TSTP Solution File: SYN036+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n010.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 19:25:14 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 50
% Syntax : Number of formulae : 212 ( 1 unt; 0 def)
% Number of atoms : 969 ( 0 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1214 ( 457 ~; 590 |; 83 &)
% ( 58 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 26 prp; 0-1 aty)
% Number of functors : 24 ( 24 usr; 20 con; 0-1 aty)
% Number of variables : 360 ( 268 !; 92 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1211,plain,
$false,
inference(avatar_sat_refutation,[],[f81,f82,f104,f121,f125,f129,f135,f136,f158,f169,f179,f186,f189,f191,f193,f198,f348,f496,f500,f502,f513,f537,f539,f592,f611,f620,f624,f625,f626,f765,f770,f778,f786,f787,f788,f789,f802,f904,f1004,f1042,f1169,f1206]) ).
fof(f1206,plain,
( ~ spl26_6
| spl26_30 ),
inference(avatar_contradiction_clause,[],[f1195]) ).
fof(f1195,plain,
( $false
| ~ spl26_6
| spl26_30 ),
inference(resolution,[],[f103,f777]) ).
fof(f777,plain,
( ~ big_q(sK15)
| spl26_30 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f775,plain,
( spl26_30
<=> big_q(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_30])]) ).
fof(f103,plain,
( ! [X2] : big_q(X2)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl26_6
<=> ! [X2] : big_q(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f1169,plain,
( ~ spl26_3
| ~ spl26_29 ),
inference(avatar_contradiction_clause,[],[f1168]) ).
fof(f1168,plain,
( $false
| ~ spl26_3
| ~ spl26_29 ),
inference(subsumption_resolution,[],[f1167,f93]) ).
fof(f93,plain,
( ! [X0] : big_p(X0)
| ~ spl26_3 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl26_3
<=> ! [X0] : big_p(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
fof(f1167,plain,
( ! [X27] : ~ big_p(X27)
| ~ spl26_3
| ~ spl26_29 ),
inference(resolution,[],[f773,f93]) ).
fof(f773,plain,
( ! [X3] :
( ~ big_p(sK14(X3))
| ~ big_p(X3) )
| ~ spl26_29 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f772,plain,
( spl26_29
<=> ! [X3] :
( ~ big_p(X3)
| ~ big_p(sK14(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_29])]) ).
fof(f1042,plain,
( ~ spl26_3
| spl26_26 ),
inference(avatar_contradiction_clause,[],[f1030]) ).
fof(f1030,plain,
( $false
| ~ spl26_3
| spl26_26 ),
inference(resolution,[],[f93,f619]) ).
fof(f619,plain,
( ~ big_p(sK12)
| spl26_26 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f617,plain,
( spl26_26
<=> big_p(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_26])]) ).
fof(f1004,plain,
( ~ spl26_11
| ~ spl26_32 ),
inference(avatar_contradiction_clause,[],[f1003]) ).
fof(f1003,plain,
( $false
| ~ spl26_11
| ~ spl26_32 ),
inference(resolution,[],[f785,f124]) ).
fof(f124,plain,
( ! [X2] : ~ big_q(X2)
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f123,plain,
( spl26_11
<=> ! [X2] : ~ big_q(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f785,plain,
( big_q(sK16)
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f783,plain,
( spl26_32
<=> big_q(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_32])]) ).
fof(f904,plain,
( ~ spl26_4
| ~ spl26_23 ),
inference(avatar_contradiction_clause,[],[f903]) ).
fof(f903,plain,
( $false
| ~ spl26_4
| ~ spl26_23 ),
inference(resolution,[],[f606,f96]) ).
fof(f96,plain,
( ! [X1] : ~ big_p(X1)
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f95,plain,
( spl26_4
<=> ! [X1] : ~ big_p(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f606,plain,
( big_p(sK13)
| ~ spl26_23 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f604,plain,
( spl26_23
<=> big_p(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_23])]) ).
fof(f802,plain,
( ~ spl26_4
| ~ spl26_31 ),
inference(avatar_contradiction_clause,[],[f801]) ).
fof(f801,plain,
( $false
| ~ spl26_4
| ~ spl26_31 ),
inference(subsumption_resolution,[],[f800,f96]) ).
fof(f800,plain,
( ! [X3] : big_p(X3)
| ~ spl26_4
| ~ spl26_31 ),
inference(subsumption_resolution,[],[f781,f96]) ).
fof(f781,plain,
( ! [X3] :
( big_p(X3)
| big_p(sK14(X3)) )
| ~ spl26_31 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f780,plain,
( spl26_31
<=> ! [X3] :
( big_p(sK14(X3))
| big_p(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_31])]) ).
fof(f789,plain,
( ~ spl26_30
| spl26_31
| spl26_11
| spl26_2 ),
inference(avatar_split_clause,[],[f632,f78,f123,f780,f775]) ).
fof(f78,plain,
( spl26_2
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
fof(f632,plain,
( ! [X3,X5] :
( ~ big_q(X5)
| big_p(sK14(X3))
| ~ big_q(sK15)
| big_p(X3) )
| spl26_2 ),
inference(resolution,[],[f80,f68]) ).
