%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP011+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:28:01 AM UTC 2026
% Result : Theorem 3.40s 1.60s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 37
% Syntax : Number of formulae : 290 ( 34 unt; 28 def)
% Number of atoms : 1393 ( 229 equ)
% Maximal formula atoms : 57 ( 4 avg)
% Number of connectives : 1819 ( 716 ~; 707 |; 214 &)
% ( 57 <=>; 124 =>; 0 <=; 1 <~>)
% Maximal formula depth : 35 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 34 ( 31 usr; 25 prp; 0-5 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-5 aty)
% Number of variables : 523 ( 0 sgn 505 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_ne) ).
fof(f3,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ne(arr(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arr_ne) ).
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
fof(f9,axiom,
! [X0] :
( ne(X0)
=> ne(ty_2Eoption_2Eoption(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eoption_2Eoption) ).
fof(f24,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME) ).
fof(f27,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
fof(f46,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,X1)
=> ! [X3] :
( mem(X3,arr(X0,X1))
=> ! [X4] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5] :
( mem(X5,X0)
=> ! [X6] :
( mem(X6,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 ) ) )
& ! [X7] :
( mem(X7,X0)
=> ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
& ! [X8] :
( mem(X8,X0)
=> c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
& ! [X9] :
( mem(X9,X0)
=> ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
& ! [X10] :
( mem(X10,X0)
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
<=> $false )
& ! [X11] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) ) )
& ! [X12] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) ) )
& ! [X13] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) )
& ! [X14] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
& ! [X15] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
& ! [X16] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) )
& ! [X17] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) )
& ! [X18] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) )
& ! [X19] :
( mem(X19,X1)
=> ! [X20] :
( mem(X20,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) )
& ! [X21] :
( mem(X21,X0)
=> ! [X22] :
( mem(X22,X1)
=> ! [X23] :
( mem(X23,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) )
& ! [X24] :
( mem(X24,arr(X0,X1))
=> ! [X25] :
( mem(X25,X0)
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) )
& ! [X26] :
( mem(X26,arr(X0,X1))
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2Eoption__CLAUSES) ).
fof(f47,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,arr(X1,bool)))
=> ! [X3] :
( mem(X3,ty_2Eoption_2Eoption(X0))
=> ! [X4] :
( mem(X4,ty_2Eoption_2Eoption(X1))
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( X3 = c_2Eoption_2ENONE(X0)
& X4 = c_2Eoption_2ENONE(X1) )
| ? [X5] :
( mem(X5,X0)
& ? [X6] :
( mem(X6,X1)
& X3 = ap(c_2Eoption_2ESOME(X0),X5)
& X4 = ap(c_2Eoption_2ESOME(X1),X6)
& p(ap(ap(X2,X5),X6)) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTREL__def) ).
fof(f48,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
<=> $true )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient__option_2EOPTION__REL__def) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
<=> $true )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f49]) ).
fof(f51,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f58,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,X1)
=> ! [X3] :
( mem(X3,arr(X0,X1))
=> ! [X4] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5] :
( mem(X5,X0)
=> ! [X6] :
( mem(X6,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 ) ) )
& ! [X7] :
( mem(X7,X0)
=> ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
& ! [X8] :
( mem(X8,X0)
=> c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
& ! [X9] :
( mem(X9,X0)
=> ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
& ! [X10] :
( mem(X10,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) ) )
& ! [X12] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) ) )
& ! [X13] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) )
& ! [X14] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
& ! [X15] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
& ! [X16] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) )
& ! [X17] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) )
& ! [X18] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) )
& ! [X19] :
( mem(X19,X1)
=> ! [X20] :
( mem(X20,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) )
& ! [X21] :
( mem(X21,X0)
=> ! [X22] :
( mem(X22,X1)
=> ! [X23] :
( mem(X23,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) )
& ! [X24] :
( mem(X24,arr(X0,X1))
=> ! [X25] :
( mem(X25,X0)
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) )
& ! [X26] :
( mem(X26,arr(X0,X1))
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f46]) ).
fof(f59,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,X1)
=> ! [X3] :
( mem(X3,arr(X0,X1))
=> ! [X4] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5] :
( mem(X5,X0)
=> ! [X6] :
( mem(X6,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 ) ) )
& ! [X7] :
( mem(X7,X0)
=> ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
& ! [X8] :
( mem(X8,X0)
=> c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
& ! [X9] :
( mem(X9,X0)
=> ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
& ! [X10] :
( mem(X10,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) ) )
& ! [X12] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) ) )
& ! [X13] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) )
& ! [X14] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
& ! [X15] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
& ! [X16] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) )
& ! [X17] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) )
& ! [X18] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) )
& ! [X19] :
( mem(X19,X1)
=> ! [X20] :
( mem(X20,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) )
& ! [X21] :
( mem(X21,X0)
=> ! [X22] :
( mem(X22,X1)
=> ! [X23] :
( mem(X23,arr(X0,X1))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) )
& ! [X24] :
( mem(X24,arr(X0,X1))
=> ! [X25] :
( mem(X25,X0)
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) )
& ! [X26] :
( mem(X26,arr(X0,X1))
=> ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
| ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<~> p(ap(ap(X1,X2),X3)) ) )
& mem(X3,X0) )
& mem(X2,X0) )
& mem(X1,arr(X0,arr(X0,bool))) )
& ne(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ne(arr(X0,X1))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( X3 = c_2Eoption_2ENONE(X0)
& X4 = c_2Eoption_2ENONE(X1) )
| ? [X5] :
( mem(X5,X0)
& ? [X6] :
( mem(X6,X1)
& X3 = ap(c_2Eoption_2ESOME(X0),X5)
& X4 = ap(c_2Eoption_2ESOME(X1),X6)
& p(ap(ap(X2,X5),X6)) ) ) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ! [X5] :
( ! [X6] :
( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
& ! [X7] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7
| ~ mem(X7,X0) )
& ! [X8] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8)
| ~ mem(X8,X0) )
& ! [X9] :
( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0)
| ~ mem(X9,X0) )
& ! [X10] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13] :
( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17))
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19] :
( ! [X20] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21)
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24] :
( ! [X25] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25))
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1)
| ~ mem(X26,arr(X0,X1)) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ! [X5] :
( ! [X6] :
( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
& ! [X7] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7
| ~ mem(X7,X0) )
& ! [X8] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8)
| ~ mem(X8,X0) )
& ! [X9] :
( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0)
| ~ mem(X9,X0) )
& ! [X10] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13] :
( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17))
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19] :
( ! [X20] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21)
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24] :
( ! [X25] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25))
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1)
| ~ mem(X26,arr(X0,X1)) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0] :
( mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0)))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f75,plain,
! [X0] :
( mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f85,plain,
! [X0] :
( ne(ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f93,definition,
! [X0,X1,X3,X4,X2] :
( sP0(X0,X1,X3,X4,X2)
<=> ? [X5] :
( mem(X5,X0)
& ? [X6] :
( mem(X6,X1)
& X3 = ap(c_2Eoption_2ESOME(X0),X5)
& X4 = ap(c_2Eoption_2ESOME(X1),X6)
& p(ap(ap(X2,X5),X6)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( X3 = c_2Eoption_2ENONE(X0)
& X4 = c_2Eoption_2ENONE(X1) )
| sP0(X0,X1,X3,X4,X2) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(definition_folding,[],[f71,f93]) ).
