution,[],[f535]) ).
fof(f535,plain,
( ! [X2,X1] :
( sK19(sK11(sK18,X1)) != sK19(X2)
| ~ in(sK19(X2),X2)
| ~ in(sK14(sK18,sK19(sK11(sK18,X1))),sK18)
| sK20(sK11(sK18,X1)) = sF24(sK11(sK18,X1))
| ~ in(sK19(X2),sF23) )
| spl26_1 ),
inference(superposition,[],[f106,f534]) ).
fof(f534,plain,
( ! [X1] :
( sK19(sK11(sK18,X1)) = sF22(sK14(sK18,sK19(sK11(sK18,X1))))
| sK20(sK11(sK18,X1)) = sF24(sK11(sK18,X1)) )
| spl26_1 ),
inference(duplicate_literal_removal,[],[f530]) ).
fof(f530,plain,
( ! [X1] :
( sK19(sK11(sK18,X1)) = sF22(sK14(sK18,sK19(sK11(sK18,X1))))
| sK20(sK11(sK18,X1)) = sF24(sK11(sK18,X1))
| sK20(sK11(sK18,X1)) = sF24(sK11(sK18,X1)) )
| spl26_1 ),
inference(superposition,[],[f403,f332]) ).
fof(f332,plain,
( ! [X4] :
( ordered_pair(sK14(sK18,sK19(sK11(sK18,X4))),sK13(sK18,sK19(sK11(sK18,X4)))) = sF22(sK14(sK18,sK19(sK11(sK18,X4))))
| sF24(sK11(sK18,X4)) = sK20(sK11(sK18,X4)) )
| spl26_1 ),
inference(superposition,[],[f104,f322]) ).
fof(f322,plain,
( ! [X12] :
( sK13(sK18,sK19(sK11(sK18,X12))) = singleton(sK14(sK18,sK19(sK11(sK18,X12))))
| sK20(sK11(sK18,X12)) = sF24(sK11(sK18,X12)) )
| spl26_1 ),
inference(resolution,[],[f159,f166]) ).
fof(f159,plain,
! [X10,X11] :
( sP1(X10)
| sF24(sK11(X10,X11)) = sK20(sK11(X10,X11))
| sK13(X10,sK19(sK11(X10,X11))) = singleton(sK14(X10,sK19(sK11(X10,X11)))) ),
inference(resolution,[],[f83,f108]) ).
fof(f83,plain,
! [X3,X0,X1] :
( ~ in(X3,sK11(X0,X1))
| sP1(X0)
| sK13(X0,X3) = singleton(sK14(X0,X3)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f104,plain,
! [X5] : sF22(X5) = ordered_pair(X5,singleton(X5)),
introduced(function_definition,[]) ).
fof(f403,plain,
( ! [X12] :
( ordered_pair(sK14(sK18,sK19(sK11(sK18,X12))),sK13(sK18,sK19(sK11(sK18,X12)))) = sK19(sK11(sK18,X12))
| sK20(sK11(sK18,X12)) = sF24(sK11(sK18,X12)) )
| spl26_1 ),
inference(resolution,[],[f178,f166]) ).
fof(f178,plain,
! [X10,X11] :
( sP1(X10)
| sF24(sK11(X10,X11)) = sK20(sK11(X10,X11))
| sK19(sK11(X10,X11)) = ordered_pair(sK14(X10,sK19(sK11(X10,X11))),sK13(X10,sK19(sK11(X10,X11)))) ),
inference(resolution,[],[f84,f108]) ).
fof(f84,plain,
! [X3,X0,X1] :
( ~ in(X3,sK11(X0,X1))
| ordered_pair(sK14(X0,X3),sK13(X0,X3)) = X3
| sP1(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f106,plain,
! [X2,X5] :
( sF22(X5) != sK19(X2)
| ~ in(X5,sK18)
| ~ in(sK19(X2),sF23)
| ~ in(sK19(X2),X2) ),
inference(definition_folding,[],[f103,f105,f104]) ).
fof(f103,plain,
! [X2,X5] :
( ~ in(X5,sK18)
| sK19(X2) != ordered_pair(X5,singleton(X5))
| ~ in(sK19(X2),cartesian_product2(sK18,sK17))
| ~ in(sK19(X2),X2) ),
inference(equality_resolution,[],[f99]) ).
