%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP009+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:27:55 AM UTC 2026
% Result : Theorem 5.40s 2.05s
% Output : Refutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 25
% Syntax : Number of formulae : 246 ( 39 unt; 15 def)
% Number of atoms : 1117 ( 48 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1541 ( 670 ~; 686 |; 99 &)
% ( 20 <=>; 64 =>; 0 <=; 2 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-4 aty)
% Number of variables : 309 ( 0 sgn 261 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ne(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bool_ne) ).
fof(f3,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ne(arr(X0,X1)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
fof(f17,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( ne(X3)
=> mem(c_2Equotient_2E_2D_2D_3E(X0,X1,X2,X3),arr(arr(X0,X2),arr(arr(X1,X3),arr(arr(X2,X1),arr(X0,X3))))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Equotient_2E_2D_2D_3E) ).
fof(f18,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> mem(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),arr(arr(X0,arr(X0,bool)),arr(arr(X1,arr(X1,bool)),arr(arr(X0,X1),arr(arr(X0,X1),bool))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Equotient_2E_3D_3D_3D_3E) ).
fof(f33,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,arr(X0,X1)))
=> ! [X3] :
( mem(X3,X0)
=> ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecombin_2EW__THM) ).
fof(f34,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,arr(X0,bool)))
=> ! [X3] :
( mem(X3,arr(X0,X1))
=> ! [X4] :
( mem(X4,arr(X1,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
=> ! [X5] :
( mem(X5,X0)
=> ! [X6] :
( mem(X6,X0)
=> ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ap(X3,X5) = ap(X3,X6) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Equotient_2EQUOTIENT__REL) ).
fof(f35,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( ne(X3)
=> ! [X4] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5] :
( mem(X5,arr(X0,X2))
=> ! [X6] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8] :
( mem(X8,arr(X1,X3))
=> ! [X9] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9))) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Equotient_2EFUN__QUOTIENT) ).
fof(f36,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> c_2Equotient_2Erespects(X0,X1) = c_2Ecombin_2EW(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Equotient_2Erespects__def) ).
fof(f37,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( ne(X3)
=> ! [X4] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5] :
( mem(X5,arr(X0,X2))
=> ! [X6] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8] :
( mem(X8,arr(X1,X3))
=> ! [X9] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> ! [X10] :
( mem(X10,arr(X0,X1))
=> ! [X11] :
( mem(X11,arr(X0,X1))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<=> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Equotient_2EFUN__REL__EQ__REL) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( ne(X3)
=> ! [X4] :
( mem(X4,arr(X0,arr(X0,bool)))
=> ! [X5] :
( mem(X5,arr(X0,X2))
=> ! [X6] :
( mem(X6,arr(X2,X0))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
=> ! [X7] :
( mem(X7,arr(X1,arr(X1,bool)))
=> ! [X8] :
( mem(X8,arr(X1,X3))
=> ! [X9] :
( mem(X9,arr(X3,X1))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
=> ! [X10] :
( mem(X10,arr(X0,X1))
=> ! [X11] :
( mem(X11,arr(X0,X1))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<=> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f42,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<~> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) )
& ne(X3) )
& ne(X2) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f43,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11))
<~> ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) ) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) )
& ne(X3) )
& ne(X2) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( c_2Equotient_2Erespects(X0,X1) = c_2Ecombin_2EW(X0,X1)
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ap(X3,X5) = ap(X3,X6) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p(ap(ap(X2,X5),X6))
<=> ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ap(X3,X5) = ap(X3,X6) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,arr(X0,X1))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| ~ mem(X9,arr(X3,X1)) )
| ~ mem(X8,arr(X1,X3)) )
| ~ mem(X7,arr(X1,arr(X1,bool))) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0)) )
| ~ mem(X5,arr(X0,X2)) )
| ~ mem(X4,arr(X0,arr(X0,bool))) )
| ~ ne(X3) )
| ~ ne(X2) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| ~ mem(X9,arr(X3,X1)) )
| ~ mem(X8,arr(X1,X3)) )
| ~ mem(X7,arr(X1,arr(X1,bool))) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0)) )
| ~ mem(X5,arr(X0,X2)) )
| ~ mem(X4,arr(X0,arr(X0,bool))) )
| ~ ne(X3) )
| ~ ne(X2) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f55]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( mem(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),arr(arr(X0,arr(X0,bool)),arr(arr(X1,arr(X1,bool)),arr(arr(X0,X1),arr(arr(X0,X1),bool)))))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( mem(c_2Equotient_2E_2D_2D_3E(X0,X1,X2,X3),arr(arr(X0,X2),arr(arr(X1,X3),arr(arr(X2,X1),arr(X0,X3)))))
| ~ ne(X3) )
| ~ ne(X2) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ne(arr(X0,X1))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) )
& ne(X3) )
& ne(X2) )
& ne(X1) )
& ne(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X10))