fof(f95,definition,
! [X0] :
( ! [X12] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> X12 = c_2Eoption_2ENONE(X0) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f96,definition,
! [X0] :
( ! [X11] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> X11 = c_2Eoption_2ENONE(X0) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f97,definition,
! [X0] :
( ! [X5] :
( ! [X6] :
( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6)
<=> X5 = X6 )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f98,definition,
! [X0,X2,X3,X1,X4] :
( ( sP3(X0)
& ! [X7] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7
| ~ mem(X7,X0) )
& ! [X8] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8)
| ~ mem(X8,X0) )
& ! [X9] :
( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0)
| ~ mem(X9,X0) )
& ! [X10] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X13] :
( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17))
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19] :
( ! [X20] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21)
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24] :
( ! [X25] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25))
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1)
| ~ mem(X26,arr(X0,X1)) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X2,X3,X1,X4) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( sP4(X0,X2,X3,X1,X4)
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(definition_folding,[],[f73,f98,f97,f96,f95]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
| ( ( ~ p(ap(ap(X1,X2),X3))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3))) )
& ( p(ap(ap(X1,X2),X3))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3))) ) ) )
& mem(X3,X0) )
& mem(X2,X0) )
& mem(X1,arr(X0,arr(X0,bool))) )
& ne(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f101,plain,
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ( ( ~ p(ap(ap(sK6,sK7),sK8))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) )
& ( p(ap(ap(sK6,sK7),sK8))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ) ) )
& mem(sK8,sK5)
& mem(sK7,sK5)
& mem(sK6,arr(sK5,arr(sK5,bool)))
& ne(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f100]) ).
fof(f113,plain,
! [X0,X1,X3,X4,X2] :
( ( sP0(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ mem(X5,X0)
| ! [X6] :
( ~ mem(X6,X1)
| ap(c_2Eoption_2ESOME(X0),X5) != X3
| ap(c_2Eoption_2ESOME(X1),X6) != X4
| ~ p(ap(ap(X2,X5),X6)) ) ) )
& ( ? [X5] :
( mem(X5,X0)
& ? [X6] :
( mem(X6,X1)
& X3 = ap(c_2Eoption_2ESOME(X0),X5)
& X4 = ap(c_2Eoption_2ESOME(X1),X6)
& p(ap(ap(X2,X5),X6)) ) )
| ~ sP0(X0,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4] :
( ( sP0(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ mem(X5,X0)
| ! [X6] :
( ~ mem(X6,X1)
| ap(c_2Eoption_2ESOME(X0),X5) != X2
| ap(c_2Eoption_2ESOME(X1),X6) != X3
| ~ p(ap(ap(X4,X5),X6)) ) ) )
& ( ? [X7] :
( mem(X7,X0)
& ? [X8] :
( mem(X8,X1)
& ap(c_2Eoption_2ESOME(X0),X7) = X2
& ap(c_2Eoption_2ESOME(X1),X8) = X3
& p(ap(ap(X4,X7),X8)) ) )
| ~ sP0(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( ( sP0(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ mem(X5,X0)
| ! [X6] :
( ~ mem(X6,X1)
| ap(c_2Eoption_2ESOME(X0),X5) != X2
| ap(c_2Eoption_2ESOME(X1),X6) != X3
| ~ p(ap(ap(X4,X5),X6)) ) ) )
& ( ( mem(sK10(X0,X1,X2,X3,X4),X0)
& mem(sK11(X0,X1,X2,X3,X4),X1)
& ap(c_2Eoption_2ESOME(X0),sK10(X0,X1,X2,X3,X4)) = X2
& ap(c_2Eoption_2ESOME(X1),sK11(X0,X1,X2,X3,X4)) = X3
& p(ap(ap(X4,sK10(X0,X1,X2,X3,X4)),sK11(X0,X1,X2,X3,X4))) )
| ~ sP0(X0,X1,X2,X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X7,sK10(X0,X1,X2,X3,X4)),skolemize(X8,sK11(X0,X1,X2,X3,X4))],[f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ( ( c_2Eoption_2ENONE(X0) != X3
| c_2Eoption_2ENONE(X1) != X4 )
& ~ sP0(X0,X1,X3,X4,X2) ) )
& ( ( X3 = c_2Eoption_2ENONE(X0)
& X4 = c_2Eoption_2ENONE(X1) )
| sP0(X0,X1,X3,X4,X2)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ( ( c_2Eoption_2ENONE(X0) != X3
| c_2Eoption_2ENONE(X1) != X4 )
& ~ sP0(X0,X1,X3,X4,X2) ) )
& ( ( X3 = c_2Eoption_2ENONE(X0)
& X4 = c_2Eoption_2ENONE(X1) )
| sP0(X0,X1,X3,X4,X2)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0,X2,X3,X1,X4] :
( ( sP3(X0)
& ! [X7] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7
| ~ mem(X7,X0) )
& ! [X8] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8)
| ~ mem(X8,X0) )
& ! [X9] :
( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0)
| ~ mem(X9,X0) )
& ! [X10] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X13] :
( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17))
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19] :
( ! [X20] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21)
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24] :
( ! [X25] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25))
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1)
| ~ mem(X26,arr(X0,X1)) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X27] :
( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X2,X3,X1,X4) ),
inference(nnf_transformation,[],[f98]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4] :
( ( sP3(X0)
& ! [X5] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5)) = X5
| ~ mem(X5,X0) )
& ! [X6] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X6)
| ~ mem(X6,X0) )
& ! [X7] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X7)
| ~ mem(X7,X0) )
& ! [X8] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X8)))
| ~ mem(X8,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X9] :
( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X9)) = X9
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X9))
| ~ mem(X9,ty_2Eoption_2Eoption(X0)) )
& ! [X10] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X10),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X10
| ~ mem(X10,ty_2Eoption_2Eoption(X0)) )
& ! [X11] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X11),X11),c_2Eoption_2ESOME(X0)) = X11
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),X12),X1),X2) = X1
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X12))
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),X13),X1),X2) = ap(X2,ap(c_2Eoption_2ETHE(X0),X13))