fof(f99,plain,
! [X2,X4,X5] :
( ~ in(X5,sK18)
| singleton(X5) != X4
| sK19(X2) != ordered_pair(X5,X4)
| ~ in(sK19(X2),cartesian_product2(sK18,sK17))
| ~ in(sK19(X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f303,plain,
( sK20(sK11(sK18,sK17)) = sF24(sK11(sK18,sK17))
| in(sK19(sK11(sK18,sK17)),sF23)
| spl26_1 ),
inference(superposition,[],[f300,f105]) ).
fof(f300,plain,
( ! [X2] :
( in(sK19(sK11(sK18,X2)),cartesian_product2(sK18,X2))
| sF24(sK11(sK18,X2)) = sK20(sK11(sK18,X2)) )
| spl26_1 ),
inference(subsumption_resolution,[],[f299,f108]) ).
fof(f299,plain,
( ! [X2] :
( sF24(sK11(sK18,X2)) = sK20(sK11(sK18,X2))
| ~ in(sK19(sK11(sK18,X2)),sK11(sK18,X2))
| in(sK19(sK11(sK18,X2)),cartesian_product2(sK18,X2)) )
| spl26_1 ),
inference(subsumption_resolution,[],[f296,f166]) ).
fof(f296,plain,
( ! [X2] :
( sF24(sK11(sK18,X2)) = sK20(sK11(sK18,X2))
| in(sK19(sK11(sK18,X2)),cartesian_product2(sK18,X2))
| ~ in(sK19(sK11(sK18,X2)),sK11(sK18,X2))
| sP1(sK18) )
| spl26_1 ),
inference(superposition,[],[f87,f289]) ).
fof(f289,plain,
( ! [X12] :
( sK12(sK18,X12,sK19(sK11(sK18,X12))) = sK19(sK11(sK18,X12))
| sK20(sK11(sK18,X12)) = sF24(sK11(sK18,X12)) )
| spl26_1 ),
inference(resolution,[],[f149,f166]) ).
fof(f149,plain,
! [X8,X7] :
( sP1(X7)
| sK12(X7,X8,sK19(sK11(X7,X8))) = sK19(sK11(X7,X8))
| sF24(sK11(X7,X8)) = sK20(sK11(X7,X8)) ),
inference(resolution,[],[f86,f108]) ).
fof(f86,plain,
! [X3,X0,X1] :
( ~ in(X3,sK11(X0,X1))
| sK12(X0,X1,X3) = X3
| sP1(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f125,plain,
! [X0] : sF22(sK21(X0)) = ordered_pair(sK21(X0),sF24(X0)),
inference(superposition,[],[f104,f107]) ).
fof(f203,plain,
( ! [X0] :
( in(sF22(X0),sK11(sK18,sK17))
| ~ in(sF22(X0),sF23)
| ~ in(X0,sK18) )
| ~ spl26_3 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f202,plain,
( spl26_3
<=> ! [X0] :
( ~ in(X0,sK18)
| in(sF22(X0),sK11(sK18,sK17))
| ~ in(sF22(X0),sF23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
fof(f819,plain,
( spl26_11
| ~ spl26_9
| ~ spl26_10
| ~ spl26_12 ),
inference(avatar_split_clause,[],[f818,f707,f695,f687,f702]) ).
fof(f702,plain,
( spl26_11
<=> ! [X0] :
( ~ in(sK19(X0),X0)
| ~ in(sK19(X0),sF23)
| sK19(sK11(sK18,sK17)) != sK19(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f687,plain,
( spl26_9
<=> singleton(sK14(sK18,sK19(sK11(sK18,sK17)))) = sK13(sK18,sK19(sK11(sK18,sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f695,plain,
( spl26_10
<=> ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f818,plain,
( ! [X0] :
( ~ in(sK19(X0),sF23)
| ~ in(sK19(X0),X0)
| sK19(sK11(sK18,sK17)) != sK19(X0) )
| ~ spl26_9
| ~ spl26_10
| ~ spl26_12 ),
inference(subsumption_resolution,[],[f794,f709]) ).