& p(ap(ap(c_2Equotient_2Erespects(arr(X0,X1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),X11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8),X11) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7),X10),X11)) )
& mem(X11,arr(X0,X1)) )
& mem(X10,arr(X0,X1)) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
& mem(X9,arr(X3,X1)) )
& mem(X8,arr(X1,X3)) )
& mem(X7,arr(X1,arr(X1,bool))) )
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
& mem(X6,arr(X2,X0)) )
& mem(X5,arr(X0,X2)) )
& mem(X4,arr(X0,arr(X0,bool))) )
& ne(X3) )
& ne(X2) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) )
& ( ( p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
& p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11) )
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) )
& mem(sK11,arr(sK0,sK1))
& mem(sK10,arr(sK0,sK1))
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,sK3),sK7),sK8),sK9))
& mem(sK9,arr(sK3,sK1))
& mem(sK8,arr(sK1,sK3))
& mem(sK7,arr(sK1,arr(sK1,bool)))
& p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK0,sK2),sK4),sK5),sK6))
& mem(sK6,arr(sK2,sK0))
& mem(sK5,arr(sK0,sK2))
& mem(sK4,arr(sK0,arr(sK0,bool)))
& ne(sK3)
& ne(sK2)
& ne(sK1)
& ne(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8),skolemize(X9,sK9),skolemize(X10,sK10),skolemize(X11,sK11)],[f77]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ( p(ap(ap(X2,X5),X6))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ap(X3,X5) != ap(X3,X6) )
& ( ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ap(X3,X5) = ap(X3,X6) )
| ~ p(ap(ap(X2,X5),X6)) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ( p(ap(ap(X2,X5),X6))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ap(X3,X5) != ap(X3,X6) )
& ( ( p(ap(ap(X2,X5),X5))
& p(ap(ap(X2,X6),X6))
& ap(X3,X5) = ap(X3,X6) )
| ~ p(ap(ap(X2,X5),X6)) ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ mem(X4,arr(X1,X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,arr(X0,bool))) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f79]) ).
fof(f99,plain,
ne(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f100,plain,
ne(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f101,plain,
ne(sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f102,plain,
ne(sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f103,plain,
mem(sK4,arr(sK0,arr(sK0,bool))),
inference(cnf_transformation,[],[f78]) ).
fof(f104,plain,
mem(sK5,arr(sK0,sK2)),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
mem(sK6,arr(sK2,sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK0,sK2),sK4),sK5),sK6)),
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
mem(sK7,arr(sK1,arr(sK1,bool))),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
mem(sK8,arr(sK1,sK3)),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
mem(sK9,arr(sK3,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f110,plain,
p(ap(ap(ap(c_2Equotient_2EQUOTIENT(sK1,sK3),sK7),sK8),sK9)),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
mem(sK10,arr(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
mem(sK11,arr(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f115,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f116,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X0,X1] :
( c_2Ecombin_2EW(X0,X1) = c_2Equotient_2Erespects(X0,X1)
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| ap(X3,X5) = ap(X3,X6)
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| p(ap(ap(X2,X6),X6))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ p(ap(ap(X2,X5),X6))
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| p(ap(ap(X2,X5),X5))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X3),X4))
| ~ p(ap(ap(X2,X5),X5))
| ~ p(ap(ap(X2,X6),X6))
| ap(X3,X5) != ap(X3,X6)
| ~ mem(X6,X0)
| ~ mem(X5,X0)
| p(ap(ap(X2,X5),X6))
| ~ mem(X4,arr(X1,X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( ~ ne(X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,arr(X0,X1)))
| ap(ap(c_2Ecombin_2EW(X0,X1),X2),X3) = ap(ap(X2,X3),X3)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X1,X3),X7),X8),X9))
| p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,X1),arr(X2,X3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),X4),X7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X2,X1,X0,X3),X6),X8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,X3,X2,X1),X5),X9)))
| ~ mem(X9,arr(X3,X1))
| ~ mem(X8,arr(X1,X3))
| ~ mem(X7,arr(X1,arr(X1,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X2),X4),X5),X6))
| ~ mem(X6,arr(X2,X0))
| ~ mem(X5,arr(X0,X2))
| ~ mem(X4,arr(X0,arr(X0,bool)))
| ~ ne(X3)
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f171,plain,
! [X0,X1] :
( mem(c_2Equotient_2E_3D_3D_3D_3E(X0,X1),arr(arr(X0,arr(X0,bool)),arr(arr(X1,arr(X1,bool)),arr(arr(X0,X1),arr(arr(X0,X1),bool)))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f181,plain,
ne(bool),
inference(cnf_transformation,[],[f1]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( mem(c_2Equotient_2E_2D_2D_3E(X0,X1,X2,X3),arr(arr(X0,X2),arr(arr(X1,X3),arr(arr(X2,X1),arr(X0,X3)))))
| ~ ne(X3)
| ~ ne(X2)
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f185,plain,
! [X0,X1] :
( ne(arr(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f202,definition,
( spl14_1
<=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f203,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11))
| spl14_1 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK11))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f206,definition,
( spl14_2
<=> ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f207,plain,
( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| spl14_2 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f209,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f113,f206,f202]) ).
