%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP002+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 : n011.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 11:27:39 AM UTC 2026
% Result : Theorem 14.48s 3.22s
% Output : Refutation 17.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 23
% Syntax : Number of formulae : 247 ( 78 unt; 4 def)
% Number of atoms : 726 ( 174 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 863 ( 384 ~; 396 |; 31 &)
% ( 9 <=>; 41 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 336 ( 0 sgn 330 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_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(f5,axiom,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
fof(f9,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(f10,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
fof(f11,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
fof(f12,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
fof(f13,axiom,
! [X0] :
( ne(X0)
=> ne(ty_2Eoption_2Eoption(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eoption_2Eoption) ).
fof(f14,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(f15,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Eoption_2ETHE(X0),arr(ty_2Eoption_2Eoption(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ETHE) ).
fof(f16,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(f17,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Eoption_2EIS__SOME(X0),arr(ty_2Eoption_2Eoption(X0),bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EIS__SOME) ).
fof(f18,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
fof(f19,axiom,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X0)
& p(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
fof(f29,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,X0)
=> ! [X2] :
( mem(X2,X0)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2ET),X1),X2) = X1
& ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X1),X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
fof(f31,axiom,
! [X0] :
( ne(X0)
=> ( ! [X1] :
( mem(X1,X0)
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
<=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EIS__SOME__DEF) ).
fof(f32,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,X0)
=> ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2ETHE__DEF) ).
fof(f33,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4] :
( mem(X4,ty_2Eoption_2Eoption(X1))
=> ! [X5] :
( mem(X5,ty_2Eoption_2Eoption(X2))
=> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTION__MAP2__DEF) ).
fof(f34,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4] :
( mem(X4,X1)
=> ! [X5] :
( mem(X5,X2)
=> ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) = ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5))
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5)) = c_2Eoption_2ENONE(X0)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2EOPTION__MAP2__THM) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4] :
( mem(X4,X1)
=> ! [X5] :
( mem(X5,X2)
=> ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) = ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5))
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5)) = c_2Eoption_2ENONE(X0)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f38,plain,
! [X0] :
( ne(X0)
=> ( ! [X1] :
( mem(X1,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) ) ),
inference(true_and_false_elimination,[],[f31]) ).
fof(f39,plain,
! [X0] :
( ne(X0)
=> ( ! [X1] :
( mem(X1,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ne(ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f41,plain,
! [X0] :
( mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0] :
( mem(c_2Eoption_2ETHE(X0),arr(ty_2Eoption_2Eoption(X0),X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f43,plain,
! [X0] :
( mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0)))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0] :
( mem(c_2Eoption_2EIS__SOME(X0),arr(ty_2Eoption_2Eoption(X0),bool))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X0)
& p(X1) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2ET),X1),X2) = X1
& ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X1),X2) = X2 )
| ~ mem(X2,X0) )
| ~ mem(X1,X0) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0] :
( ( ! [X1] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| ~ mem(X1,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1
| ~ mem(X1,X0) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0))
| ~ mem(X5,ty_2Eoption_2Eoption(X2)) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,arr(X1,arr(X2,X0))) )
| ~ ne(X2) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) != ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5))
| c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2))
| c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5))
| c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) )
& mem(X5,X2) )
& mem(X4,X1) )
& mem(X3,arr(X1,arr(X2,X0))) )
& ne(X2) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f60]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f45]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f66]) ).
fof(f75,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) != ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) )
& mem(sK6,sK3)
& mem(sK5,sK2)
& mem(sK4,arr(sK2,arr(sK3,sK1)))
& ne(sK3)
& ne(sK2)
& ne(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f59]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f61]) ).
fof(f78,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[],[f9]) ).
fof(f79,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[],[f10]) ).
fof(f80,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[],[f11]) ).
fof(f81,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[],[f12]) ).
fof(f82,plain,
! [X0] :
( ne(ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
! [X0] :
( mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
! [X0] :
( mem(c_2Eoption_2ETHE(X0),arr(ty_2Eoption_2Eoption(X0),X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
! [X0] :
( mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0)))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f86,plain,
! [X0] :
( mem(c_2Eoption_2EIS__SOME(X0),arr(ty_2Eoption_2Eoption(X0),bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f87,plain,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[],[f18]) ).
fof(f88,plain,
! [X0,X1] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f67]) ).
fof(f89,plain,
! [X0,X1] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f67]) ).
fof(f90,plain,
! [X0,X1] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ ne(X0)
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X1),X2) = X2 ),
inference(cnf_transformation,[],[f54]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ ne(X0)
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2ET),X1),X2) = X1 ),
inference(cnf_transformation,[],[f54]) ).
fof(f112,plain,
! [X0] :
( ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f113,plain,
! [X0,X1] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f114,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ mem(X1,X0)
| ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f115,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ mem(X5,ty_2Eoption_2Eoption(X2))
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0))
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f116,plain,
ne(sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f117,plain,
ne(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f118,plain,
ne(sK3),
inference(cnf_transformation,[],[f75]) ).
fof(f119,plain,
mem(sK4,arr(sK2,arr(sK3,sK1))),
inference(cnf_transformation,[],[f75]) ).
fof(f120,plain,
mem(sK5,sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
mem(sK6,sK3),
inference(cnf_transformation,[],[f75]) ).
fof(f122,plain,
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) != ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6))
| c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f123,plain,
ne(bool),
inference(cnf_transformation,[],[f1]) ).
fof(f124,plain,
! [X0,X1] :
( ~ mem(X0,bool)
| p(X1)
| p(X0)
| ~ mem(X1,bool)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f125,plain,
! [X0,X1] :
( ~ mem(X0,bool)
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f134,definition,
( spl8_1
<=> c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f135,plain,
( c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3))
| spl8_1 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl8_2
<=> c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f138,plain,
( c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6))
| spl8_2 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl8_3
<=> c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f141,plain,
( c_2Eoption_2ENONE(sK1) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3))
| spl8_3 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,definition,
( spl8_4
<=> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6)) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f144,plain,
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) != ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))
| spl8_4 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f122,f143,f140,f137,f134]) ).