fof(f709,plain,
( in(sK14(sK18,sK19(sK11(sK18,sK17))),sK18)
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f794,plain,
( ! [X0] :
( ~ in(sK14(sK18,sK19(sK11(sK18,sK17))),sK18)
| sK19(sK11(sK18,sK17)) != sK19(X0)
| ~ in(sK19(X0),sF23)
| ~ in(sK19(X0),X0) )
| ~ spl26_9
| ~ spl26_10 ),
inference(superposition,[],[f106,f793]) ).
fof(f793,plain,
( sK19(sK11(sK18,sK17)) = sF22(sK14(sK18,sK19(sK11(sK18,sK17))))
| ~ spl26_9
| ~ spl26_10 ),
inference(forward_demodulation,[],[f790,f697]) ).
fof(f697,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17))
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f790,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sF22(sK14(sK18,sK19(sK11(sK18,sK17))))
| ~ spl26_9 ),
inference(superposition,[],[f104,f689]) ).
fof(f689,plain,
( singleton(sK14(sK18,sK19(sK11(sK18,sK17)))) = sK13(sK18,sK19(sK11(sK18,sK17)))
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f814,plain,
( spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6
| ~ spl26_11 ),
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f813,plain,
( $false
| spl26_1
| ~ spl26_3
| ~ spl26_4
| ~ spl26_6
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f805,f808]) ).
fof(f805,plain,
( ~ in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| ~ spl26_6
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f804,f275]) ).
fof(f804,plain,
( ~ in(sK19(sK11(sK18,sK17)),sF23)
| ~ in(sK19(sK11(sK18,sK17)),sK11(sK18,sK17))
| ~ spl26_11 ),
inference(equality_resolution,[],[f703]) ).
fof(f703,plain,
( ! [X0] :
( sK19(sK11(sK18,sK17)) != sK19(X0)
| ~ in(sK19(X0),X0)
| ~ in(sK19(X0),sF23) )
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f737,plain,
( spl26_8
| spl26_1
| spl26_6 ),
inference(avatar_split_clause,[],[f736,f273,f165,f681]) ).
fof(f736,plain,
( sK19(sK11(sK18,sK17)) = sK12(sK18,sK17,sK19(sK11(sK18,sK17)))
| spl26_1
| spl26_6 ),
inference(subsumption_resolution,[],[f730,f166]) ).
fof(f730,plain,
( sP1(sK18)
| sK19(sK11(sK18,sK17)) = sK12(sK18,sK17,sK19(sK11(sK18,sK17)))
| spl26_6 ),
inference(resolution,[],[f274,f150]) ).
fof(f150,plain,
! [X10,X9] :
( in(sK19(sK11(X9,X10)),sF23)
| sK12(X9,X10,sK19(sK11(X9,X10))) = sK19(sK11(X9,X10))
| sP1(X9) ),
inference(resolution,[],[f86,f111]) ).
fof(f274,plain,
( ~ in(sK19(sK11(sK18,sK17)),sF23)
| spl26_6 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f735,plain,
( spl26_10
| spl26_1
| spl26_6 ),
inference(avatar_split_clause,[],[f734,f273,f165,f695]) ).
fof(f734,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17))
| spl26_1
| spl26_6 ),
inference(subsumption_resolution,[],[f728,f166]) ).
fof(f728,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17))
| sP1(sK18)
| spl26_6 ),
inference(resolution,[],[f274,f179]) ).
fof(f179,plain,
! [X12,X13] :
( in(sK19(sK11(X12,X13)),sF23)
| sK19(sK11(X12,X13)) = ordered_pair(sK14(X12,sK19(sK11(X12,X13))),sK13(X12,sK19(sK11(X12,X13))))
| sP1(X12) ),
inference(resolution,[],[f84,f111]) ).
fof(f726,plain,
( spl26_10
| spl26_1
| spl26_7 ),
inference(avatar_split_clause,[],[f725,f677,f165,f695]) ).
fof(f677,plain,
( spl26_7
<=> in(sK21(sK11(sK18,sK17)),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
fof(f725,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17))
| spl26_1
| spl26_7 ),
inference(subsumption_resolution,[],[f717,f166]) ).