fof(f68,plain,
! [X2,X0] :
( big_p(sK14(X0))
| ~ big_q(sK15)
| ~ big_q(X2)
| sP0
| big_p(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
( ( sP0
| ( ( ! [X0] :
( ( ~ big_p(sK14(X0))
| ~ big_p(X0) )
& ( big_p(sK14(X0))
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ~ big_q(sK15) )
& ( big_q(sK16)
| ! [X5] : big_q(X5) ) ) )
& ( ! [X7] :
( ( big_p(sK17)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(sK17) ) )
| ( ( ! [X8] : big_q(X8)
| ! [X9] : ~ big_q(X9) )
& ( big_q(sK18)
| ~ big_q(sK19) ) ) ) ) )
& ( ( ( ( ( ! [X12] : big_q(X12)
| ! [X13] : ~ big_q(X13) )
& ( big_q(sK20)
| ~ big_q(sK21) ) )
| ! [X16] :
( ( ~ big_p(sK22(X16))
| ~ big_p(X16) )
& ( big_p(sK22(X16))
| big_p(X16) ) ) )
& ( ! [X19] :
( ( big_p(sK23)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(sK23) ) )
| ( ( ! [X20] : ~ big_q(X20)
| ~ big_q(sK24) )
& ( big_q(sK25)
| ! [X23] : big_q(X23) ) ) ) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25])],[f24,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
=> ( ( ~ big_p(sK14(X0))
| ~ big_p(X0) )
& ( big_p(sK14(X0))
| big_p(X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ? [X3] : ~ big_q(X3)
=> ~ big_q(sK15) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
( ? [X4] : big_q(X4)
=> big_q(sK16) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X6] :
! [X7] :
( ( big_p(X6)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(X6) ) )
=> ! [X7] :
( ( big_p(sK17)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(sK17) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ? [X10] : big_q(X10)
=> big_q(sK18) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ? [X11] : ~ big_q(X11)
=> ~ big_q(sK19) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
( ? [X14] : big_q(X14)
=> big_q(sK20) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X15] : ~ big_q(X15)
=> ~ big_q(sK21) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X16] :
( ? [X17] :
( ( ~ big_p(X17)
| ~ big_p(X16) )
& ( big_p(X17)
| big_p(X16) ) )
=> ( ( ~ big_p(sK22(X16))
| ~ big_p(X16) )
& ( big_p(sK22(X16))
| big_p(X16) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ? [X18] :
! [X19] :
( ( big_p(X18)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(X18) ) )
=> ! [X19] :
( ( big_p(sK23)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(sK23) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
( ? [X21] : ~ big_q(X21)
=> ~ big_q(sK24) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ? [X22] : big_q(X22)
=> big_q(sK25) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ( sP0
| ( ( ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ? [X3] : ~ big_q(X3) )
& ( ? [X4] : big_q(X4)
| ! [X5] : big_q(X5) ) ) )
& ( ? [X6] :
! [X7] :
( ( big_p(X6)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(X6) ) )
| ( ( ! [X8] : big_q(X8)
| ! [X9] : ~ big_q(X9) )
& ( ? [X10] : big_q(X10)
| ? [X11] : ~ big_q(X11) ) ) ) ) )
& ( ( ( ( ( ! [X12] : big_q(X12)
| ! [X13] : ~ big_q(X13) )
& ( ? [X14] : big_q(X14)
| ? [X15] : ~ big_q(X15) ) )
| ! [X16] :
? [X17] :
( ( ~ big_p(X17)
| ~ big_p(X16) )
& ( big_p(X17)
| big_p(X16) ) ) )
& ( ? [X18] :
! [X19] :
( ( big_p(X18)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(X18) ) )
| ( ( ! [X20] : ~ big_q(X20)
| ? [X21] : ~ big_q(X21) )
& ( ? [X22] : big_q(X22)
| ! [X23] : big_q(X23) ) ) ) )
| ~ sP0 ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
( ( sP0
| ( ( ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
| ( ( ! [X3] : ~ big_q(X3)
| ? [X2] : ~ big_q(X2) )
& ( ? [X3] : big_q(X3)
| ! [X2] : big_q(X2) ) ) )
& ( ? [X0] :
! [X1] :
( ( big_p(X0)
| ~ big_p(X1) )
& ( big_p(X1)
| ~ big_p(X0) ) )
| ( ( ! [X2] : big_q(X2)
| ! [X3] : ~ big_q(X3) )
& ( ? [X3] : big_q(X3)
| ? [X2] : ~ big_q(X2) ) ) ) ) )
& ( ( ( ( ( ! [X2] : big_q(X2)
| ! [X3] : ~ big_q(X3) )
& ( ? [X3] : big_q(X3)
| ? [X2] : ~ big_q(X2) ) )
| ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) ) )
& ( ? [X0] :
! [X1] :
( ( big_p(X0)
| ~ big_p(X1) )
& ( big_p(X1)
| ~ big_p(X0) ) )
| ( ( ! [X3] : ~ big_q(X3)
| ? [X2] : ~ big_q(X2) )
& ( ? [X3] : big_q(X3)
| ! [X2] : big_q(X2) ) ) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,plain,
( sP0
<=> ( ( ! [X2] : big_q(X2)
<=> ? [X3] : big_q(X3) )
<=> ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f80,plain,
( ~ sP0
| spl26_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f788,plain,
( spl26_32
| spl26_6
| spl26_29
| spl26_2 ),
inference(avatar_split_clause,[],[f633,f78,f772,f102,f783]) ).