fof(f211,definition,
( spl14_3
<=> p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f212,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| spl14_3 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f114,f211,f202]) ).
fof(f216,definition,
( spl14_4
<=> p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f217,plain,
( ~ p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| spl14_4 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( p(ap(ap(c_2Equotient_2Erespects(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,plain,
( spl14_1
| spl14_4 ),
inference(avatar_split_clause,[],[f115,f216,f202]) ).
fof(f220,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f116,f216,f211,f206,f202]) ).
fof(f223,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| ~ spl14_4 ),
inference(superposition,[],[f218,f117]) ).
fof(f224,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| ~ spl14_3 ),
inference(superposition,[],[f213,f117]) ).
fof(f225,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ~ ne(arr(sK0,sK1))
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f224,f181]) ).
fof(f226,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ ne(arr(sK0,sK1))
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f223,f181]) ).
fof(f228,definition,
( spl14_5
<=> ne(arr(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f229,plain,
( ne(arr(sK0,sK1))
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f230,plain,
( ~ ne(arr(sK0,sK1))
| spl14_5 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl14_6
<=> p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f233,plain,
( ~ p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| spl14_6 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( ~ spl14_5
| spl14_6
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f225,f211,f232,f228]) ).
fof(f237,definition,
( spl14_7
<=> p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
fof(f238,plain,
( ~ p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| spl14_7 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f239,plain,
( p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( ~ spl14_5
| spl14_7
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f226,f216,f237,f228]) ).
fof(f241,plain,
( ~ ne(sK1)
| ~ ne(sK0)
| spl14_5 ),
inference(resolution,[],[f230,f185]) ).
fof(f242,plain,
( ~ ne(sK0)
| spl14_5 ),
inference(forward_subsumption_resolution,[],[f241,f100]) ).
fof(f243,plain,
( $false
| spl14_5 ),
inference(forward_subsumption_resolution,[],[f242,f99]) ).
fof(f244,plain,
spl14_5,
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ mem(X2,arr(X1,arr(X1,bool)))
| ~ mem(X0,X1)
| ap(ap(c_2Ecombin_2EW(X1,bool),X2),X0) = ap(ap(X2,X0),X0)
| ~ ne(X1) ),
inference(resolution,[],[f122,f181]) ).
fof(f378,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ mem(sK9,arr(sK3,sK1))
| ~ mem(sK8,arr(sK1,sK3))
| ~ mem(sK7,arr(sK1,arr(sK1,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(sK3)
| ~ ne(X1)
| ~ ne(sK1)
| ~ ne(X0) ),
inference(resolution,[],[f131,f110]) ).
fof(f379,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ mem(sK8,arr(sK1,sK3))
| ~ mem(sK7,arr(sK1,arr(sK1,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(sK3)
| ~ ne(X1)
| ~ ne(sK1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f378,f109]) ).
fof(f381,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ mem(sK7,arr(sK1,arr(sK1,bool)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(sK3)
| ~ ne(X1)
| ~ ne(sK1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f379,f108]) ).
fof(f383,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(sK3)
| ~ ne(X1)
| ~ ne(sK1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f381,f107]) ).
fof(f385,plain,
! [X2,X3,X0,X1,X4] :
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(sK1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f383,f102]) ).