fof(f717,plain,
( ordered_pair(sK14(sK18,sK19(sK11(sK18,sK17))),sK13(sK18,sK19(sK11(sK18,sK17)))) = sK19(sK11(sK18,sK17))
| sP1(sK18)
| spl26_7 ),
inference(resolution,[],[f679,f180]) ).
fof(f180,plain,
! [X14,X15] :
( in(sK21(sK11(X14,X15)),sK18)
| ordered_pair(sK14(X14,sK19(sK11(X14,X15))),sK13(X14,sK19(sK11(X14,X15)))) = sK19(sK11(X14,X15))
| sP1(X14) ),
inference(resolution,[],[f84,f98]) ).
fof(f679,plain,
( ~ in(sK21(sK11(sK18,sK17)),sK18)
| spl26_7 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f724,plain,
( spl26_9
| spl26_1
| spl26_7 ),
inference(avatar_split_clause,[],[f723,f677,f165,f687]) ).
fof(f723,plain,
( singleton(sK14(sK18,sK19(sK11(sK18,sK17)))) = sK13(sK18,sK19(sK11(sK18,sK17)))
| spl26_1
| spl26_7 ),
inference(subsumption_resolution,[],[f718,f166]) ).
fof(f718,plain,
( sP1(sK18)
| singleton(sK14(sK18,sK19(sK11(sK18,sK17)))) = sK13(sK18,sK19(sK11(sK18,sK17)))
| spl26_7 ),
inference(resolution,[],[f679,f161]) ).
fof(f161,plain,
! [X14,X15] :
( in(sK21(sK11(X14,X15)),sK18)
| sP1(X14)
| sK13(X14,sK19(sK11(X14,X15))) = singleton(sK14(X14,sK19(sK11(X14,X15)))) ),
inference(resolution,[],[f83,f98]) ).
fof(f704,plain,
( ~ spl26_7
| spl26_11
| spl26_1
| ~ spl26_4
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f665,f273,f261,f165,f702,f677]) ).
fof(f665,plain,
( ! [X0] :
( ~ in(sK19(X0),X0)
| sK19(sK11(sK18,sK17)) != sK19(X0)
| ~ in(sK19(X0),sF23)
| ~ in(sK21(sK11(sK18,sK17)),sK18) )
| spl26_1
| ~ spl26_4
| ~ spl26_6 ),
inference(superposition,[],[f106,f664]) ).
fof(f664,plain,
( sK19(sK11(sK18,sK17)) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1
| ~ spl26_4
| ~ spl26_6 ),
inference(forward_demodulation,[],[f663,f263]) ).
fof(f663,plain,
( sF25(sK11(sK18,sK17)) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1
| ~ spl26_6 ),
inference(forward_demodulation,[],[f662,f109]) ).
fof(f662,plain,
( ordered_pair(sK21(sK11(sK18,sK17)),sK20(sK11(sK18,sK17))) = sF22(sK21(sK11(sK18,sK17)))
| spl26_1
| ~ spl26_6 ),
inference(superposition,[],[f125,f657]) ).
fof(f657,plain,
( sK20(sK11(sK18,sK17)) = sF24(sK11(sK18,sK17))
| spl26_1
| ~ spl26_6 ),
inference(resolution,[],[f656,f275]) ).
fof(f642,plain,
( spl26_4
| spl26_1
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f637,f273,f165,f261]) ).
fof(f637,plain,
( sK19(sK11(sK18,sK17)) = sF25(sK11(sK18,sK17))
| spl26_1
| ~ spl26_6 ),
inference(resolution,[],[f636,f275]) ).
fof(f636,plain,
( ! [X1] :
( ~ in(sK19(sK11(sK18,X1)),sF23)
| sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1)) )
| spl26_1 ),
inference(subsumption_resolution,[],[f635,f166]) ).
fof(f635,plain,
( ! [X1] :
( ~ in(sK19(sK11(sK18,X1)),sF23)
| sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1))
| sP1(sK18) )
| spl26_1 ),
inference(duplicate_literal_removal,[],[f632]) ).