fof(f633,plain,
( ! [X3,X4] :
( ~ big_p(sK14(X3))
| big_q(X4)
| ~ big_p(X3)
| big_q(sK16) )
| spl26_2 ),
inference(resolution,[],[f80,f69]) ).
fof(f69,plain,
! [X0,X5] :
( sP0
| big_q(sK16)
| ~ big_p(sK14(X0))
| big_q(X5)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f787,plain,
( spl26_11
| spl26_6
| ~ spl26_28
| spl26_3
| spl26_2 ),
inference(avatar_split_clause,[],[f628,f78,f92,f767,f102,f123]) ).
fof(f767,plain,
( spl26_28
<=> big_p(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_28])]) ).
fof(f628,plain,
( ! [X2,X0,X1] :
( big_p(X0)
| ~ big_p(sK17)
| big_q(X2)
| ~ big_q(X1) )
| spl26_2 ),
inference(resolution,[],[f80,f64]) ).
fof(f64,plain,
! [X8,X9,X7] :
( sP0
| big_p(X7)
| ~ big_q(X9)
| ~ big_p(sK17)
| big_q(X8) ),
inference(cnf_transformation,[],[f37]) ).
fof(f786,plain,
( spl26_31
| spl26_32
| spl26_6
| spl26_2 ),
inference(avatar_split_clause,[],[f631,f78,f102,f783,f780]) ).
fof(f631,plain,
( ! [X3,X4] :
( big_q(X4)
| big_q(sK16)
| big_p(sK14(X3))
| big_p(X3) )
| spl26_2 ),
inference(resolution,[],[f80,f67]) ).
fof(f67,plain,
! [X0,X5] :
( big_p(X0)
| big_p(sK14(X0))
| big_q(sK16)
| sP0
| big_q(X5) ),
inference(cnf_transformation,[],[f37]) ).
fof(f778,plain,
( spl26_11
| spl26_29
| ~ spl26_30
| spl26_2 ),
inference(avatar_split_clause,[],[f634,f78,f775,f772,f123]) ).
fof(f634,plain,
( ! [X3,X5] :
( ~ big_q(sK15)
| ~ big_p(X3)
| ~ big_q(X5)
| ~ big_p(sK14(X3)) )
| spl26_2 ),
inference(resolution,[],[f80,f70]) ).
fof(f70,plain,
! [X2,X0] :
( ~ big_p(sK14(X0))
| ~ big_q(X2)
| ~ big_q(sK15)
| sP0
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f770,plain,
( spl26_28
| spl26_4
| spl26_11
| spl26_6
| spl26_2 ),
inference(avatar_split_clause,[],[f630,f78,f102,f123,f95,f767]) ).
fof(f630,plain,
( ! [X2,X0,X1] :
( big_q(X2)
| ~ big_q(X1)
| ~ big_p(X0)
| big_p(sK17) )
| spl26_2 ),
inference(resolution,[],[f80,f66]) ).
fof(f66,plain,
! [X8,X9,X7] :
( big_p(sK17)
| big_q(X8)
| sP0
| ~ big_q(X9)
| ~ big_p(X7) ),
inference(cnf_transformation,[],[f37]) ).
fof(f765,plain,
( ~ spl26_11
| ~ spl26_27 ),
inference(avatar_contradiction_clause,[],[f764]) ).
fof(f764,plain,
( $false
| ~ spl26_11
| ~ spl26_27 ),
inference(subsumption_resolution,[],[f763,f124]) ).
fof(f763,plain,
( ! [X31] : big_q(X31)
| ~ spl26_11
| ~ spl26_27 ),
inference(resolution,[],[f623,f124]) ).
fof(f623,plain,
( ! [X4] :
( big_q(sK10(X4))
| big_q(X4) )
| ~ spl26_27 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f622,plain,
( spl26_27
<=> ! [X4] :
( big_q(X4)
| big_q(sK10(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_27])]) ).
fof(f626,plain,
( spl26_23
| ~ spl26_24
| spl26_6
| spl26_3
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f595,f74,f92,f102,f608,f604]) ).
fof(f608,plain,
( spl26_24
<=> big_q(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_24])]) ).
fof(f74,plain,
( spl26_1
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
fof(f595,plain,
( ! [X0,X1] :
( big_p(X1)
| big_q(X0)
| ~ big_q(sK11)
| big_p(sK13) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f39]) ).