fof(f147,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0)) = X0 ),
inference(resolution,[],[f114,f118]) ).
fof(f148,plain,
! [X0] :
( ~ mem(X0,sK2)
| ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0)) = X0 ),
inference(resolution,[],[f114,f117]) ).
fof(f150,plain,
! [X0] :
( mem(ap(sK4,X0),arr(sK3,sK1))
| ~ mem(X0,sK2) ),
inference(resolution,[],[f127,f119]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0)
| ~ ne(X2) ),
inference(resolution,[],[f115,f83]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ~ ne(X0)
| mem(ap(c_2Eoption_2ETHE(X0),X1),X0) ),
inference(resolution,[],[f84,f127]) ).
fof(f154,plain,
! [X0,X1] :
( ~ mem(X1,sK3)
| ~ mem(X0,sK2)
| mem(ap(ap(sK4,X0),X1),sK1) ),
inference(resolution,[],[f150,f127]) ).
fof(f155,plain,
! [X0,X1] :
( mem(ap(c_2Eoption_2ESOME(X0),X1),ty_2Eoption_2Eoption(X0))
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(resolution,[],[f85,f127]) ).
fof(f156,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ mem(X0,X1)
| ~ ne(X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X2,X3,X1),X4),X5),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X2)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X3),X5)),ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)))),ap(c_2Eoption_2ESOME(X2),ap(ap(X4,ap(c_2Eoption_2ETHE(X3),X5)),ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X0))))),c_2Eoption_2ENONE(X2))
| ~ mem(X5,ty_2Eoption_2Eoption(X3))
| ~ mem(X4,arr(X3,arr(X1,X2)))
| ~ ne(X1)
| ~ ne(X3)
| ~ ne(X2) ),
inference(resolution,[],[f155,f115]) ).
fof(f157,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ mem(X5,ty_2Eoption_2Eoption(X3))
| ~ ne(X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X2,X3,X1),X4),X5),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X2)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X3),X5)),ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)))),ap(c_2Eoption_2ESOME(X2),ap(ap(X4,ap(c_2Eoption_2ETHE(X3),X5)),ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X0))))),c_2Eoption_2ENONE(X2))
| ~ mem(X0,X1)
| ~ mem(X4,arr(X3,arr(X1,X2)))
| ~ ne(X3)
| ~ ne(X2) ),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f164,plain,
! [X2,X3,X0,X1,X4] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X4))),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X4))),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0)
| ~ mem(X4,X1)
| ~ ne(X1) ),
inference(resolution,[],[f152,f155]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),c_2Eoption_2ENONE(X1))),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),c_2Eoption_2ENONE(X1))),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0)
| ~ ne(X1) ),
inference(resolution,[],[f152,f83]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ mem(X3,arr(X1,arr(X2,X0)))
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),c_2Eoption_2ENONE(X1))),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),c_2Eoption_2ENONE(X1))),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f167,plain,
! [X2,X3,X0,X1,X4] :
( ~ mem(X3,arr(X1,arr(X2,X0)))
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X4))),ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2)))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X4))),ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))))),c_2Eoption_2ENONE(X0))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0)
| ~ mem(X4,X1) ),
inference(duplicate_literal_removal,[],[f164]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ mem(X2,ty_2Eoption_2Eoption(X0))
| ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ~ ne(X0)
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2EF),X2),X1) = X1 ),
inference(resolution,[],[f82,f108]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ mem(X2,ty_2Eoption_2Eoption(X0))
| ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ~ ne(X0)
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2ET),X2),X1) = X2 ),
inference(resolution,[],[f82,f109]) ).
fof(f176,plain,
sK5 = ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)),
inference(resolution,[],[f148,f120]) ).
fof(f177,plain,
sK6 = ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)),
inference(resolution,[],[f147,f121]) ).
fof(f180,plain,
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK3)
| ~ ne(sK2)
| ~ ne(sK1) ),
inference(resolution,[],[f166,f119]) ).
fof(f181,plain,
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK2)
| ~ ne(sK1) ),
inference(forward_subsumption_resolution,[],[f180,f118]) ).
fof(f184,plain,
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK1) ),
inference(forward_subsumption_resolution,[],[f181,f117]) ).
fof(f186,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_subsumption_resolution,[],[f184,f116]) ).
fof(f189,plain,
! [X0] :
( ~ p(X0)
| ~ p(c_2Ebool_2ET)
| ~ mem(X0,bool)
| c_2Ebool_2ET = X0 ),
inference(resolution,[],[f80,f125]) ).
fof(f191,plain,
! [X0] :
( ~ mem(X0,bool)
| ~ p(X0)
| c_2Ebool_2ET = X0 ),
inference(forward_subsumption_resolution,[],[f189,f81]) ).
fof(f194,plain,
! [X0] :
( ~ ne(X0)
| mem(ap(c_2Eoption_2ETHE(X0),c_2Eoption_2ENONE(X0)),X0)
| ~ ne(X0) ),
inference(resolution,[],[f153,f83]) ).
fof(f195,plain,
! [X0] :
( ~ ne(X0)
| mem(ap(c_2Eoption_2ETHE(X0),c_2Eoption_2ENONE(X0)),X0) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f200,plain,
mem(ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)),sK2),
inference(resolution,[],[f195,f117]) ).
fof(f201,plain,
mem(ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3)),sK3),
inference(resolution,[],[f195,f118]) ).
fof(f212,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ~ ne(X0)
| mem(ap(c_2Eoption_2EIS__SOME(X0),X1),bool) ),
inference(resolution,[],[f86,f127]) ).
fof(f213,plain,
! [X0,X1] :
( ~ ne(X0)
| mem(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)),bool)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(resolution,[],[f212,f155]) ).
fof(f214,plain,
! [X0] :
( ~ ne(X0)
| mem(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)),bool)
| ~ ne(X0) ),
inference(resolution,[],[f212,f83]) ).