fof(f632,plain,
( ! [X1] :
( sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1))
| sP1(sK18)
| sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1))
| ~ in(sK19(sK11(sK18,X1)),sF23) )
| spl26_1 ),
inference(resolution,[],[f630,f142]) ).
fof(f142,plain,
! [X6,X5] :
( in(sK14(X5,sK19(sK11(X5,X6))),X5)
| sK19(sK11(X5,X6)) = sF25(sK11(X5,X6))
| sP1(X5) ),
inference(resolution,[],[f85,f110]) ).
fof(f110,plain,
! [X2] :
( in(sK19(X2),X2)
| sK19(X2) = sF25(X2) ),
inference(definition_folding,[],[f96,f109]) ).
fof(f96,plain,
! [X2] :
( sK19(X2) = ordered_pair(sK21(X2),sK20(X2))
| in(sK19(X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f630,plain,
( ! [X0] :
( ~ in(sK14(sK18,sK19(sK11(sK18,X0))),sK18)
| ~ in(sK19(sK11(sK18,X0)),sF23)
| sF25(sK11(sK18,X0)) = sK19(sK11(sK18,X0)) )
| spl26_1 ),
inference(subsumption_resolution,[],[f629,f110]) ).
fof(f629,plain,
( ! [X0] :
( ~ in(sK19(sK11(sK18,X0)),sF23)
| ~ in(sK14(sK18,sK19(sK11(sK18,X0))),sK18)
| sF25(sK11(sK18,X0)) = sK19(sK11(sK18,X0))
| ~ in(sK19(sK11(sK18,X0)),sK11(sK18,X0)) )
| spl26_1 ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
( ! [X0,X1] :
( sK19(X1) != sK19(sK11(sK18,X0))
| ~ in(sK19(X1),X1)
| sF25(sK11(sK18,X0)) = sK19(sK11(sK18,X0))
| ~ in(sK14(sK18,sK19(sK11(sK18,X0))),sK18)
| ~ in(sK19(X1),sF23) )
| spl26_1 ),
inference(superposition,[],[f106,f517]) ).
fof(f517,plain,
( ! [X1] :
( sK19(sK11(sK18,X1)) = sF22(sK14(sK18,sK19(sK11(sK18,X1))))
| sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1)) )
| spl26_1 ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f514,plain,
( ! [X1] :
( sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1))
| sF25(sK11(sK18,X1)) = sK19(sK11(sK18,X1))
| sK19(sK11(sK18,X1)) = sF22(sK14(sK18,sK19(sK11(sK18,X1)))) )
| spl26_1 ),
inference(superposition,[],[f349,f327]) ).
fof(f327,plain,
( ! [X3] :
( ordered_pair(sK14(sK18,sK19(sK11(sK18,X3))),sK13(sK18,sK19(sK11(sK18,X3)))) = sF22(sK14(sK18,sK19(sK11(sK18,X3))))
| sF25(sK11(sK18,X3)) = sK19(sK11(sK18,X3)) )
| spl26_1 ),
inference(superposition,[],[f104,f312]) ).
fof(f312,plain,
( ! [X12] :
( sK13(sK18,sK19(sK11(sK18,X12))) = singleton(sK14(sK18,sK19(sK11(sK18,X12))))
| sF25(sK11(sK18,X12)) = sK19(sK11(sK18,X12)) )
| spl26_1 ),
inference(resolution,[],[f158,f166]) ).
fof(f158,plain,
! [X8,X9] :
( sP1(X8)
| sK19(sK11(X8,X9)) = sF25(sK11(X8,X9))
| singleton(sK14(X8,sK19(sK11(X8,X9)))) = sK13(X8,sK19(sK11(X8,X9))) ),
inference(resolution,[],[f83,f110]) ).
fof(f349,plain,
( ! [X12] :
( ordered_pair(sK14(sK18,sK19(sK11(sK18,X12))),sK13(sK18,sK19(sK11(sK18,X12)))) = sK19(sK11(sK18,X12))
| sF25(sK11(sK18,X12)) = sK19(sK11(sK18,X12)) )
| spl26_1 ),
inference(resolution,[],[f177,f166]) ).