fof(f39,plain,
! [X19,X22] :
( ~ big_q(sK11)
| big_p(sK13)
| ~ sP1
| big_q(X19)
| big_p(X22) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ( sP1
| ( ( ! [X0] :
( ( ~ big_q(sK2(X0))
| ~ big_q(X0) )
& ( big_q(sK2(X0))
| big_q(X0) ) )
| ( ( ~ big_p(sK3)
| ! [X3] : ~ big_p(X3) )
& ( ! [X4] : big_p(X4)
| big_p(sK4) ) ) )
& ( ! [X7] :
( ( big_q(sK5)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(sK5) ) )
| ( ( big_p(sK6)
| ~ big_p(sK7) )
& ( ! [X10] : big_p(X10)
| ! [X11] : ~ big_p(X11) ) ) ) ) )
& ( ( ( ( ( big_p(sK8)
| ~ big_p(sK9) )
& ( ! [X14] : big_p(X14)
| ! [X15] : ~ big_p(X15) ) )
| ! [X16] :
( ( ~ big_q(sK10(X16))
| ~ big_q(X16) )
& ( big_q(sK10(X16))
| big_q(X16) ) ) )
& ( ! [X19] :
( ( big_q(sK11)
| ~ big_q(X19) )
& ( big_q(X19)
| ~ big_q(sK11) ) )
| ( ( ~ big_p(sK12)
| ! [X21] : ~ big_p(X21) )
& ( ! [X22] : big_p(X22)
| big_p(sK13) ) ) ) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f9,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( ( ~ big_q(X1)
| ~ big_q(X0) )
& ( big_q(X1)
| big_q(X0) ) )
=> ( ( ~ big_q(sK2(X0))
| ~ big_q(X0) )
& ( big_q(sK2(X0))
| big_q(X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
( ? [X2] : ~ big_p(X2)
=> ~ big_p(sK3) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
( ? [X5] : big_p(X5)
=> big_p(sK4) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ? [X6] :
! [X7] :
( ( big_q(X6)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(X6) ) )
=> ! [X7] :
( ( big_q(sK5)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(sK5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X8] : big_p(X8)
=> big_p(sK6) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X9] : ~ big_p(X9)
=> ~ big_p(sK7) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X12] : big_p(X12)
=> big_p(sK8) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X13] : ~ big_p(X13)
=> ~ big_p(sK9) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X16] :
( ? [X17] :
( ( ~ big_q(X17)
| ~ big_q(X16) )
& ( big_q(X17)
| big_q(X16) ) )
=> ( ( ~ big_q(sK10(X16))
| ~ big_q(X16) )
& ( big_q(sK10(X16))
| big_q(X16) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
( ? [X18] :
! [X19] :
( ( big_q(X18)
| ~ big_q(X19) )
& ( big_q(X19)
| ~ big_q(X18) ) )
=> ! [X19] :
( ( big_q(sK11)
| ~ big_q(X19) )
& ( big_q(X19)
| ~ big_q(sK11) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
( ? [X20] : ~ big_p(X20)
=> ~ big_p(sK12) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ? [X23] : big_p(X23)
=> big_p(sK13) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
( ( sP1
| ( ( ! [X0] :
? [X1] :
( ( ~ big_q(X1)
| ~ big_q(X0) )
& ( big_q(X1)
| big_q(X0) ) )
| ( ( ? [X2] : ~ big_p(X2)
| ! [X3] : ~ big_p(X3) )
& ( ! [X4] : big_p(X4)
| ? [X5] : big_p(X5) ) ) )
& ( ? [X6] :
! [X7] :
( ( big_q(X6)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(X6) ) )
| ( ( ? [X8] : big_p(X8)
| ? [X9] : ~ big_p(X9) )
& ( ! [X10] : big_p(X10)
| ! [X11] : ~ big_p(X11) ) ) ) ) )
& ( ( ( ( ( ? [X12] : big_p(X12)
| ? [X13] : ~ big_p(X13) )
& ( ! [X14] : big_p(X14)
| ! [X15] : ~ big_p(X15) ) )
| ! [X16] :
? [X17] :
( ( ~ big_q(X17)
| ~ big_q(X16) )
& ( big_q(X17)
| big_q(X16) ) ) )
& ( ? [X18] :
! [X19] :
( ( big_q(X18)
| ~ big_q(X19) )
& ( big_q(X19)
| ~ big_q(X18) ) )
| ( ( ? [X20] : ~ big_p(X20)
| ! [X21] : ~ big_p(X21) )
& ( ! [X22] : big_p(X22)
| ? [X23] : big_p(X23) ) ) ) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f8,plain,
( ( sP1
| ( ( ! [X6] :
? [X7] :
( ( ~ big_q(X7)
| ~ big_q(X6) )
& ( big_q(X7)
| big_q(X6) ) )
| ( ( ? [X5] : ~ big_p(X5)
| ! [X4] : ~ big_p(X4) )
& ( ! [X5] : big_p(X5)
| ? [X4] : big_p(X4) ) ) )
& ( ? [X6] :
! [X7] :
( ( big_q(X6)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(X6) ) )
| ( ( ? [X4] : big_p(X4)
| ? [X5] : ~ big_p(X5) )
& ( ! [X5] : big_p(X5)
| ! [X4] : ~ big_p(X4) ) ) ) ) )
& ( ( ( ( ( ? [X4] : big_p(X4)
| ? [X5] : ~ big_p(X5) )
& ( ! [X5] : big_p(X5)
| ! [X4] : ~ big_p(X4) ) )
| ! [X6] :
? [X7] :
( ( ~ big_q(X7)
| ~ big_q(X6) )
& ( big_q(X7)
| big_q(X6) ) ) )
& ( ? [X6] :
! [X7] :
( ( big_q(X6)
| ~ big_q(X7) )
& ( big_q(X7)
| ~ big_q(X6) ) )
| ( ( ? [X5] : ~ big_p(X5)
| ! [X4] : ~ big_p(X4) )
& ( ! [X5] : big_p(X5)
| ? [X4] : big_p(X4) ) ) ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,plain,
( sP1
<=> ( ( ? [X4] : big_p(X4)
<=> ! [X5] : big_p(X5) )
<=> ? [X6] :
! [X7] :
( big_q(X6)
<=> big_q(X7) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f75,plain,
( sP1
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f625,plain,
( ~ spl26_26
| ~ spl26_24
| spl26_6
| spl26_4
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f596,f74,f95,f102,f608,f617]) ).