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),X4),c_2Eoption_2ESOME(X0)) = X14
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X14))
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15] :
( ! [X16] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),c_2Eoption_2ENONE(X0)),X15),X16) = X15
| ~ mem(X16,arr(X0,X3)) )
| ~ mem(X15,X3) )
& ! [X17] :
( ! [X18] :
( ! [X19] :
( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),ap(c_2Eoption_2ESOME(X0),X17)),X18),X19) = ap(X19,X17)
| ~ mem(X19,arr(X0,X3)) )
| ~ mem(X18,X3) )
| ~ mem(X17,X0) )
& ! [X20] :
( ! [X21] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X3),X20),ap(c_2Eoption_2ESOME(X0),X21)) = ap(c_2Eoption_2ESOME(X3),ap(X20,X21))
| ~ mem(X21,X0) )
| ~ mem(X20,arr(X0,X3)) )
& ! [X22] :
( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X3),X22),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X3)
| ~ mem(X22,arr(X0,X3)) )
& ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0)
& ! [X23] :
( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X23)) = X23
| ~ mem(X23,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f118]) ).
fof(f129,plain,
ne(sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f130,plain,
mem(sK6,arr(sK5,arr(sK5,bool))),
inference(cnf_transformation,[],[f101]) ).
fof(f131,plain,
mem(sK7,sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f132,plain,
mem(sK8,sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f133,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| p(ap(ap(sK6,sK7),sK8))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f134,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ p(ap(ap(sK6,sK7),sK8))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f135,plain,
ne(bool),
inference(cnf_transformation,[],[f1]) ).
fof(f136,plain,
! [X0,X1] :
( ne(arr(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f173,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(X4,sK10(X0,X1,X2,X3,X4)),sK11(X0,X1,X2,X3,X4)))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f115]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3,X4)
| ap(c_2Eoption_2ESOME(X1),sK11(X0,X1,X2,X3,X4)) = X3 ),
inference(cnf_transformation,[],[f115]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3,X4)
| ap(c_2Eoption_2ESOME(X0),sK10(X0,X1,X2,X3,X4)) = X2 ),
inference(cnf_transformation,[],[f115]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X4] :
( mem(sK11(X0,X1,X2,X3,X4),X1)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f115]) ).
fof(f177,plain,
! [X2,X3,X0,X1,X4] :
( mem(sK10(X0,X1,X2,X3,X4),X0)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f115]) ).
fof(f178,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP0(X0,X1,X2,X3,X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ap(c_2Eoption_2ESOME(X0),X5) != X2
| ap(c_2Eoption_2ESOME(X1),X6) != X3
| ~ p(ap(ap(X4,X5),X6)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| sP0(X0,X1,X3,X4,X2)
| c_2Eoption_2ENONE(X1) = X4
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| sP0(X0,X1,X3,X4,X2)
| c_2Eoption_2ENONE(X0) = X3
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ~ sP0(X0,X1,X3,X4,X2)
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| c_2Eoption_2ENONE(X0) != X3
| c_2Eoption_2ENONE(X1) != X4
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f199,plain,
! [X2,X3,X0,X1,X7,X4] :
( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X7)
| ~ mem(X7,X0)
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f119]) ).
fof(f201,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP4(X0,X1,X2,X3,X4)
| ~ mem(X5,X0)
| ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5)) = X5 ),
inference(cnf_transformation,[],[f119]) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( sP4(X0,X2,X3,X1,X4)
| ~ mem(X4,ty_2Eoption_2Eoption(X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,X1)
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f210,plain,
! [X0] :
( mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0)))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f211,plain,
! [X0] :
( mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f222,plain,
! [X0] :
( ne(ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f230,plain,
! [X3,X0,X1,X6,X4,X5] :
( sP0(X0,X1,ap(c_2Eoption_2ESOME(X0),X5),X3,X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ap(c_2Eoption_2ESOME(X1),X6) != X3
| ~ p(ap(ap(X4,X5),X6)) ),
inference(equality_resolution,[],[f178]) ).
fof(f231,plain,
! [X0,X1,X6,X4,X5] :
( sP0(X0,X1,ap(c_2Eoption_2ESOME(X0),X5),ap(c_2Eoption_2ESOME(X1),X6),X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ~ p(ap(ap(X4,X5),X6)) ),
inference(equality_resolution,[],[f230]) ).
fof(f232,plain,
! [X2,X0,X1,X4] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),X4))
| c_2Eoption_2ENONE(X1) != X4
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(equality_resolution,[],[f182]) ).
fof(f233,plain,
! [X2,X0,X1] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(c_2Eoption_2ENONE(X1),ty_2Eoption_2Eoption(X1))
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(equality_resolution,[],[f232]) ).
fof(f250,plain,
! [X2,X0,X1] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f233,f211]) ).
fof(f252,definition,
( spl13_1
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f253,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| spl13_1 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f256,definition,
( spl13_2
<=> p(ap(ap(sK6,sK7),sK8)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f257,plain,
( ~ p(ap(ap(sK6,sK7),sK8))
| spl13_2 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( p(ap(ap(sK6,sK7),sK8))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f260,definition,
( spl13_3
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f262,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f264,definition,
( spl13_4
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f266,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f268,definition,
( spl13_5
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f270,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| spl13_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( spl13_1
| spl13_2
| spl13_3
| spl13_4
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f133,f268,f264,f260,f256,f252]) ).