fof(f177,plain,
! [X8,X9] :
( sP1(X8)
| sK19(sK11(X8,X9)) = sF25(sK11(X8,X9))
| ordered_pair(sK14(X8,sK19(sK11(X8,X9))),sK13(X8,sK19(sK11(X8,X9)))) = sK19(sK11(X8,X9)) ),
inference(resolution,[],[f84,f110]) ).
fof(f219,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f218,plain,
( $false
| ~ spl26_1 ),
inference(subsumption_resolution,[],[f217,f167]) ).
fof(f167,plain,
( sP1(sK18)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f217,plain,
( ~ sP1(sK18)
| ~ spl26_1 ),
inference(subsumption_resolution,[],[f213,f212]) ).
fof(f212,plain,
( sK4(sK18) = sK5(sK18)
| ~ spl26_1 ),
inference(resolution,[],[f167,f72]) ).
fof(f72,plain,
! [X0] :
( ~ sP1(X0)
| sK5(X0) = sK4(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ( ordered_pair(sK8(X0),sK7(X0)) = sK4(X0)
& in(sK8(X0),X0)
& sK7(X0) = singleton(sK8(X0))
& sK5(X0) = sK6(X0)
& sP0(X0,sK6(X0))
& sK4(X0) != sK6(X0)
& sK5(X0) = sK4(X0) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f37,f39,f38]) ).
fof(f38,plain,
! [X0] :
( ? [X1,X2,X3] :
( ? [X4,X5] :
( ordered_pair(X5,X4) = X1
& in(X5,X0)
& singleton(X5) = X4 )
& X2 = X3
& sP0(X0,X3)
& X1 != X3
& X1 = X2 )
=> ( ? [X5,X4] :
( ordered_pair(X5,X4) = sK4(X0)
& in(X5,X0)
& singleton(X5) = X4 )
& sK5(X0) = sK6(X0)
& sP0(X0,sK6(X0))
& sK4(X0) != sK6(X0)
& sK5(X0) = sK4(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0] :
( ? [X5,X4] :
( ordered_pair(X5,X4) = sK4(X0)
& in(X5,X0)
& singleton(X5) = X4 )
=> ( ordered_pair(sK8(X0),sK7(X0)) = sK4(X0)
& in(sK8(X0),X0)
& sK7(X0) = singleton(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0] :
( ? [X1,X2,X3] :
( ? [X4,X5] :
( ordered_pair(X5,X4) = X1
& in(X5,X0)
& singleton(X5) = X4 )
& X2 = X3
& sP0(X0,X3)
& X1 != X3
& X1 = X2 )
| ~ sP1(X0) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ? [X4,X3,X2] :
( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(X8,X0)
& singleton(X8) = X7 )
& X2 = X3
& sP0(X0,X2)
& X2 != X4
& X3 = X4 )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f30]) ).
fof(f213,plain,
( sK4(sK18) != sK5(sK18)
| ~ sP1(sK18)
| ~ spl26_1 ),
inference(superposition,[],[f73,f211]) ).
fof(f211,plain,
( sK6(sK18) = sK5(sK18)
| ~ spl26_1 ),
inference(resolution,[],[f167,f75]) ).
fof(f75,plain,
! [X0] :
( ~ sP1(X0)
| sK5(X0) = sK6(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X0] :
( sK4(X0) != sK6(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f204,plain,
( spl26_1
| spl26_3 ),
inference(avatar_split_clause,[],[f200,f202,f165]) ).
fof(f200,plain,
! [X0] :
( ~ in(X0,sK18)
| sP1(sK18)
| ~ in(sF22(X0),sF23)
| in(sF22(X0),sK11(sK18,sK17)) ),
inference(forward_demodulation,[],[f199,f104]) ).
fof(f199,plain,
! [X0] :
( in(sF22(X0),sK11(sK18,sK17))
| ~ in(ordered_pair(X0,singleton(X0)),sF23)
| ~ in(X0,sK18)
| sP1(sK18) ),
inference(forward_demodulation,[],[f198,f104]) ).
fof(f198,plain,
! [X0] :
( sP1(sK18)
| in(ordered_pair(X0,singleton(X0)),sK11(sK18,sK17))
| ~ in(ordered_pair(X0,singleton(X0)),sF23)
| ~ in(X0,sK18) ),
inference(superposition,[],[f102,f105]) ).