fof(f596,plain,
( ! [X2,X0] :
( ~ big_p(X2)
| big_q(X0)
| ~ big_q(sK11)
| ~ big_p(sK12) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f40]) ).
fof(f40,plain,
! [X21,X19] :
( big_q(X19)
| ~ big_p(sK12)
| ~ sP1
| ~ big_p(X21)
| ~ big_q(sK11) ),
inference(cnf_transformation,[],[f22]) ).
fof(f624,plain,
( spl26_3
| spl26_4
| spl26_27
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f599,f74,f622,f95,f92]) ).
fof(f599,plain,
( ! [X3,X4,X5] :
( big_q(X4)
| ~ big_p(X3)
| big_p(X5)
| big_q(sK10(X4)) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f43]) ).
fof(f43,plain,
! [X16,X14,X15] :
( ~ big_p(X15)
| big_q(X16)
| big_q(sK10(X16))
| big_p(X14)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f620,plain,
( spl26_4
| ~ spl26_26
| spl26_24
| spl26_11
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f598,f74,f123,f608,f617,f95]) ).
fof(f598,plain,
( ! [X2,X0] :
( ~ big_q(X0)
| big_q(sK11)
| ~ big_p(sK12)
| ~ big_p(X2) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f42]) ).
fof(f42,plain,
! [X21,X19] :
( ~ sP1
| big_q(sK11)
| ~ big_p(sK12)
| ~ big_p(X21)
| ~ big_q(X19) ),
inference(cnf_transformation,[],[f22]) ).
fof(f611,plain,
( spl26_11
| spl26_23
| spl26_3
| spl26_24
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f597,f74,f608,f92,f604,f123]) ).
fof(f597,plain,
( ! [X0,X1] :
( big_q(sK11)
| big_p(X1)
| big_p(sK13)
| ~ big_q(X0) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f41]) ).
fof(f41,plain,
! [X19,X22] :
( big_q(sK11)
| ~ big_q(X19)
| ~ sP1
| big_p(sK13)
| big_p(X22) ),
inference(cnf_transformation,[],[f22]) ).
fof(f592,plain,
( ~ spl26_3
| spl26_13 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f572,plain,
( $false
| ~ spl26_3
| spl26_13 ),
inference(resolution,[],[f93,f134]) ).
fof(f134,plain,
( ~ big_p(sK3)
| spl26_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f132,plain,
( spl26_13
<=> big_p(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_13])]) ).
fof(f539,plain,
( ~ spl26_3
| ~ spl26_4 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f538,plain,
( $false
| ~ spl26_3
| ~ spl26_4 ),
inference(subsumption_resolution,[],[f93,f96]) ).
fof(f537,plain,
( spl26_2
| ~ spl26_4
| ~ spl26_6 ),
inference(avatar_contradiction_clause,[],[f536]) ).
fof(f536,plain,
( $false
| spl26_2
| ~ spl26_4
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f535,f96]) ).
fof(f535,plain,
( ! [X3] : big_p(X3)
| spl26_2
| ~ spl26_4
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f534,f103]) ).
fof(f534,plain,
( ! [X3,X5] :
( ~ big_q(X5)
| big_p(X3) )
| spl26_2
| ~ spl26_4
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f533,f103]) ).
fof(f533,plain,
( ! [X3,X5] :
( ~ big_q(sK15)
| big_p(X3)
| ~ big_q(X5) )
| spl26_2
| ~ spl26_4 ),
inference(subsumption_resolution,[],[f530,f96]) ).
fof(f530,plain,
( ! [X3,X5] :
( big_p(sK14(X3))
| big_p(X3)
| ~ big_q(sK15)
| ~ big_q(X5) )
| spl26_2 ),
inference(resolution,[],[f80,f68]) ).