fof(f215,plain,
! [X0] :
( mem(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)),bool)
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( mem(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)),bool)
| ~ ne(X0)
| ~ mem(X1,X0) ),
inference(duplicate_literal_removal,[],[f213]) ).
fof(f225,plain,
! [X0,X1] :
( ~ ne(X0)
| p(X1)
| p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
| ~ mem(X1,bool)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = X1 ),
inference(resolution,[],[f215,f124]) ).
fof(f226,plain,
! [X0,X1] :
( ~ mem(X1,bool)
| p(X1)
| ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = X1 ),
inference(forward_subsumption_resolution,[],[f225,f112]) ).
fof(f227,plain,
! [X0,X1] :
( p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
| ~ ne(X1)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = ap(c_2Eoption_2EIS__SOME(X1),c_2Eoption_2ENONE(X1))
| ~ ne(X0) ),
inference(resolution,[],[f226,f215]) ).
fof(f229,plain,
! [X0,X1] :
( ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = ap(c_2Eoption_2EIS__SOME(X1),c_2Eoption_2ENONE(X1))
| ~ ne(X1) ),
inference(forward_subsumption_resolution,[],[f227,f112]) ).
fof(f233,plain,
! [X0] :
( ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1)) ),
inference(resolution,[],[f229,f116]) ).
fof(f234,plain,
! [X0] :
( ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) = ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)) ),
inference(resolution,[],[f229,f117]) ).
fof(f240,plain,
ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)) = ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f233,f117]) ).
fof(f241,plain,
ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)) = ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f233,f118]) ).
fof(f249,plain,
ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)) = ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)),
inference(superposition,[],[f241,f240]) ).
fof(f250,plain,
( mem(ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)),bool)
| ~ ne(sK1) ),
inference(superposition,[],[f215,f240]) ).
fof(f251,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))
| ~ ne(sK1) ),
inference(superposition,[],[f112,f240]) ).
fof(f252,plain,
~ p(ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),
inference(forward_subsumption_resolution,[],[f251,f116]) ).
fof(f253,plain,
mem(ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)),bool),
inference(forward_subsumption_resolution,[],[f250,f116]) ).
fof(f260,plain,
ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)) = ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)),
inference(resolution,[],[f234,f123]) ).
fof(f289,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK3)
| ~ ne(sK2)
| ~ ne(sK1)
| ~ mem(X0,sK2) ),
inference(resolution,[],[f167,f119]) ).
fof(f290,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK2)
| ~ ne(sK1)
| ~ mem(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f289,f118]) ).
fof(f294,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK1)
| ~ mem(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f290,f117]) ).
fof(f297,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f294,f116]) ).
fof(f299,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK2) ),
inference(forward_demodulation,[],[f297,f249]) ).
fof(f300,plain,
! [X0] :
( ~ mem(X0,sK2)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X0)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X0))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)) ),
inference(forward_demodulation,[],[f299,f260]) ).
fof(f301,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f300,f120]) ).
fof(f302,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f301,f176]) ).
fof(f306,plain,
! [X0] :
( p(c_2Ebool_2EF)
| ~ ne(X0)
| c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) ),
inference(resolution,[],[f78,f226]) ).
fof(f309,plain,
! [X0] :
( p(X0)
| p(c_2Ebool_2EF)
| ~ mem(X0,bool)
| c_2Ebool_2EF = X0 ),
inference(resolution,[],[f78,f124]) ).
fof(f310,plain,
! [X0] :
( ~ mem(X0,bool)
| p(X0)
| c_2Ebool_2EF = X0 ),
inference(forward_subsumption_resolution,[],[f309,f79]) ).
fof(f311,plain,
! [X0] :
( ~ ne(X0)
| c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) ),
inference(forward_subsumption_resolution,[],[f306,f79]) ).
fof(f314,plain,
( p(ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))
| c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)) ),
inference(resolution,[],[f310,f253]) ).
fof(f317,plain,
c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)),
inference(forward_subsumption_resolution,[],[f314,f252]) ).
fof(f327,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(sK3),c_2Eoption_2ENONE(sK3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(superposition,[],[f186,f317]) ).
fof(f330,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f327,f249]) ).
fof(f331,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f330,f260]) ).
fof(f332,plain,
c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool)),
inference(resolution,[],[f311,f123]) ).
fof(f410,plain,
! [X0] :
( ~ mem(X0,sK2)
| mem(ap(ap(sK4,X0),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))),sK1) ),
inference(resolution,[],[f154,f201]) ).
fof(f411,plain,
! [X0] :
( ~ mem(X0,sK2)
| mem(ap(ap(sK4,X0),sK6),sK1) ),
inference(resolution,[],[f154,f121]) ).
fof(f412,plain,
mem(ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK6),sK1),
inference(resolution,[],[f411,f200]) ).
fof(f413,plain,
mem(ap(ap(sK4,sK5),sK6),sK1),
inference(resolution,[],[f411,f120]) ).
fof(f467,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(superposition,[],[f302,f332]) ).
fof(f570,plain,
! [X0] :
( mem(ap(c_2Ebool_2E_2F_5C,X0),arr(bool,bool))
| ~ mem(X0,bool) ),
inference(resolution,[],[f87,f127]) ).
fof(f579,plain,
! [X0,X1] :
( mem(ap(ap(c_2Ebool_2E_2F_5C,X0),X1),bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f570,f127]) ).
fof(f583,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ mem(X1,X0)
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) ),
inference(resolution,[],[f216,f191]) ).
fof(f584,plain,
! [X2,X0,X1] :
( ~ ne(X0)
| ~ mem(X1,X0)
| ~ p(X2)
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| ~ mem(X2,bool)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X2 ),
inference(resolution,[],[f216,f125]) ).
fof(f586,plain,
! [X2,X0,X1] :
( ~ p(X2)
| ~ mem(X1,X0)
| ~ ne(X0)
| ~ mem(X2,bool)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X2 ),
inference(forward_subsumption_resolution,[],[f584,f113]) ).
fof(f587,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ mem(X1,X0)
| c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) ),
inference(forward_subsumption_resolution,[],[f583,f113]) ).