fof(f272,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_3
| spl13_4
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f134,f268,f264,f260,f256,f252]) ).
fof(f273,plain,
! [X2,X0,X1] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(X2,arr(X0,arr(X1,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f250,f211]) ).
fof(f304,plain,
! [X0,X1] :
( mem(ap(c_2Eoption_2ESOME(X1),X0),ty_2Eoption_2Eoption(X1))
| ~ mem(X0,X1)
| ~ ne(X1) ),
inference(resolution,[],[f172,f210]) ).
fof(f306,plain,
! [X0] :
( mem(ap(sK6,X0),arr(sK5,bool))
| ~ mem(X0,sK5) ),
inference(resolution,[],[f172,f130]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ mem(X2,arr(X1,X3))
| ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ mem(X4,X3)
| ~ ne(X3)
| ~ ne(X1)
| ~ mem(X5,X1)
| ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X5)) = X5 ),
inference(resolution,[],[f209,f201]) ).
fof(f453,plain,
( ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ ne(sK5)
| spl13_5 ),
inference(resolution,[],[f273,f270]) ).
fof(f454,plain,
( ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| spl13_5 ),
inference(duplicate_literal_removal,[],[f453]) ).
fof(f455,plain,
( ~ ne(sK5)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f454,f130]) ).
fof(f456,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f455,f129]) ).
fof(f457,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f499,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ ne(sK5)
| ~ spl13_3 ),
inference(resolution,[],[f179,f262]) ).
fof(f505,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_3 ),
inference(duplicate_literal_removal,[],[f499]) ).
fof(f507,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f505,f211]) ).
fof(f508,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ ne(sK5)
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f507,f130]) ).
fof(f509,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f508,f129]) ).
fof(f511,definition,
( spl13_10
<=> mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f512,plain,
( mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f513,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| spl13_10 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f515,definition,
( spl13_11
<=> c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f517,plain,
( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f519,definition,
( spl13_12
<=> sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f521,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f522,plain,
( ~ spl13_10
| spl13_11
| spl13_12
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f509,f260,f519,f515,f511]) ).
fof(f603,plain,
( ~ mem(sK8,sK5)
| ~ ne(sK5)
| spl13_10 ),
inference(resolution,[],[f304,f513]) ).
fof(f608,plain,
( ~ ne(sK5)
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f603,f132]) ).
fof(f609,plain,
( $false
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f608,f129]) ).
fof(f610,plain,
spl13_10,
inference(avatar_contradiction_clause,[],[f609]) ).
fof(f626,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ ne(sK5)
| spl13_1 ),
inference(resolution,[],[f253,f181]) ).
fof(f627,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| spl13_1 ),
inference(duplicate_literal_removal,[],[f626]) ).
fof(f628,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| spl13_1
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f627,f512]) ).
fof(f629,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ ne(sK5)
| spl13_1
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f628,f130]) ).
fof(f630,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| spl13_1
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f629,f129]) ).
fof(f632,definition,
( spl13_16
<=> mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f633,plain,
( mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f634,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| spl13_16 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f636,definition,
( spl13_17
<=> sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
fof(f637,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f638,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl13_17 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f639,plain,
( ~ spl13_16
| ~ spl13_17
| spl13_1
| ~ spl13_10 ),
inference(avatar_split_clause,[],[f630,f511,f252,f636,f632]) ).
fof(f640,plain,
( ~ mem(sK7,sK5)
| ~ ne(sK5)
| spl13_16 ),
inference(resolution,[],[f634,f304]) ).
fof(f641,plain,
( ~ ne(sK5)
| spl13_16 ),
inference(forward_subsumption_resolution,[],[f640,f131]) ).
fof(f642,plain,
( $false
| spl13_16 ),
inference(forward_subsumption_resolution,[],[f641,f129]) ).
fof(f643,plain,
spl13_16,
inference(avatar_contradiction_clause,[],[f642]) ).
fof(f647,plain,
( ~ mem(sK7,sK5)
| ~ mem(sK8,sK5)
| ~ p(ap(ap(sK6,sK7),sK8))
| spl13_17 ),
inference(resolution,[],[f638,f231]) ).
fof(f648,plain,
( ~ mem(sK8,sK5)
| ~ p(ap(ap(sK6,sK7),sK8))
| spl13_17 ),
inference(forward_subsumption_resolution,[],[f647,f131]) ).
fof(f649,plain,
( ~ p(ap(ap(sK6,sK7),sK8))
| spl13_17 ),
inference(forward_subsumption_resolution,[],[f648,f132]) ).
fof(f650,plain,
( $false
| ~ spl13_2
| spl13_17 ),
inference(forward_subsumption_resolution,[],[f649,f258]) ).
fof(f651,plain,
( ~ spl13_2
| spl13_17 ),
inference(avatar_contradiction_clause,[],[f650]) ).
fof(f652,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ ne(sK5)
| ~ spl13_4 ),
inference(resolution,[],[f266,f180]) ).
fof(f655,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_4 ),
inference(duplicate_literal_removal,[],[f652]) ).
fof(f656,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f655,f211]) ).
fof(f657,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_4
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f656,f633]) ).
fof(f658,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ ne(sK5)
| ~ spl13_4
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f657,f130]) ).
fof(f659,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ spl13_4
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f658,f129]) ).
fof(f661,definition,
( spl13_18
<=> c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f662,plain,
( c_2Eoption_2ENONE(sK5) != ap(c_2Eoption_2ESOME(sK5),sK7)
| spl13_18 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f663,plain,
( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f665,definition,
( spl13_19
<=> sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6) ),
introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition]) ).
fof(f667,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f668,plain,
( spl13_18
| spl13_19
| ~ spl13_4
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f659,f632,f264,f665,f661]) ).
fof(f677,plain,
( ! [X2,X3,X0,X1] :
( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5)
| ~ mem(sK8,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_11 ),
inference(superposition,[],[f199,f517]) ).
fof(f678,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(sK8,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_11 ),
inference(trivial_inequality_removal,[],[f677]) ).
fof(f679,plain,
( ! [X2,X3,X0,X1] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f678,f132]) ).