fof(f513,plain,
( spl26_4
| spl26_3
| ~ spl26_1
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f512,f102,f74,f92,f95]) ).
fof(f512,plain,
( ! [X3,X5] :
( big_p(X5)
| ~ big_p(X3) )
| ~ spl26_1
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f511,f103]) ).
fof(f511,plain,
( ! [X3,X4,X5] :
( ~ big_q(sK10(X4))
| big_p(X5)
| ~ big_p(X3) )
| ~ spl26_1
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f508,f103]) ).
fof(f508,plain,
( ! [X3,X4,X5] :
( big_p(X5)
| ~ big_q(X4)
| ~ big_q(sK10(X4))
| ~ big_p(X3) )
| ~ spl26_1 ),
inference(resolution,[],[f75,f44]) ).
fof(f44,plain,
! [X16,X14,X15] :
( big_p(X14)
| ~ big_q(sK10(X16))
| ~ sP1
| ~ big_q(X16)
| ~ big_p(X15) ),
inference(cnf_transformation,[],[f22]) ).
fof(f502,plain,
( ~ spl26_6
| spl26_17 ),
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f501,plain,
( $false
| ~ spl26_6
| spl26_17 ),
inference(subsumption_resolution,[],[f168,f103]) ).
fof(f168,plain,
( ~ big_q(sK24)
| spl26_17 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f166,plain,
( spl26_17
<=> big_q(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_17])]) ).
fof(f500,plain,
( spl26_4
| ~ spl26_2
| ~ spl26_6
| spl26_16 ),
inference(avatar_split_clause,[],[f499,f162,f102,f78,f95]) ).
fof(f162,plain,
( spl26_16
<=> big_p(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_16])]) ).
fof(f499,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl26_2
| ~ spl26_6
| spl26_16 ),
inference(subsumption_resolution,[],[f498,f103]) ).
fof(f498,plain,
( ! [X2,X0] :
( ~ big_p(X0)
| ~ big_q(X2) )
| ~ spl26_2
| ~ spl26_6
| spl26_16 ),
inference(subsumption_resolution,[],[f497,f103]) ).
fof(f497,plain,
( ! [X2,X0] :
( ~ big_q(sK24)
| ~ big_q(X2)
| ~ big_p(X0) )
| ~ spl26_2
| spl26_16 ),
inference(subsumption_resolution,[],[f140,f164]) ).
fof(f164,plain,
( ~ big_p(sK23)
| spl26_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f140,plain,
( ! [X2,X0] :
( big_p(sK23)
| ~ big_p(X0)
| ~ big_q(sK24)
| ~ big_q(X2) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f58]) ).
fof(f58,plain,
! [X19,X20] :
( ~ big_q(X20)
| ~ big_p(X19)
| ~ sP0
| big_p(sK23)
| ~ big_q(sK24) ),
inference(cnf_transformation,[],[f37]) ).
fof(f79,plain,
( sP0
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f496,plain,
( spl26_11
| spl26_6
| ~ spl26_2
| ~ spl26_4 ),
inference(avatar_split_clause,[],[f495,f95,f78,f102,f123]) ).
fof(f495,plain,
( ! [X4,X5] :
( big_q(X5)
| ~ big_q(X4) )
| ~ spl26_2
| ~ spl26_4 ),
inference(subsumption_resolution,[],[f494,f96]) ).
fof(f494,plain,
( ! [X3,X4,X5] :
( big_q(X5)
| ~ big_q(X4)
| big_p(sK22(X3)) )
| ~ spl26_2
| ~ spl26_4 ),
inference(subsumption_resolution,[],[f143,f96]) ).
fof(f143,plain,
( ! [X3,X4,X5] :
( ~ big_q(X4)
| big_q(X5)
| big_p(X3)
| big_p(sK22(X3)) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f61]) ).
fof(f61,plain,
! [X16,X12,X13] :
( ~ big_q(X13)
| big_p(X16)
| big_q(X12)
| big_p(sK22(X16))
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f348,plain,
( ~ spl26_4
| ~ spl26_9 ),
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f347,plain,
( $false
| ~ spl26_4
| ~ spl26_9 ),
inference(resolution,[],[f117,f96]) ).
fof(f117,plain,
( big_p(sK4)
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl26_9
<=> big_p(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f198,plain,
( ~ spl26_6
| ~ spl26_10 ),
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f197,plain,
( $false
| ~ spl26_6
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f196,f103]) ).
fof(f196,plain,
( ! [X3] : ~ big_q(sK2(X3))
| ~ spl26_6
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f120,f103]) ).
fof(f120,plain,
( ! [X3] :
( ~ big_q(sK2(X3))
| ~ big_q(X3) )
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f119,plain,
( spl26_10
<=> ! [X3] :
( ~ big_q(X3)
| ~ big_q(sK2(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f193,plain,
( ~ spl26_6
| ~ spl26_11 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f192,plain,
( $false
| ~ spl26_6
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f103,f124]) ).