fof(f592,plain,
! [X0] :
( ~ mem(X0,sK2)
| c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X0)) ),
inference(resolution,[],[f587,f117]) ).
fof(f593,plain,
! [X0] :
( ~ mem(X0,sK3)
| c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)) ),
inference(resolution,[],[f587,f118]) ).
fof(f596,plain,
! [X2,X3,X0,X1] :
( ~ mem(X0,X1)
| ~ ne(X1)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,X2),X3),bool)
| ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(c_2Ebool_2E_2F_5C,X2),X3)
| ~ p(X2)
| ~ p(X3)
| ~ mem(X3,bool)
| ~ mem(X2,bool) ),
inference(resolution,[],[f586,f90]) ).
fof(f600,plain,
! [X2,X3,X0,X1] :
( ~ p(X3)
| ~ ne(X1)
| ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(c_2Ebool_2E_2F_5C,X2),X3)
| ~ p(X2)
| ~ mem(X0,X1)
| ~ mem(X3,bool)
| ~ mem(X2,bool) ),
inference(forward_subsumption_resolution,[],[f596,f579]) ).
fof(f603,plain,
c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)),
inference(resolution,[],[f592,f120]) ).
fof(f611,plain,
c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)),
inference(resolution,[],[f593,f121]) ).
fof(f802,plain,
! [X2,X3,X0,X1,X4] :
( ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = ap(ap(c_2Ebool_2E_2F_5C,X2),ap(c_2Eoption_2EIS__SOME(X3),ap(c_2Eoption_2ESOME(X3),X4)))
| ~ p(X2)
| ~ mem(X1,X0)
| ~ mem(ap(c_2Eoption_2EIS__SOME(X3),ap(c_2Eoption_2ESOME(X3),X4)),bool)
| ~ mem(X2,bool)
| ~ mem(X4,X3)
| ~ ne(X3) ),
inference(resolution,[],[f600,f113]) ).
fof(f810,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(X2)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = ap(ap(c_2Ebool_2E_2F_5C,X2),ap(c_2Eoption_2EIS__SOME(X3),ap(c_2Eoption_2ESOME(X3),X4)))
| ~ ne(X0)
| ~ mem(X1,X0)
| ~ mem(X2,bool)
| ~ mem(X4,X3)
| ~ ne(X3) ),
inference(forward_subsumption_resolution,[],[f802,f216]) ).
fof(f811,plain,
mem(ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))),sK1),
inference(resolution,[],[f410,f200]) ).
fof(f812,plain,
mem(ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))),sK1),
inference(resolution,[],[f410,f120]) ).
fof(f867,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(superposition,[],[f467,f603]) ).
fof(f997,plain,
! [X2,X3,X0,X1] :
( ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(X2),ap(c_2Eoption_2ESOME(X2),X3)))
| ~ ne(X0)
| ~ mem(X1,X0)
| ~ mem(c_2Ebool_2ET,bool)
| ~ mem(X3,X2)
| ~ ne(X2) ),
inference(resolution,[],[f810,f81]) ).
fof(f998,plain,
! [X2,X3,X0,X1] :
( ~ ne(X2)
| ~ ne(X0)
| ~ mem(X1,X0)
| ~ mem(X3,X2)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(X2),ap(c_2Eoption_2ESOME(X2),X3))) ),
inference(forward_subsumption_resolution,[],[f997,f80]) ).
fof(f1006,plain,
! [X2,X0,X1] :
( ~ mem(X2,sK2)
| ~ mem(X1,X0)
| ~ ne(X0)
| ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X2))) ),
inference(resolution,[],[f998,f117]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ mem(X0,X1)
| ~ ne(X1)
| ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))) ),
inference(resolution,[],[f1006,f120]) ).
fof(f1010,plain,
! [X0,X1] :
( ~ ne(X1)
| ~ mem(X0,X1)
| ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X0)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET) ),
inference(forward_demodulation,[],[f1009,f603]) ).
fof(f1027,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET) ),
inference(resolution,[],[f1010,f118]) ).
fof(f1033,plain,
ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET),
inference(resolution,[],[f1027,f121]) ).
fof(f1034,plain,
c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET),
inference(forward_demodulation,[],[f1033,f611]) ).
fof(f1095,plain,
! [X0,X1] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X1),X0))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X1),X0) ),
inference(resolution,[],[f579,f310]) ).
fof(f1102,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ne(X0)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X1,X2,X0),X3),ap(c_2Eoption_2ESOME(X2),X4)),ap(c_2Eoption_2ESOME(X0),X5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X2),ap(c_2Eoption_2ESOME(X2),X4))),ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X5)))),ap(c_2Eoption_2ESOME(X1),ap(ap(X3,ap(c_2Eoption_2ETHE(X2),ap(c_2Eoption_2ESOME(X2),X4))),ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5))))),c_2Eoption_2ENONE(X1))
| ~ mem(X5,X0)
| ~ mem(X3,arr(X2,arr(X0,X1)))
| ~ ne(X2)
| ~ ne(X1)
| ~ mem(X4,X2)
| ~ ne(X2) ),
inference(resolution,[],[f157,f155]) ).
fof(f1103,plain,
! [X2,X3,X0,X1,X4] :
( ~ ne(X0)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X1,X2,X0),X3),c_2Eoption_2ENONE(X2)),ap(c_2Eoption_2ESOME(X0),X4)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2))),ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X4)))),ap(c_2Eoption_2ESOME(X1),ap(ap(X3,ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))),ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X4))))),c_2Eoption_2ENONE(X1))
| ~ mem(X4,X0)
| ~ mem(X3,arr(X2,arr(X0,X1)))
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X2) ),
inference(resolution,[],[f157,f83]) ).
fof(f1104,plain,
! [X2,X3,X0,X1,X4] :
( ~ ne(X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X1,X2,X0),X3),c_2Eoption_2ENONE(X2)),ap(c_2Eoption_2ESOME(X0),X4)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X2),c_2Eoption_2ENONE(X2))),ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X4)))),ap(c_2Eoption_2ESOME(X1),ap(ap(X3,ap(c_2Eoption_2ETHE(X2),c_2Eoption_2ENONE(X2))),ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X4))))),c_2Eoption_2ENONE(X1))
| ~ mem(X4,X0)
| ~ mem(X3,arr(X2,arr(X0,X1)))
| ~ ne(X2)
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f1103]) ).