fof(f720,definition,
( spl13_22
<=> ! [X2,X1,X3] :
( ~ mem(X1,arr(sK5,X2))
| ~ ne(X2)
| ~ mem(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
fof(f721,plain,
( ! [X2,X3,X1] :
( ~ mem(X1,arr(sK5,X2))
| ~ ne(X2)
| ~ mem(X3,X2) )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f723,definition,
( spl13_23
<=> ! [X0] : ~ mem(X0,ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl13_23])],[avatar_definition]) ).
fof(f724,plain,
( ! [X0] : ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f728,plain,
( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6))
| ~ spl13_12 ),
inference(resolution,[],[f521,f175]) ).
fof(f880,definition,
( spl13_28
<=> ne(arr(sK5,bool)) ),
introduced(definition,[new_symbols(definition,[spl13_28])],[avatar_definition]) ).
fof(f881,plain,
( ne(arr(sK5,bool))
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f882,plain,
( ~ ne(arr(sK5,bool))
| spl13_28 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f884,definition,
( spl13_29
<=> ! [X1] : ~ mem(X1,arr(sK5,bool)) ),
introduced(definition,[new_symbols(definition,[spl13_29])],[avatar_definition]) ).
fof(f885,plain,
( ! [X1] : ~ mem(X1,arr(sK5,bool))
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f903,definition,
( spl13_33
<=> ! [X2] : ~ mem(X2,sK5) ),
introduced(definition,[new_symbols(definition,[spl13_33])],[avatar_definition]) ).
fof(f904,plain,
( ! [X2] : ~ mem(X2,sK5)
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f906,plain,
( ~ ne(bool)
| ~ ne(sK5)
| spl13_28 ),
inference(resolution,[],[f882,f136]) ).
fof(f907,plain,
( ~ ne(sK5)
| spl13_28 ),
inference(forward_subsumption_resolution,[],[f906,f135]) ).
fof(f908,plain,
( $false
| spl13_28 ),
inference(forward_subsumption_resolution,[],[f907,f129]) ).
fof(f909,plain,
spl13_28,
inference(avatar_contradiction_clause,[],[f908]) ).
fof(f979,plain,
( ! [X0] :
( ~ mem(X0,sK5)
| ~ ne(sK5) )
| ~ spl13_23 ),
inference(resolution,[],[f724,f304]) ).
fof(f989,plain,
( ! [X0] : ~ mem(X0,sK5)
| ~ spl13_23 ),
inference(forward_subsumption_resolution,[],[f979,f129]) ).
fof(f992,plain,
( spl13_33
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f989,f723,f903]) ).
fof(f1224,plain,
( ! [X2,X3,X0,X1] :
( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5)
| ~ mem(sK10(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_12 ),
inference(superposition,[],[f199,f728]) ).
fof(f1225,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(sK10(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_12 ),
inference(trivial_inequality_removal,[],[f1224]) ).
fof(f1227,definition,
( spl13_35
<=> ! [X2,X0,X1,X3] : ~ sP4(sK5,X0,X1,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl13_35])],[avatar_definition]) ).
fof(f1228,plain,
( ! [X2,X3,X0,X1] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f1230,definition,
( spl13_36
<=> mem(sK10(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl13_36])],[avatar_definition]) ).
fof(f1232,plain,
( ~ mem(sK10(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl13_36 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f1233,plain,
( spl13_35
| ~ spl13_36
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f1225,f519,f1230,f1227]) ).
fof(f1255,plain,
( ~ sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl13_36 ),
inference(resolution,[],[f1232,f177]) ).
fof(f1256,plain,
( $false
| ~ spl13_12
| spl13_36 ),
inference(forward_subsumption_resolution,[],[f1255,f521]) ).
fof(f1257,plain,
( ~ spl13_12
| spl13_36 ),
inference(avatar_contradiction_clause,[],[f1256]) ).
fof(f1271,plain,
( ! [X2,X3,X0,X1] :
( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5)
| ~ mem(sK7,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_18 ),
inference(superposition,[],[f199,f663]) ).
fof(f1272,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(sK7,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_18 ),
inference(trivial_inequality_removal,[],[f1271]) ).
fof(f1273,plain,
( ! [X2,X3,X0,X1] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f1272,f131]) ).
fof(f1276,plain,
( spl13_35
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f1273,f661,f1227]) ).
fof(f1286,plain,
( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6))
| ~ spl13_19 ),
inference(resolution,[],[f667,f174]) ).
fof(f1341,plain,
( ! [X0] : ~ mem(X0,sK5)
| ~ spl13_29 ),
inference(resolution,[],[f885,f306]) ).
fof(f1354,plain,
( spl13_33
| ~ spl13_29 ),
inference(avatar_split_clause,[],[f1341,f884,f903]) ).
fof(f1355,plain,
( $false
| ~ spl13_33 ),
inference(resolution,[],[f904,f131]) ).
fof(f1370,plain,
~ spl13_33,
inference(avatar_contradiction_clause,[],[f1355]) ).
fof(f1381,plain,
( ! [X2,X3,X0,X1] :
( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5)
| ~ mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_19 ),
inference(superposition,[],[f199,f1286]) ).
fof(f1382,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl13_19 ),
inference(trivial_inequality_removal,[],[f1381]) ).
fof(f1384,definition,
( spl13_40
<=> mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl13_40])],[avatar_definition]) ).
fof(f1386,plain,
( ~ mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| spl13_40 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f1387,plain,
( spl13_35
| ~ spl13_40
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f1382,f665,f1384,f1227]) ).
fof(f1397,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| spl13_40 ),
inference(resolution,[],[f1386,f176]) ).
fof(f1398,plain,
( $false
| ~ spl13_19
| spl13_40 ),
inference(forward_subsumption_resolution,[],[f1397,f667]) ).
fof(f1399,plain,
( ~ spl13_19
| spl13_40 ),
inference(avatar_contradiction_clause,[],[f1398]) ).
fof(f1400,plain,
( spl13_35
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f679,f515,f1227]) ).
fof(f1411,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,X2))
| ~ mem(X3,X2)
| ~ ne(X2)
| ~ ne(sK5) )
| ~ spl13_35 ),
inference(resolution,[],[f1228,f209]) ).