fof(f387,plain,
! [X2,X3,X0,X1,X4] :
( ~ p(ap(ap(ap(c_2Equotient_2EQUOTIENT(X0,X1),X2),X4),X3))
| p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(X0,sK1),arr(X1,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(X0,sK1),X2),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(X1,sK1,X0,sK3),X3),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(X0,sK3,X1,sK1),X4),sK9)))
| ~ mem(X3,arr(X1,X0))
| ~ mem(X4,arr(X0,X1))
| ~ mem(X2,arr(X0,arr(X0,bool)))
| ~ ne(X1)
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[],[f385,f100]) ).
fof(f407,plain,
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9)))
| ~ mem(sK6,arr(sK2,sK0))
| ~ mem(sK5,arr(sK0,sK2))
| ~ mem(sK4,arr(sK0,arr(sK0,bool)))
| ~ ne(sK2)
| ~ ne(sK0) ),
inference(resolution,[],[f387,f106]) ).
fof(f410,plain,
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9)))
| ~ mem(sK5,arr(sK0,sK2))
| ~ mem(sK4,arr(sK0,arr(sK0,bool)))
| ~ ne(sK2)
| ~ ne(sK0) ),
inference(forward_subsumption_resolution,[],[f407,f105]) ).
fof(f412,plain,
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9)))
| ~ mem(sK4,arr(sK0,arr(sK0,bool)))
| ~ ne(sK2)
| ~ ne(sK0) ),
inference(forward_subsumption_resolution,[],[f410,f104]) ).
fof(f414,plain,
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9)))
| ~ ne(sK2)
| ~ ne(sK0) ),
inference(forward_subsumption_resolution,[],[f412,f103]) ).
fof(f416,plain,
( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9)))
| ~ ne(sK0) ),
inference(forward_subsumption_resolution,[],[f414,f101]) ).
fof(f418,plain,
p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(sK0,sK1),arr(sK2,sK3)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8)),ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9))),
inference(forward_subsumption_resolution,[],[f416,f99]) ).
fof(f595,plain,
! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3))
| ~ ne(arr(sK0,sK1)) ),
inference(resolution,[],[f418,f118]) ).
fof(f596,plain,
! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3))
| ~ ne(arr(sK0,sK1)) ),
inference(resolution,[],[f418,f119]) ).
fof(f597,plain,
! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3))
| ~ ne(arr(sK0,sK1)) ),
inference(resolution,[],[f418,f120]) ).
fof(f598,plain,
! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3))
| ~ ne(arr(sK0,sK1)) ),
inference(resolution,[],[f418,f121]) ).
fof(f605,plain,
( ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3)) )
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f598,f229]) ).
fof(f606,plain,
( ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3)) )
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f597,f229]) ).
fof(f607,plain,
( ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3)) )
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f596,f229]) ).
fof(f608,plain,
( ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X1,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ ne(arr(sK2,sK3)) )
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f595,f229]) ).
fof(f610,definition,
( spl14_23
<=> ne(arr(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl14_23])],[avatar_definition]) ).
fof(f612,plain,
( ~ ne(arr(sK2,sK3))
| spl14_23 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f614,definition,
( spl14_24
<=> mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool))) ),
introduced(definition,[new_symbols(definition,[spl14_24])],[avatar_definition]) ).
fof(f615,plain,
( mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f616,plain,
( ~ mem(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))
| spl14_24 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f618,definition,
( spl14_25
<=> mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
fof(f620,plain,
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),arr(arr(sK0,sK1),arr(sK2,sK3)))
| spl14_25 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f622,definition,
( spl14_26
<=> mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl14_26])],[avatar_definition]) ).
fof(f624,plain,
( ~ mem(ap(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),sK9),arr(arr(sK2,sK3),arr(sK0,sK1)))
| spl14_26 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f640,definition,
( spl14_30
<=> ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1)) ) ),
introduced(definition,[new_symbols(definition,[spl14_30])],[avatar_definition]) ).
fof(f641,plain,
( ! [X0,X1] :
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1)) )
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f642,plain,
( ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_30
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f605,f228,f640,f622,f618,f614,f610]) ).
fof(f644,definition,
( spl14_31
<=> ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl14_31])],[avatar_definition]) ).
fof(f645,plain,
( ! [X0,X1] :
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) )
| ~ spl14_31 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f646,plain,
( ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_31
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f606,f228,f644,f622,f618,f614,f610]) ).
fof(f648,definition,
( spl14_32
<=> ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl14_32])],[avatar_definition]) ).