fof(f1105,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ne(X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X1,X2,X0),X3),ap(c_2Eoption_2ESOME(X2),X4)),ap(c_2Eoption_2ESOME(X0),X5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X2),ap(c_2Eoption_2ESOME(X2),X4))),ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X5)))),ap(c_2Eoption_2ESOME(X1),ap(ap(X3,ap(c_2Eoption_2ETHE(X2),ap(c_2Eoption_2ESOME(X2),X4))),ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5))))),c_2Eoption_2ENONE(X1))
| ~ mem(X5,X0)
| ~ mem(X3,arr(X2,arr(X0,X1)))
| ~ ne(X2)
| ~ ne(X0)
| ~ mem(X4,X2) ),
inference(duplicate_literal_removal,[],[f1102]) ).
fof(f1109,plain,
! [X2,X3,X0,X1] :
( ~ mem(X2,arr(X0,arr(X1,sK1)))
| ~ mem(X3,X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,X0,X1),X2),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X1),X3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))),ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X3)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(X2,ap(c_2Eoption_2ETHE(X0),c_2Eoption_2ENONE(X0))),ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X3))))),c_2Eoption_2ENONE(sK1))
| ~ ne(X0)
| ~ ne(X1) ),
inference(resolution,[],[f1104,f116]) ).
fof(f1136,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK2)
| ~ ne(sK3) ),
inference(resolution,[],[f1109,f119]) ).
fof(f1139,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK3) ),
inference(forward_subsumption_resolution,[],[f1136,f117]) ).
fof(f1142,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1)) ),
inference(forward_subsumption_resolution,[],[f1139,f118]) ).
fof(f1217,plain,
! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ ne(X1)
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(X1),X2)),X0) = X0
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(resolution,[],[f172,f155]) ).
fof(f1220,plain,
! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ ne(X1)
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(X1),X2)),X0) = X0
| ~ mem(X2,X1) ),
inference(duplicate_literal_removal,[],[f1217]) ).
fof(f1222,plain,
! [X0,X1] :
( ~ ne(X0)
| c_2Eoption_2ENONE(X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(X0),X1)),c_2Eoption_2ENONE(X0))
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(resolution,[],[f1220,f83]) ).
fof(f1223,plain,
! [X0,X1] :
( ~ ne(X0)
| c_2Eoption_2ENONE(X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(X0),X1)),c_2Eoption_2ENONE(X0))
| ~ mem(X1,X0) ),
inference(duplicate_literal_removal,[],[f1222]) ).
fof(f1228,plain,
! [X0] :
( ~ mem(X0,sK1)
| c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),X0)),c_2Eoption_2ENONE(sK1)) ),
inference(resolution,[],[f1223,f116]) ).
fof(f1309,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK6))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f412,f1228]) ).
fof(f1608,plain,
! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ ne(X1)
| ap(c_2Eoption_2ESOME(X1),X2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(X1),X2)),X0)
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(resolution,[],[f173,f155]) ).
fof(f1612,plain,
! [X2,X0,X1] :
( ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ ne(X1)
| ap(c_2Eoption_2ESOME(X1),X2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X1)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(X1),X2)),X0)
| ~ mem(X2,X1) ),
inference(duplicate_literal_removal,[],[f1608]) ).
fof(f1616,plain,
! [X0,X1] :
( ~ ne(X0)
| ap(c_2Eoption_2ESOME(X0),X1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(X0),X1)),c_2Eoption_2ENONE(X0))
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(resolution,[],[f1612,f83]) ).
fof(f1617,plain,
! [X0,X1] :
( ~ ne(X0)
| ap(c_2Eoption_2ESOME(X0),X1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(X0),X1)),c_2Eoption_2ENONE(X0))
| ~ mem(X1,X0) ),
inference(duplicate_literal_removal,[],[f1616]) ).
fof(f1623,plain,
! [X0] :
( ~ mem(X0,sK1)
| ap(c_2Eoption_2ESOME(sK1),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(sK1),X0)),c_2Eoption_2ENONE(sK1)) ),
inference(resolution,[],[f1617,f116]) ).
fof(f1634,plain,
ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f1623,f413]) ).
fof(f1905,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(superposition,[],[f331,f332]) ).
fof(f2389,plain,
! [X2,X3,X0,X1,X4] :
( ~ mem(X2,arr(X0,arr(X1,sK1)))
| ~ mem(X4,X1)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,X0,X1),X2),ap(c_2Eoption_2ESOME(X0),X3)),ap(c_2Eoption_2ESOME(X1),X4)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X3))),ap(c_2Eoption_2EIS__SOME(X1),ap(c_2Eoption_2ESOME(X1),X4)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(X2,ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X3))),ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X4))))),c_2Eoption_2ENONE(sK1))
| ~ ne(X0)
| ~ ne(X1)
| ~ mem(X3,X0) ),
inference(resolution,[],[f1105,f116]) ).
fof(f2409,plain,
! [X0,X1] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X1)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK2)
| ~ ne(sK3)
| ~ mem(X1,sK2) ),
inference(resolution,[],[f2389,f119]) ).
fof(f2412,plain,
! [X0,X1] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X1)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ ne(sK3)
| ~ mem(X1,sK2) ),
inference(forward_subsumption_resolution,[],[f2409,f117]) ).
fof(f2415,plain,
! [X0,X1] :
( ~ mem(X1,sK2)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),X1)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),X1))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f2412,f118]) ).
fof(f2417,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK3) ),
inference(resolution,[],[f2415,f120]) ).
fof(f2418,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK3) ),
inference(forward_demodulation,[],[f2417,f176]) ).
fof(f2420,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1)) ),
inference(forward_demodulation,[],[f2418,f603]) ).