fof(f1432,plain,
( ! [X0] :
( ~ ne(ty_2Eoption_2Eoption(sK5))
| ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ ne(sK5) )
| ~ spl13_22 ),
inference(resolution,[],[f721,f210]) ).
fof(f1445,plain,
( ! [X0] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ ne(sK5) )
| ~ spl13_22 ),
inference(forward_subsumption_resolution,[],[f1432,f222]) ).
fof(f1449,plain,
( ! [X0] : ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ spl13_22 ),
inference(forward_subsumption_resolution,[],[f1445,f129]) ).
fof(f1450,plain,
( spl13_23
| ~ spl13_22 ),
inference(avatar_split_clause,[],[f1449,f720,f723]) ).
fof(f1451,plain,
( ! [X2,X3,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,X2))
| ~ mem(X3,X2)
| ~ ne(X2) )
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1411,f129]) ).
fof(f1452,plain,
( spl13_22
| spl13_23
| ~ spl13_35 ),
inference(avatar_split_clause,[],[f1451,f1227,f723,f720]) ).
fof(f1455,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ ne(sK5)
| ~ spl13_1 ),
inference(resolution,[],[f254,f180]) ).
fof(f1458,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_1 ),
inference(duplicate_literal_removal,[],[f1455]) ).
fof(f1460,plain,
( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_1
| spl13_17 ),
inference(forward_subsumption_resolution,[],[f1458,f638]) ).
fof(f1462,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_1
| spl13_17
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f1460,f662]) ).
fof(f1464,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_1
| ~ spl13_10
| spl13_17
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f1462,f512]) ).
fof(f1466,plain,
( ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ ne(sK5)
| ~ spl13_1
| ~ spl13_10
| ~ spl13_16
| spl13_17
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f1464,f633]) ).
fof(f1468,plain,
( ~ ne(sK5)
| ~ spl13_1
| ~ spl13_10
| ~ spl13_16
| spl13_17
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f1466,f130]) ).
fof(f1471,plain,
( $false
| ~ spl13_1
| ~ spl13_10
| ~ spl13_16
| spl13_17
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f1468,f129]) ).
fof(f1472,plain,
( ~ spl13_1
| ~ spl13_10
| ~ spl13_16
| spl13_17
| spl13_18 ),
inference(avatar_contradiction_clause,[],[f1471]) ).
fof(f1477,plain,
( ap(c_2Eoption_2ESOME(sK5),sK7) = ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6))
| ~ spl13_17 ),
inference(resolution,[],[f637,f175]) ).
fof(f1478,plain,
( ap(c_2Eoption_2ESOME(sK5),sK8) = ap(c_2Eoption_2ESOME(sK5),sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6))
| ~ spl13_17 ),
inference(resolution,[],[f637,f174]) ).
fof(f1544,plain,
! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,bool))
| ~ ne(arr(sK5,bool))
| ~ ne(sK5)
| ~ mem(X2,sK5)
| ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 ),
inference(resolution,[],[f450,f130]) ).
fof(f1560,plain,
( ! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,bool))
| ~ ne(sK5)
| ~ mem(X2,sK5)
| ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 )
| ~ spl13_28 ),
inference(forward_subsumption_resolution,[],[f1544,f881]) ).
fof(f1568,plain,
( ! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,bool))
| ~ mem(X2,sK5)
| ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 )
| ~ spl13_28 ),
inference(forward_subsumption_resolution,[],[f1560,f129]) ).
fof(f1571,definition,
( spl13_44
<=> ! [X2] :
( ~ mem(X2,sK5)
| ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 ) ),
introduced(definition,[new_symbols(definition,[spl13_44])],[avatar_definition]) ).
fof(f1572,plain,
( ! [X2] :
( ~ mem(X2,sK5)
| ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 )
| ~ spl13_44 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f1573,plain,
( spl13_44
| spl13_29
| spl13_23
| ~ spl13_28 ),
inference(avatar_split_clause,[],[f1568,f880,f723,f884,f1571]) ).
fof(f1574,plain,
( sK7 = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK7))
| ~ spl13_44 ),
inference(resolution,[],[f1572,f131]) ).
fof(f1575,plain,
( sK8 = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8))
| ~ spl13_44 ),
inference(resolution,[],[f1572,f132]) ).
fof(f2496,definition,
( spl13_61
<=> mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl13_61])],[avatar_definition]) ).
fof(f2497,plain,
( mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ spl13_61 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f2498,plain,
( ~ mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl13_61 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f2512,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl13_61 ),
inference(resolution,[],[f2498,f177]) ).
fof(f2513,plain,
( $false
| ~ spl13_17
| spl13_61 ),
inference(forward_subsumption_resolution,[],[f2512,f637]) ).
fof(f2514,plain,
( ~ spl13_17
| spl13_61 ),
inference(avatar_contradiction_clause,[],[f2513]) ).
fof(f2525,definition,
( spl13_65
<=> mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl13_65])],[avatar_definition]) ).
fof(f2526,plain,
( mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ spl13_65 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f2527,plain,
( ~ mem(sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl13_65 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f2580,plain,
( sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)))
| ~ spl13_44
| ~ spl13_61 ),
inference(resolution,[],[f2497,f1572]) ).
fof(f2583,plain,
( ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK7)) = sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61 ),
inference(forward_demodulation,[],[f2580,f1477]) ).
fof(f2584,plain,
( sK7 = sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61 ),
inference(forward_demodulation,[],[f2583,f1574]) ).
fof(f2592,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl13_65 ),
inference(resolution,[],[f2527,f176]) ).
fof(f2593,plain,
( $false
| ~ spl13_17
| spl13_65 ),
inference(forward_subsumption_resolution,[],[f2592,f637]) ).
fof(f2594,plain,
( ~ spl13_17
| spl13_65 ),
inference(avatar_contradiction_clause,[],[f2593]) ).
fof(f2636,plain,
( sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)))
| ~ spl13_44
| ~ spl13_65 ),
inference(resolution,[],[f2526,f1572]) ).
fof(f2639,plain,
( ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8)) = sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17
| ~ spl13_44
| ~ spl13_65 ),
inference(forward_demodulation,[],[f2636,f1478]) ).
fof(f2640,plain,
( sK8 = sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17
| ~ spl13_44
| ~ spl13_65 ),
inference(forward_demodulation,[],[f2639,f1575]) ).