fof(f102,plain,
! [X0,X1,X9] :
( ~ in(ordered_pair(X9,singleton(X9)),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| sP1(X0)
| in(ordered_pair(X9,singleton(X9)),sK11(X0,X1)) ),
inference(equality_resolution,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X8,X9] :
( sP1(X0)
| in(ordered_pair(X9,X8),sK11(X0,X1))
| ~ in(ordered_pair(X9,X8),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| singleton(X9) != X8 ),
inference(equality_resolution,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X8,X9,X7] :
( sP1(X0)
| in(X7,sK11(X0,X1))
| ~ in(X7,cartesian_product2(X0,X1))
| ~ in(X9,X0)
| ordered_pair(X9,X8) != X7
| singleton(X9) != X8 ),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X3,X0,X1,X8,X9,X7] :
( sP1(X0)
| in(X3,sK11(X0,X1))
| ~ in(X7,cartesian_product2(X0,X1))
| X3 != X7
| ~ in(X9,X0)
| ordered_pair(X9,X8) != X3
| singleton(X9) != X8 ),
inference(cnf_transformation,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU281+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
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 15:18:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.47 % (18553)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.47 % (18560)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)
% 0.20/0.48 % (18578)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)
% 0.20/0.50 % (18570)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.52 % (18562)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (18571)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)
% 0.20/0.52 % (18563)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 % (18577)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.53 % (18549)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)
% 0.20/0.53 % (18555)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 TRYING [1]
% 0.20/0.53 % (18550)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 TRYING [2]
% 0.20/0.53 % (18559)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (18550)Refutation not found, incomplete strategy% (18550)------------------------------
% 0.20/0.53 % (18550)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (18550)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (18550)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (18550)Memory used [KB]: 5500
% 0.20/0.53 % (18550)Time elapsed: 0.123 s
% 0.20/0.53 % (18550)Instructions burned: 3 (million)
% 0.20/0.53 % (18550)------------------------------
% 0.20/0.53 % (18550)------------------------------
% 0.20/0.53 % (18561)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54 TRYING [1]
% 0.20/0.54 % (18565)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)
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (18564)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 % (18573)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54 % (18552)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)
% 0.20/0.54 TRYING [3]
% 1.48/0.55 % (18558)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)
% 1.48/0.55 % (18556)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.48/0.55 TRYING [3]
% 1.48/0.55 % (18557)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.48/0.55 % (18557)Instruction limit reached!
% 1.48/0.55 % (18557)------------------------------
% 1.48/0.55 % (18557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.55 % (18557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.55 % (18557)Termination reason: Unknown
% 1.48/0.55 % (18557)Termination phase: Property scanning
% 1.48/0.55
% 1.48/0.55 % (18557)Memory used [KB]: 895
% 1.48/0.55 % (18557)Time elapsed: 0.002 s
% 1.48/0.55 % (18557)Instructions burned: 3 (million)
% 1.48/0.55 % (18557)------------------------------
% 1.48/0.55 % (18557)------------------------------
% 1.48/0.55 % (18554)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)
% 1.48/0.56 % (18572)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)
% 1.48/0.56 % (18556)Instruction limit reached!
% 1.48/0.56 % (18556)------------------------------
% 1.48/0.56 % (18556)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.56 % (18556)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.56 % (18556)Termination reason: Unknown
% 1.48/0.56 % (18556)Termination phase: Saturation
% 1.48/0.56
% 1.48/0.56 % (18556)Memory used [KB]: 5500
% 1.48/0.56 % (18556)Time elapsed: 0.150 s
% 1.48/0.56 % (18556)Instructions burned: 7 (million)
% 1.48/0.56 % (18556)------------------------------
% 1.48/0.56 % (18556)------------------------------
% 1.48/0.56 % (18551)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)
% 1.48/0.56 % (18575)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)
% 1.65/0.56 % (18568)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)
% 1.65/0.56 % (18574)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.65/0.56 % (18576)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)
% 1.65/0.57 % (18553)Instruction limit reached!