fof(f2424,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),sK6))))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f2420,f121]) ).
fof(f2425,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f2424,f177]) ).
fof(f2427,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET)),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f2425,f611]) ).
fof(f2429,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f2427,f1034]) ).
fof(f2431,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),sK6)),
inference(forward_demodulation,[],[f2429,f1634]) ).
fof(f3623,plain,
! [X0,X1] :
( ~ mem(X0,bool)
| ~ mem(X1,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f1095,f89]) ).
fof(f3624,plain,
! [X0,X1] :
( ~ mem(X0,bool)
| ~ mem(X1,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1)
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f1095,f88]) ).
fof(f3635,plain,
! [X0,X1] :
( ~ mem(X1,bool)
| ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1)
| p(X1) ),
inference(duplicate_literal_removal,[],[f3624]) ).
fof(f3636,plain,
! [X0,X1] :
( ~ mem(X1,bool)
| ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1)
| p(X0) ),
inference(duplicate_literal_removal,[],[f3623]) ).
fof(f3657,plain,
! [X0] :
( ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF)
| p(c_2Ebool_2EF) ),
inference(resolution,[],[f3635,f78]) ).
fof(f3659,plain,
! [X0] :
( ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF) ),
inference(forward_subsumption_resolution,[],[f3657,f79]) ).
fof(f3680,plain,
! [X0] :
( ~ mem(X0,bool)
| c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2ET)
| p(X0) ),
inference(resolution,[],[f3636,f80]) ).
fof(f3701,plain,
( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)
| p(c_2Ebool_2EF) ),
inference(resolution,[],[f3680,f78]) ).
fof(f3703,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),
inference(forward_subsumption_resolution,[],[f3701,f79]) ).
fof(f3723,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),
inference(resolution,[],[f3659,f78]) ).
fof(f3724,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),
inference(resolution,[],[f3659,f80]) ).
fof(f3769,plain,
! [X0] :
( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(bool),c_2Eoption_2ENONE(bool))),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1))
| ~ mem(X0,sK3) ),
inference(forward_demodulation,[],[f1142,f260]) ).
fof(f3821,plain,
! [X0] :
( ~ mem(X0,sK3)
| ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),X0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),X0)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),X0))))),c_2Eoption_2ENONE(sK1)) ),
inference(forward_demodulation,[],[f3769,f332]) ).
fof(f3865,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f1905,f3723]) ).
fof(f3914,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f812,f1228]) ).
fof(f4236,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),ap(c_2Eoption_2ESOME(sK3),sK6))))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f3821,f121]) ).
fof(f4237,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),ap(c_2Eoption_2EIS__SOME(sK3),ap(c_2Eoption_2ESOME(sK3),sK6)))),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f4236,f177]) ).
fof(f4648,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f4237,f611]) ).
fof(f4669,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK6))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f4648,f3703]) ).
fof(f4677,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),ap(c_2Eoption_2ESOME(sK3),sK6)),
inference(forward_demodulation,[],[f4669,f1309]) ).
fof(f5181,plain,
( $false
| spl8_4 ),
inference(forward_subsumption_resolution,[],[f144,f2431]) ).
fof(f5182,plain,
spl8_4,
inference(avatar_contradiction_clause,[],[f5181]) ).
fof(f5184,plain,
( $false
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f138,f4677]) ).
fof(f5185,plain,
spl8_2,
inference(avatar_contradiction_clause,[],[f5184]) ).
fof(f5267,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,sK5),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(forward_demodulation,[],[f867,f3724]) ).
fof(f5272,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),ap(c_2Eoption_2ESOME(sK2),sK5)),c_2Eoption_2ENONE(sK3)),
inference(forward_demodulation,[],[f5267,f3914]) ).
fof(f5527,plain,
( $false
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f141,f5272]) ).
fof(f5528,plain,
spl8_3,
inference(avatar_contradiction_clause,[],[f5527]) ).
fof(f6133,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK1)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK1),ap(ap(sK4,ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),ap(c_2Eoption_2ETHE(sK3),c_2Eoption_2ENONE(sK3))))),c_2Eoption_2ENONE(sK1)),
inference(resolution,[],[f811,f1228]) ).
fof(f10202,plain,
c_2Eoption_2ENONE(sK1) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK1,sK2,sK3),sK4),c_2Eoption_2ENONE(sK2)),c_2Eoption_2ENONE(sK3)),
inference(superposition,[],[f6133,f3865]) ).
fof(f10206,plain,
( $false
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f10202,f135]) ).
fof(f10207,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f10206]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4 ),
inference(sat_conversion,[],[f145]) ).
cnf(s174,plain,
spl8_4,
inference(sat_conversion,[],[f5182]) ).
cnf(s175,plain,
spl8_2,
inference(sat_conversion,[],[f5185]) ).
cnf(s200,plain,
spl8_3,
inference(sat_conversion,[],[f5528]) ).
cnf(s397,plain,
spl8_1,
inference(sat_conversion,[],[f10207]) ).
cnf(s444,plain,
$false,
inference(rat,[],[s1,s174,s200,s175,s397]) ).
fof(f10208,plain,
$false,
inference(avatar_sat_refutation,[],[s444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP002+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 : n011.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 11:47:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 12.77/2.75 % (2257145)Detected formulas, will run a generic FOF schedule.
% 12.77/2.75 % (2257195)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=515271230:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.77/2.75 % (2257194)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1606845458:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.77/2.75 % (2257190)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=1147459656:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.77/2.75 % (2257196)dis-21_1_sil=8000:lcm=predicate:random_seed=2502068365: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)
% 12.77/2.75 % (2257192)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=2823407676:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.77/2.75 % (2257191)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=1807558164:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.77/2.75 % (2257193)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3639753914:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.77/2.75 % (2257193)Refutation not found, incomplete strategy
% 12.77/2.75 % (2257193)------------------------------
% 12.77/2.75 % (2257193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.77/2.75 % (2257193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.77/2.75 % (2257193)CaDiCaL version: 2.1.3
% 12.77/2.75 % (2257193)Termination reason: Refutation not found, incomplete strategy
% 12.77/2.75 % (2257193)Time elapsed: 0.003 s
% 12.77/2.75 % (2257193)Peak memory usage: 88 MB
% 12.77/2.75 % (2257193)Instructions burned: 3 (million)
% 12.77/2.75 % (2257195)Instruction limit reached!