fof(f2655,plain,
( p(ap(ap(sK6,sK7),sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)))
| ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61 ),
inference(superposition,[],[f173,f2584]) ).
fof(f2657,plain,
( p(ap(ap(sK6,sK7),sK11(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)))
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61 ),
inference(forward_subsumption_resolution,[],[f2655,f637]) ).
fof(f2658,plain,
( p(ap(ap(sK6,sK7),sK8))
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61
| ~ spl13_65 ),
inference(forward_demodulation,[],[f2657,f2640]) ).
fof(f2659,plain,
( $false
| spl13_2
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61
| ~ spl13_65 ),
inference(forward_subsumption_resolution,[],[f2658,f257]) ).
fof(f2660,plain,
( spl13_2
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61
| ~ spl13_65 ),
inference(avatar_contradiction_clause,[],[f2659]) ).
cnf(s1,plain,
( spl13_1
| spl13_2
| spl13_3
| spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f271]) ).
cnf(s2,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_3
| spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s6,plain,
spl13_5,
inference(sat_conversion,[],[f457]) ).
cnf(s7,plain,
( ~ spl13_3
| ~ spl13_10
| spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f522]) ).
cnf(s10,plain,
spl13_10,
inference(sat_conversion,[],[f610]) ).
cnf(s13,plain,
( spl13_1
| ~ spl13_10
| ~ spl13_16
| ~ spl13_17 ),
inference(sat_conversion,[],[f639]) ).
cnf(s14,plain,
spl13_16,
inference(sat_conversion,[],[f643]) ).
cnf(s15,plain,
( ~ spl13_2
| spl13_17 ),
inference(sat_conversion,[],[f651]) ).
cnf(s16,plain,
( ~ spl13_4
| ~ spl13_16
| spl13_18
| spl13_19 ),
inference(sat_conversion,[],[f668]) ).
cnf(s28,plain,
spl13_28,
inference(sat_conversion,[],[f909]) ).
cnf(s32,plain,
( ~ spl13_23
| spl13_33 ),
inference(sat_conversion,[],[f992]) ).
cnf(s34,plain,
( ~ spl13_12
| spl13_35
| ~ spl13_36 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s37,plain,
( ~ spl13_12
| spl13_36 ),
inference(sat_conversion,[],[f1257]) ).
cnf(s39,plain,
( ~ spl13_18
| spl13_35 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s41,plain,
( ~ spl13_29
| spl13_33 ),
inference(sat_conversion,[],[f1354]) ).
cnf(s46,plain,
~ spl13_33,
inference(sat_conversion,[],[f1370]) ).
cnf(s48,plain,
( ~ spl13_19
| spl13_35
| ~ spl13_40 ),
inference(sat_conversion,[],[f1387]) ).
cnf(s51,plain,
( ~ spl13_19
| spl13_40 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s53,plain,
( ~ spl13_11
| spl13_35 ),
inference(sat_conversion,[],[f1400]) ).
cnf(s58,plain,
( ~ spl13_22
| spl13_23 ),
inference(sat_conversion,[],[f1450]) ).
cnf(s59,plain,
( spl13_22
| spl13_23
| ~ spl13_35 ),
inference(sat_conversion,[],[f1452]) ).
cnf(s61,plain,
( ~ spl13_1
| ~ spl13_10
| ~ spl13_16
| spl13_17
| spl13_18 ),
inference(sat_conversion,[],[f1472]) ).
cnf(s63,plain,
( spl13_23
| ~ spl13_28
| spl13_29
| spl13_44 ),
inference(sat_conversion,[],[f1573]) ).
cnf(s80,plain,
( ~ spl13_17
| spl13_61 ),
inference(sat_conversion,[],[f2514]) ).
cnf(s86,plain,
( ~ spl13_17
| spl13_65 ),
inference(sat_conversion,[],[f2594]) ).
cnf(s89,plain,
( spl13_2
| ~ spl13_17
| ~ spl13_44
| ~ spl13_61
| ~ spl13_65 ),
inference(sat_conversion,[],[f2660]) ).
cnf(s90,plain,
~ spl13_29,
inference(rat,[],[s41,s46]) ).
cnf(s92,plain,
~ spl13_23,
inference(rat,[],[s32,s46]) ).
cnf(s93,plain,
~ spl13_22,
inference(rat,[],[s58,s92]) ).
cnf(s94,plain,
~ spl13_35,
inference(rat,[],[s59,s92,s93]) ).
cnf(s95,plain,
~ spl13_11,
inference(rat,[],[s53,s94]) ).
cnf(s96,plain,
~ spl13_18,
inference(rat,[],[s39,s94]) ).
cnf(s103,plain,
spl13_44,
inference(rat,[],[s63,s92,s90,s28]) ).
cnf(s111,plain,
( ~ spl13_4
| ~ spl13_16
| spl13_19 ),
inference(rat,[],[s16,s96]) ).
cnf(s112,plain,
( spl13_1
| ~ spl13_10
| ~ spl13_17 ),
inference(rat,[],[s13,s14]) ).
cnf(s115,plain,
( ~ spl13_3
| spl13_12 ),
inference(rat,[],[s7,s95,s10]) ).
cnf(s117,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_3
| spl13_4 ),
inference(rat,[],[s2,s6]) ).
cnf(s118,plain,
( spl13_1
| spl13_2
| spl13_3
| spl13_4 ),
inference(rat,[],[s1,s6]) ).
cnf(s119,plain,
~ spl13_19,
inference(rat,[],[s48,s51,s94]) ).
cnf(s120,plain,
~ spl13_4,
inference(rat,[],[s111,s14,s119]) ).
cnf(s121,plain,
~ spl13_12,
inference(rat,[],[s34,s37,s94]) ).
cnf(s122,plain,
~ spl13_3,
inference(rat,[],[s115,s121]) ).
cnf(s123,plain,
spl13_1,
inference(rat,[],[s15,s118,s112,s122,s120,s10]) ).
cnf(s124,plain,
spl13_17,
inference(rat,[],[s61,s96,s10,s14,s123]) ).
cnf(s125,plain,
~ spl13_2,
inference(rat,[],[s117,s120,s122,s123]) ).
cnf(s126,plain,
spl13_65,
inference(rat,[],[s86,s124]) ).
cnf(s127,plain,
spl13_61,
inference(rat,[],[s80,s124]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s89,s126,s127,s103,s124,s125]) ).
fof(f2661,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP011+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 12:03:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.40/1.60 % (3432051)Detected formulas, will run a generic FOF schedule.