fof(f191,plain,
( ~ spl26_11
| ~ spl26_19 ),
inference(avatar_contradiction_clause,[],[f190]) ).
fof(f190,plain,
( $false
| ~ spl26_11
| ~ spl26_19 ),
inference(subsumption_resolution,[],[f178,f124]) ).
fof(f178,plain,
( big_q(sK25)
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f176,plain,
( spl26_19
<=> big_q(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_19])]) ).
fof(f189,plain,
( spl26_4
| spl26_16
| ~ spl26_2
| ~ spl26_11 ),
inference(avatar_split_clause,[],[f188,f123,f78,f162,f95]) ).
fof(f188,plain,
( ! [X0] :
( big_p(sK23)
| ~ big_p(X0) )
| ~ spl26_2
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f187,f124]) ).
fof(f187,plain,
( ! [X0] :
( ~ big_p(X0)
| big_q(sK25)
| big_p(sK23) )
| ~ spl26_2
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f139,f124]) ).
fof(f139,plain,
( ! [X0,X1] :
( big_q(X1)
| big_p(sK23)
| big_q(sK25)
| ~ big_p(X0) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f57]) ).
fof(f57,plain,
! [X19,X23] :
( big_q(X23)
| ~ sP0
| big_p(sK23)
| big_q(sK25)
| ~ big_p(X19) ),
inference(cnf_transformation,[],[f37]) ).
fof(f186,plain,
( ~ spl26_11
| ~ spl26_12 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f185,plain,
( $false
| ~ spl26_11
| ~ spl26_12 ),
inference(subsumption_resolution,[],[f184,f124]) ).
fof(f184,plain,
( ! [X3] : big_q(sK2(X3))
| ~ spl26_11
| ~ spl26_12 ),
inference(subsumption_resolution,[],[f128,f124]) ).
fof(f128,plain,
( ! [X3] :
( big_q(sK2(X3))
| big_q(X3) )
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f127,plain,
( spl26_12
<=> ! [X3] :
( big_q(sK2(X3))
| big_q(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f179,plain,
( spl26_6
| spl26_19
| ~ spl26_16
| spl26_3
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f137,f78,f92,f162,f176,f102]) ).
fof(f137,plain,
( ! [X0,X1] :
( big_p(X0)
| ~ big_p(sK23)
| big_q(sK25)
| big_q(X1) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f55]) ).
fof(f55,plain,
! [X19,X23] :
( big_p(X19)
| big_q(X23)
| big_q(sK25)
| ~ sP0
| ~ big_p(sK23) ),
inference(cnf_transformation,[],[f37]) ).
fof(f169,plain,
( spl26_3
| ~ spl26_16
| spl26_11
| ~ spl26_17
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f138,f78,f166,f123,f162,f92]) ).
fof(f138,plain,
( ! [X2,X0] :
( ~ big_q(sK24)
| ~ big_q(X2)
| ~ big_p(sK23)
| big_p(X0) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f56]) ).
fof(f56,plain,
! [X19,X20] :
( ~ big_q(X20)
| big_p(X19)
| ~ big_q(sK24)
| ~ big_p(sK23)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f158,plain,
( spl26_11
| spl26_6
| ~ spl26_2
| ~ spl26_3 ),
inference(avatar_split_clause,[],[f157,f92,f78,f102,f123]) ).
fof(f157,plain,
( ! [X4,X5] :
( big_q(X5)
| ~ big_q(X4) )
| ~ spl26_2
| ~ spl26_3 ),
inference(subsumption_resolution,[],[f156,f93]) ).
fof(f156,plain,
( ! [X3,X4,X5] :
( ~ big_p(sK22(X3))
| big_q(X5)
| ~ big_q(X4) )
| ~ spl26_2
| ~ spl26_3 ),
inference(subsumption_resolution,[],[f144,f93]) ).
fof(f144,plain,
( ! [X3,X4,X5] :
( big_q(X5)
| ~ big_q(X4)
| ~ big_p(sK22(X3))
| ~ big_p(X3) )
| ~ spl26_2 ),
inference(resolution,[],[f79,f62]) ).
fof(f62,plain,
! [X16,X12,X13] :
( ~ big_p(sK22(X16))
| ~ big_p(X16)
| ~ big_q(X13)
| big_q(X12)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f136,plain,
( spl26_4
| ~ spl26_13
| spl26_12
| spl26_1 ),
inference(avatar_split_clause,[],[f88,f74,f127,f132,f95]) ).
fof(f88,plain,
( ! [X3,X5] :
( big_q(X3)
| ~ big_p(sK3)
| big_q(sK2(X3))
| ~ big_p(X5) )
| spl26_1 ),
inference(resolution,[],[f76,f52]) ).
fof(f52,plain,
! [X3,X0] :
( big_q(X0)
| sP1
| big_q(sK2(X0))
| ~ big_p(sK3)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f76,plain,
( ~ sP1
| spl26_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f135,plain,
( spl26_4
| ~ spl26_13
| spl26_10
| spl26_1 ),
inference(avatar_split_clause,[],[f90,f74,f119,f132,f95]) ).