% 12.77/2.75 % (2257195)------------------------------
% 12.77/2.75 % (2257195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.77/2.75 % (2257195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.77/2.75 % (2257195)CaDiCaL version: 2.1.3
% 12.77/2.75 % (2257195)Termination reason: Instruction limit
% 12.77/2.75 % (2257195)Termination phase: Saturation
% 12.77/2.75 % (2257195)Time elapsed: 0.053 s
% 12.77/2.75 % (2257195)Peak memory usage: 90 MB
% 12.77/2.75 % (2257195)Instructions burned: 139 (million)
% 12.77/2.75 % (2257194)Instruction limit reached!
% 12.77/2.75 % (2257194)------------------------------
% 12.77/2.75 % (2257194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.77/2.75 % (2257194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.77/2.75 % (2257194)CaDiCaL version: 2.1.3
% 12.77/2.75 % (2257194)Termination reason: Instruction limit
% 12.77/2.75 % (2257194)Termination phase: Saturation
% 12.77/2.75 % (2257194)Time elapsed: 0.069 s
% 12.77/2.75 % (2257194)Peak memory usage: 88 MB
% 12.77/2.75 % (2257194)Instructions burned: 119 (million)
% 12.77/2.75 % (2257196)Instruction limit reached!
% 12.77/2.75 % (2257196)------------------------------
% 12.77/2.75 % (2257196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.77/2.75 % (2257196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.77/2.75 % (2257196)CaDiCaL version: 2.1.3
% 12.77/2.75 % (2257196)Termination reason: Instruction limit
% 12.77/2.75 % (2257196)Termination phase: Saturation
% 12.77/2.75 % (2257196)Time elapsed: 0.071 s
% 12.77/2.75 % (2257196)Peak memory usage: 90 MB
% 12.77/2.75 % (2257196)Instructions burned: 130 (million)
% 12.77/2.75 % (2257204)lrs+10_1_sil=8000:sp=occurrence:random_seed=2006753839:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.77/2.75 % (2257206)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1582793019:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.77/2.75 % (2257205)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3316445636:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.77/2.75 % (2257204)Instruction limit reached!
% 12.77/2.75 % (2257204)------------------------------
% 12.77/2.75 % (2257204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.77/2.75 % (2257204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257204)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257204)Termination reason: Instruction limit
% 14.48/3.22 % (2257204)Termination phase: Saturation
% 14.48/3.22 % (2257204)Time elapsed: 0.096 s
% 14.48/3.22 % (2257204)Peak memory usage: 93 MB
% 14.48/3.22 % (2257204)Instructions burned: 286 (million)
% 14.48/3.22 % (2257193)------------------------------
% 14.48/3.22 % (2257193)------------------------------
% 14.48/3.22 % (2257205)Instruction limit reached!
% 14.48/3.22 % (2257205)------------------------------
% 14.48/3.22 % (2257205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257205)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257205)Termination reason: Instruction limit
% 14.48/3.22 % (2257205)Termination phase: Saturation
% 14.48/3.22 % (2257205)Time elapsed: 0.071 s
% 14.48/3.22 % (2257205)Peak memory usage: 92 MB
% 14.48/3.22 % (2257205)Instructions burned: 157 (million)
% 14.48/3.22 % (2257210)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=1143574253:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 14.48/3.22 % (2257211)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2426564743:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 14.48/3.22 % (2257211)Refutation not found, incomplete strategy
% 14.48/3.22 % (2257211)------------------------------
% 14.48/3.22 % (2257211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257211)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257211)Termination reason: Refutation not found, incomplete strategy
% 14.48/3.22 % (2257211)Time elapsed: 0.004 s
% 14.48/3.22 % (2257211)Peak memory usage: 88 MB
% 14.48/3.22 % (2257211)Instructions burned: 4 (million)
% 14.48/3.22 % (2257206)Instruction limit reached!
% 14.48/3.22 % (2257206)------------------------------
% 14.48/3.22 % (2257206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257206)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257206)Termination reason: Instruction limit
% 14.48/3.22 % (2257206)Termination phase: Saturation
% 14.48/3.22 % (2257206)Time elapsed: 0.210 s
% 14.48/3.22 % (2257206)Peak memory usage: 91 MB
% 14.48/3.22 % (2257206)Instructions burned: 325 (million)
% 14.48/3.22 % (2257210)Instruction limit reached!
% 14.48/3.22 % (2257210)------------------------------
% 14.48/3.22 % (2257210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257210)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257210)Termination reason: Instruction limit
% 14.48/3.22 % (2257210)Termination phase: Saturation
% 14.48/3.22 % (2257210)Time elapsed: 0.072 s
% 14.48/3.22 % (2257210)Peak memory usage: 95 MB
% 14.48/3.22 % (2257210)Instructions burned: 252 (million)
% 14.48/3.22 % (2257212)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2834965129:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 14.48/3.22 % (2257217)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=157852491:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 14.48/3.22 % (2257215)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=333974035:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 14.48/3.22 % (2257217)Instruction limit reached!
% 14.48/3.22 % (2257217)------------------------------
% 14.48/3.22 % (2257217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257217)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257217)Termination reason: Instruction limit
% 14.48/3.22 % (2257217)Termination phase: Saturation
% 14.48/3.22 % (2257217)Time elapsed: 0.034 s
% 14.48/3.22 % (2257217)Peak memory usage: 89 MB
% 14.48/3.22 % (2257217)Instructions burned: 127 (million)
% 14.48/3.22 % (2257215)Instruction limit reached!