% 3.40/1.60 % (3432155)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1800007510:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.60 % (3432156)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3255851545:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.60 % (3432158)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1419083422:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.60 % (3432157)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3047807143:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.60 % (3432158)Refutation not found, incomplete strategy
% 3.40/1.60 % (3432158)------------------------------
% 3.40/1.60 % (3432158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432158)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432158)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.60 % (3432158)Time elapsed: 0.005 s
% 3.40/1.60 % (3432158)Peak memory usage: 88 MB
% 3.40/1.60 % (3432158)Instructions burned: 6 (million)
% 3.40/1.60 % (3432159)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2971438476:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.60 % (3432161)dis-21_1_sil=8000:lcm=predicate:random_seed=2471503651:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.40/1.60 % (3432160)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3842640689:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.60 % (3432159)Instruction limit reached!
% 3.40/1.60 % (3432159)------------------------------
% 3.40/1.60 % (3432159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432159)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432159)Termination reason: Instruction limit
% 3.40/1.60 % (3432159)Termination phase: Saturation
% 3.40/1.60 % (3432159)Time elapsed: 0.073 s
% 3.40/1.60 % (3432159)Peak memory usage: 88 MB
% 3.40/1.60 % (3432159)Instructions burned: 119 (million)
% 3.40/1.60 % (3432161)Instruction limit reached!
% 3.40/1.60 % (3432161)------------------------------
% 3.40/1.60 % (3432161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432161)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432161)Termination reason: Instruction limit
% 3.40/1.60 % (3432161)Termination phase: Saturation
% 3.40/1.60 % (3432161)Time elapsed: 0.075 s
% 3.40/1.60 % (3432161)Peak memory usage: 89 MB
% 3.40/1.60 % (3432161)Instructions burned: 129 (million)
% 3.40/1.60 % (3432182)lrs+10_1_sil=8000:sp=occurrence:random_seed=3879740704:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.40/1.60 % (3432183)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3483216291:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.40/1.60 % (3432160)Instruction limit reached!
% 3.40/1.60 % (3432160)------------------------------
% 3.40/1.60 % (3432160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432160)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432160)Termination reason: Instruction limit
% 3.40/1.60 % (3432160)Termination phase: Saturation
% 3.40/1.60 % (3432160)Time elapsed: 0.159 s
% 3.40/1.60 % (3432160)Peak memory usage: 90 MB
% 3.40/1.60 % (3432160)Instructions burned: 139 (million)
% 3.40/1.60 % (3432158)------------------------------
% 3.40/1.60 % (3432158)------------------------------
% 3.40/1.60 % (3432183)Instruction limit reached!
% 3.40/1.60 % (3432183)------------------------------
% 3.40/1.60 % (3432183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432183)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432183)Termination reason: Instruction limit
% 3.40/1.60 % (3432183)Termination phase: Saturation
% 3.40/1.60 % (3432183)Time elapsed: 0.080 s
% 3.40/1.60 % (3432183)Peak memory usage: 92 MB
% 3.40/1.60 % (3432183)Instructions burned: 157 (million)
% 3.40/1.60 % (3432182)First to succeed.
% 3.40/1.60 % (3432182)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3432051"
% 3.40/1.60 % (3432186)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1261898744:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.40/1.60 % (3432187)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3693588978:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.40/1.60 % (3432188)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1768073528:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.40/1.60 % (3432187)Instruction limit reached!
% 3.40/1.60 % (3432187)------------------------------
% 3.40/1.60 % (3432187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432187)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432187)Termination reason: Instruction limit
% 3.40/1.60 % (3432187)Termination phase: Saturation
% 3.40/1.60 % (3432187)Time elapsed: 0.138 s
% 3.40/1.60 % (3432187)Peak memory usage: 95 MB
% 3.40/1.60 % (3432187)Instructions burned: 250 (million)
% 3.40/1.60 % (3432155)Also succeeded, but the first one will report.
% 3.40/1.60 % (3432186)Instruction limit reached!
% 3.40/1.60 % (3432186)------------------------------
% 3.40/1.60 % (3432186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432186)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432186)Termination reason: Instruction limit
% 3.40/1.60 % (3432186)Termination phase: Saturation
% 3.40/1.60 % (3432186)Time elapsed: 0.219 s
% 3.40/1.60 % (3432186)Peak memory usage: 92 MB
% 3.40/1.60 % (3432186)Instructions burned: 325 (million)
% 3.40/1.60 % (3432188)Instruction limit reached!
% 3.40/1.60 % (3432188)------------------------------
% 3.40/1.60 % (3432188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.60 % (3432188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.60 % (3432188)CaDiCaL version: 2.1.3
% 3.40/1.60 % (3432188)Termination reason: Instruction limit
% 3.40/1.60 % (3432188)Termination phase: Saturation
% 3.40/1.60 % (3432188)Time elapsed: 0.156 s
% 3.40/1.60 % (3432188)Peak memory usage: 89 MB
% 3.40/1.60 % (3432188)Instructions burned: 295 (million)
% 3.40/1.60 % (3432182)Refutation found. Thanks to Tanya!
% 3.40/1.60 % SZS status Theorem for theBenchmark
% 3.40/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.80 % (3432182)------------------------------
% 0.16/1.80 % (3432182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.80 % (3432182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.80 % (3432182)CaDiCaL version: 2.1.3
% 0.16/1.80 % (3432182)Termination reason: Refutation
% 0.16/1.80 % (3432182)Time elapsed: 0.125 s
% 0.16/1.80 % (3432182)Peak memory usage: 92 MB
% 0.16/1.80 % (3432182)Instructions burned: 196 (million)
% 0.16/1.80 % (3432182)------------------------------
% 0.16/1.80 % (3432182)------------------------------
% 0.16/1.80 % (3432051)Success in time 0.733 s
% 0.16/1.80 % Vampire exiting
%------------------------------------------------------------------------------