% 1.65/0.57 % (18553)------------------------------
% 1.65/0.57 % (18553)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.57 % (18566)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.65/0.57 % (18567)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.65/0.58 % (18569)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)
% 1.65/0.59 % (18553)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.59 % (18553)Termination reason: Unknown
% 1.65/0.59 % (18553)Termination phase: Saturation
% 1.65/0.59
% 1.65/0.59 % (18553)Memory used [KB]: 6012
% 1.65/0.59 % (18553)Time elapsed: 0.179 s
% 1.65/0.59 % (18553)Instructions burned: 52 (million)
% 1.65/0.59 % (18553)------------------------------
% 1.65/0.59 % (18553)------------------------------
% 1.65/0.59 TRYING [1]
% 1.65/0.59 TRYING [2]
% 1.65/0.59 TRYING [3]
% 1.65/0.59 TRYING [4]
% 1.65/0.60 TRYING [4]
% 1.65/0.60 % (18555)Instruction limit reached!
% 1.65/0.60 % (18555)------------------------------
% 1.65/0.60 % (18555)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.61 % (18560)Instruction limit reached!
% 1.65/0.61 % (18560)------------------------------
% 1.65/0.61 % (18560)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.61 % (18560)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.61 % (18560)Termination reason: Unknown
% 1.65/0.61 % (18560)Termination phase: Saturation
% 1.65/0.61
% 1.65/0.61 % (18560)Memory used [KB]: 5884
% 1.65/0.61 % (18560)Time elapsed: 0.222 s
% 1.65/0.61 % (18560)Instructions burned: 101 (million)
% 1.65/0.61 % (18560)------------------------------
% 1.65/0.61 % (18560)------------------------------
% 1.65/0.62 % (18562)First to succeed.
% 1.65/0.62 % (18555)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.62 % (18555)Termination reason: Unknown
% 1.65/0.62 % (18555)Termination phase: Finite model building SAT solving
% 1.65/0.62
% 1.65/0.62 % (18555)Memory used [KB]: 7036
% 1.65/0.62 % (18555)Time elapsed: 0.147 s
% 1.65/0.62 % (18555)Instructions burned: 52 (million)
% 1.65/0.62 % (18555)------------------------------
% 1.65/0.62 % (18555)------------------------------
% 1.65/0.63 % (18559)Instruction limit reached!
% 1.65/0.63 % (18559)------------------------------
% 1.65/0.63 % (18559)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.63 % (18559)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.63 % (18559)Termination reason: Unknown
% 1.65/0.63 % (18559)Termination phase: Saturation
% 1.65/0.63
% 1.65/0.63 % (18559)Memory used [KB]: 6012
% 1.65/0.63 % (18559)Time elapsed: 0.215 s
% 1.65/0.63 % (18559)Instructions burned: 50 (million)
% 1.65/0.63 % (18559)------------------------------
% 1.65/0.63 % (18559)------------------------------
% 2.16/0.63 % (18551)Instruction limit reached!
% 2.16/0.63 % (18551)------------------------------
% 2.16/0.63 % (18551)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.16/0.63 % (18551)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.16/0.63 % (18551)Termination reason: Unknown
% 2.16/0.63 % (18551)Termination phase: Saturation
% 2.16/0.63
% 2.16/0.63 % (18551)Memory used [KB]: 1279
% 2.16/0.63 % (18551)Time elapsed: 0.226 s
% 2.16/0.63 % (18551)Instructions burned: 38 (million)
% 2.16/0.63 % (18551)------------------------------
% 2.16/0.63 % (18551)------------------------------
% 2.16/0.63 % (18562)Refutation found. Thanks to Tanya!
% 2.16/0.63 % SZS status Theorem for theBenchmark
% 2.16/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 2.16/0.63 % (18562)------------------------------
% 2.16/0.63 % (18562)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.16/0.63 % (18562)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.16/0.63 % (18562)Termination reason: Refutation
% 2.16/0.63
% 2.16/0.63 % (18562)Memory used [KB]: 6012
% 2.16/0.63 % (18562)Time elapsed: 0.202 s
% 2.16/0.63 % (18562)Instructions burned: 61 (million)
% 2.16/0.63 % (18562)------------------------------
% 2.16/0.63 % (18562)------------------------------
% 2.16/0.63 % (18548)Success in time 0.275 s
%------------------------------------------------------------------------------