% 14.48/3.22 % (2257215)------------------------------
% 14.48/3.22 % (2257215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257215)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257215)Termination reason: Instruction limit
% 14.48/3.22 % (2257215)Termination phase: Saturation
% 14.48/3.22 % (2257215)Time elapsed: 0.074 s
% 14.48/3.22 % (2257215)Peak memory usage: 91 MB
% 14.48/3.22 % (2257215)Instructions burned: 113 (million)
% 14.48/3.22 % (2257211)------------------------------
% 14.48/3.22 % (2257211)------------------------------
% 14.48/3.22 % (2257220)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=581772465:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 14.48/3.22 % (2257220)Instruction limit reached!
% 14.48/3.22 % (2257220)------------------------------
% 14.48/3.22 % (2257220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257220)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257220)Termination reason: Instruction limit
% 14.48/3.22 % (2257220)Termination phase: Saturation
% 14.48/3.22 % (2257220)Time elapsed: 0.035 s
% 14.48/3.22 % (2257220)Peak memory usage: 89 MB
% 14.48/3.22 % (2257220)Instructions burned: 114 (million)
% 14.48/3.22 % (2257221)lrs+10_1_sil=8000:sp=occurrence:random_seed=452158667:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 14.48/3.22 % (2257222)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3152073150:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 14.48/3.22 % (2257222)Refutation not found, incomplete strategy
% 14.48/3.22 % (2257222)------------------------------
% 14.48/3.22 % (2257222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257222)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257222)Termination reason: Refutation not found, incomplete strategy
% 14.48/3.22 % (2257222)Time elapsed: 0.003 s
% 14.48/3.22 % (2257222)Peak memory usage: 88 MB
% 14.48/3.22 % (2257222)Instructions burned: 3 (million)
% 14.48/3.22 % (2257224)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2332058897:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 14.48/3.22 % (2257222)------------------------------
% 14.48/3.22 % (2257222)------------------------------
% 14.48/3.22 % (2257228)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1454874373:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 14.48/3.22 % (2257228)Instruction limit reached!
% 14.48/3.22 % (2257228)------------------------------
% 14.48/3.22 % (2257228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257228)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257228)Termination reason: Instruction limit
% 14.48/3.22 % (2257228)Termination phase: Saturation
% 14.48/3.22 % (2257228)Time elapsed: 0.068 s
% 14.48/3.22 % (2257228)Peak memory usage: 93 MB
% 14.48/3.22 % (2257228)Instructions burned: 134 (million)
% 14.48/3.22 % (2257221)Instruction limit reached!
% 14.48/3.22 % (2257221)------------------------------
% 14.48/3.22 % (2257221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257221)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257221)Termination reason: Instruction limit
% 14.48/3.22 % (2257221)Termination phase: Saturation
% 14.48/3.22 % (2257221)Time elapsed: 0.526 s
% 14.48/3.22 % (2257221)Peak memory usage: 101 MB
% 14.48/3.22 % (2257221)Instructions burned: 909 (million)
% 14.48/3.22 % (2257230)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3871248589:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 14.48/3.22 % (2257231)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4134952539:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 14.48/3.22 % (2257230)Instruction limit reached!
% 14.48/3.22 % (2257230)------------------------------
% 14.48/3.22 % (2257230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257230)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257230)Termination reason: Instruction limit
% 14.48/3.22 % (2257230)Termination phase: Saturation
% 14.48/3.22 % (2257230)Time elapsed: 0.284 s
% 14.48/3.22 % (2257230)Peak memory usage: 90 MB
% 14.48/3.22 % (2257230)Instructions burned: 593 (million)
% 14.48/3.22 % (2257234)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=197856657:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/125Mi)
% 14.48/3.22 % (2257191)First to succeed.
% 14.48/3.22 % (2257191)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2257145"
% 14.48/3.22 % (2257212)Instruction limit reached!
% 14.48/3.22 % (2257212)------------------------------
% 14.48/3.22 % (2257212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257212)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257212)Termination reason: Instruction limit
% 14.48/3.22 % (2257212)Termination phase: Saturation
% 14.48/3.22 % (2257212)Time elapsed: 1.520 s
% 14.48/3.22 % (2257212)Peak memory usage: 142 MB
% 14.48/3.22 % (2257212)Instructions burned: 2350 (million)
% 14.48/3.22 % (2257234)Instruction limit reached!
% 14.48/3.22 % (2257234)------------------------------
% 14.48/3.22 % (2257234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.48/3.22 % (2257234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.48/3.22 % (2257234)CaDiCaL version: 2.1.3
% 14.48/3.22 % (2257234)Termination reason: Instruction limit
% 14.48/3.22 % (2257234)Termination phase: Saturation
% 14.48/3.22 % (2257234)Time elapsed: 0.072 s
% 14.48/3.22 % (2257234)Peak memory usage: 91 MB
% 14.48/3.22 % (2257234)Instructions burned: 125 (million)
% 14.48/3.22 % (2257236)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3110125529:i=134:gtgl=5:slsql=off:gtg=exists_sym_2978 on theBenchmark for (2978ds/134Mi)
% 14.48/3.22 % (2257237)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1255630651:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2978 on theBenchmark for (2978ds/141Mi)
% 14.48/3.22 % (2257191)Refutation found. Thanks to Tanya!
% 14.48/3.22 % SZS status Theorem for theBenchmark
% 14.48/3.22 % SZS output start Proof for theBenchmark
% See solution above
% 17.39/3.42 % (2257191)------------------------------
% 17.39/3.42 % (2257191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.39/3.42 % (2257191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.39/3.42 % (2257191)CaDiCaL version: 2.1.3
% 17.39/3.42 % (2257191)Termination reason: Refutation
% 17.39/3.42 % (2257191)Time elapsed: 1.943 s
% 17.39/3.42 % (2257191)Peak memory usage: 145 MB
% 17.39/3.42 % (2257191)Instructions burned: 2956 (million)
% 17.39/3.42 % (2257191)------------------------------
% 17.39/3.42 % (2257191)------------------------------
% 17.39/3.42 % (2257145)Success in time 2.374 s
% 17.39/3.42 % Vampire exiting
%------------------------------------------------------------------------------