fof(f90,plain,
( ! [X3,X5] :
( ~ big_q(sK2(X3))
| ~ big_p(sK3)
| ~ big_p(X5)
| ~ big_q(X3) )
| spl26_1 ),
inference(resolution,[],[f76,f54]) ).
fof(f54,plain,
! [X3,X0] :
( ~ big_p(sK3)
| ~ big_q(sK2(X0))
| sP1
| ~ big_q(X0)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f129,plain,
( spl26_3
| spl26_12
| spl26_9
| spl26_1 ),
inference(avatar_split_clause,[],[f87,f74,f115,f127,f92]) ).
fof(f87,plain,
( ! [X3,X4] :
( big_p(sK4)
| big_q(sK2(X3))
| big_q(X3)
| big_p(X4) )
| spl26_1 ),
inference(resolution,[],[f76,f51]) ).
fof(f51,plain,
! [X0,X4] :
( big_q(X0)
| big_p(X4)
| big_q(sK2(X0))
| sP1
| big_p(sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f125,plain,
( spl26_5
| spl26_11
| spl26_4
| spl26_3
| spl26_1 ),
inference(avatar_split_clause,[],[f85,f74,f92,f95,f123,f98]) ).
fof(f98,plain,
( spl26_5
<=> big_q(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
fof(f85,plain,
( ! [X2,X0,X1] :
( big_p(X0)
| ~ big_p(X1)
| ~ big_q(X2)
| big_q(sK5) )
| spl26_1 ),
inference(resolution,[],[f76,f49]) ).
fof(f49,plain,
! [X10,X11,X7] :
( ~ big_p(X11)
| big_p(X10)
| sP1
| ~ big_q(X7)
| big_q(sK5) ),
inference(cnf_transformation,[],[f22]) ).
fof(f121,plain,
( spl26_9
| spl26_3
| spl26_10
| spl26_1 ),
inference(avatar_split_clause,[],[f89,f74,f119,f92,f115]) ).
fof(f89,plain,
( ! [X3,X4] :
( ~ big_q(X3)
| big_p(X4)
| ~ big_q(sK2(X3))
| big_p(sK4) )
| spl26_1 ),
inference(resolution,[],[f76,f53]) ).
fof(f53,plain,
! [X0,X4] :
( sP1
| big_p(X4)
| ~ big_q(sK2(X0))
| ~ big_q(X0)
| big_p(sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f104,plain,
( spl26_3
| spl26_4
| ~ spl26_5
| spl26_6
| spl26_1 ),
inference(avatar_split_clause,[],[f83,f74,f102,f98,f95,f92]) ).
fof(f83,plain,
( ! [X2,X0,X1] :
( big_q(X2)
| ~ big_q(sK5)
| ~ big_p(X1)
| big_p(X0) )
| spl26_1 ),
inference(resolution,[],[f76,f47]) ).
fof(f47,plain,
! [X10,X11,X7] :
( big_p(X10)
| ~ big_p(X11)
| sP1
| ~ big_q(sK5)
| big_q(X7) ),
inference(cnf_transformation,[],[f22]) ).
fof(f82,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f71,f78,f74]) ).
fof(f71,plain,
( sP0
| sP1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( ( ~ sP1
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,plain,
( sP0
<~> sP1 ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f4,plain,
( ( ( ! [X2] : big_q(X2)
<=> ? [X3] : big_q(X3) )
<=> ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) ) )
<~> ( ( ? [X4] : big_p(X4)
<=> ! [X5] : big_p(X5) )
<=> ? [X6] :
! [X7] :
( big_q(X6)
<=> big_q(X7) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ( ( ! [X2] : big_q(X2)
<=> ? [X3] : big_q(X3) )
<=> ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) ) )
<=> ( ( ? [X4] : big_p(X4)
<=> ! [X5] : big_p(X5) )
<=> ? [X6] :
! [X7] :
( big_q(X6)
<=> big_q(X7) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ! [X3] : big_q(X3)
<=> ? [X2] : big_q(X2) ) )
<=> ( ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) )
<=> ? [X4] :
! [X5] :
( big_q(X5)
<=> big_q(X4) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ! [X3] : big_q(X3)
<=> ? [X2] : big_q(X2) ) )
<=> ( ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) )
<=> ? [X4] :
! [X5] :
( big_q(X5)
<=> big_q(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel34) ).
fof(f81,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f72,f78,f74]) ).
fof(f72,plain,
( ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 21:14:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (31297)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.49 % (31283)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.50 % (31283)First to succeed.
% 0.19/0.50 % (31288)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (31283)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (31283)------------------------------
% 0.19/0.52 % (31283)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (31283)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (31283)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (31283)Memory used [KB]: 6268
% 0.19/0.52 % (31283)Time elapsed: 0.103 s
% 0.19/0.52 % (31283)Instructions burned: 9 (million)
% 0.19/0.52 % (31283)------------------------------
% 0.19/0.52 % (31283)------------------------------
% 0.19/0.52 % (31272)Success in time 0.166 s
%------------------------------------------------------------------------------