fof(f649,plain,
( ! [X0,X1] :
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X1),X1))
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) )
| ~ spl14_32 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f650,plain,
( ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_32
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f607,f228,f648,f622,f618,f614,f610]) ).
fof(f652,definition,
( spl14_33
<=> ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl14_33])],[avatar_definition]) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X0) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),X1)
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(X1,arr(sK0,sK1)) )
| ~ spl14_33 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f654,plain,
( ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_33
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f608,f228,f652,f622,f618,f614,f610]) ).
fof(f655,plain,
( ~ ne(sK3)
| ~ ne(sK2)
| spl14_23 ),
inference(resolution,[],[f612,f185]) ).
fof(f656,plain,
( ~ ne(sK2)
| spl14_23 ),
inference(forward_subsumption_resolution,[],[f655,f102]) ).
fof(f657,plain,
( $false
| spl14_23 ),
inference(forward_subsumption_resolution,[],[f656,f101]) ).
fof(f658,plain,
spl14_23,
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f864,plain,
( ! [X0] :
( ~ mem(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),arr(X0,arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool))))
| ~ mem(sK7,X0) )
| spl14_24 ),
inference(resolution,[],[f616,f187]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ mem(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),arr(X1,arr(X0,arr(arr(sK0,sK1),arr(arr(sK0,sK1),bool)))))
| ~ mem(sK4,X1)
| ~ mem(sK7,X0) )
| spl14_24 ),
inference(resolution,[],[f864,f187]) ).
fof(f982,plain,
( ~ mem(sK4,arr(sK0,arr(sK0,bool)))
| ~ mem(sK7,arr(sK1,arr(sK1,bool)))
| ~ ne(sK1)
| ~ ne(sK0)
| spl14_24 ),
inference(resolution,[],[f880,f171]) ).
fof(f983,plain,
( ~ mem(sK7,arr(sK1,arr(sK1,bool)))
| ~ ne(sK1)
| ~ ne(sK0)
| spl14_24 ),
inference(forward_subsumption_resolution,[],[f982,f103]) ).
fof(f984,plain,
( ~ ne(sK1)
| ~ ne(sK0)
| spl14_24 ),
inference(forward_subsumption_resolution,[],[f983,f107]) ).
fof(f985,plain,
( ~ ne(sK0)
| spl14_24 ),
inference(forward_subsumption_resolution,[],[f984,f100]) ).
fof(f986,plain,
( $false
| spl14_24 ),
inference(forward_subsumption_resolution,[],[f985,f99]) ).
fof(f987,plain,
spl14_24,
inference(avatar_contradiction_clause,[],[f986]) ).
fof(f991,plain,
( ! [X0] :
( ~ mem(X0,arr(sK0,sK1))
| ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0) = ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),X0)
| ~ ne(arr(sK0,sK1)) )
| ~ spl14_24 ),
inference(resolution,[],[f615,f309]) ).
fof(f996,plain,
( ! [X0] :
( ~ mem(X0,arr(sK0,sK1))
| ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),X0) = ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),X0) )
| ~ spl14_5
| ~ spl14_24 ),
inference(forward_subsumption_resolution,[],[f991,f229]) ).
fof(f1002,plain,
( ! [X0] :
( ~ mem(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),arr(X0,arr(arr(sK0,sK1),arr(sK2,sK3))))
| ~ mem(sK8,X0) )
| spl14_25 ),
inference(resolution,[],[f620,f187]) ).
fof(f1003,plain,
( ! [X0,X1] :
( ~ mem(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),arr(X1,arr(X0,arr(arr(sK0,sK1),arr(sK2,sK3)))))
| ~ mem(sK6,X1)
| ~ mem(sK8,X0) )
| spl14_25 ),
inference(resolution,[],[f1002,f187]) ).
fof(f1096,plain,
( ~ mem(sK6,arr(sK2,sK0))
| ~ mem(sK8,arr(sK1,sK3))
| ~ ne(sK3)
| ~ ne(sK0)
| ~ ne(sK1)
| ~ ne(sK2)
| spl14_25 ),
inference(resolution,[],[f1003,f184]) ).
fof(f1097,plain,
( ~ mem(sK8,arr(sK1,sK3))
| ~ ne(sK3)
| ~ ne(sK0)
| ~ ne(sK1)
| ~ ne(sK2)
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1096,f105]) ).
fof(f1098,plain,
( ~ ne(sK3)
| ~ ne(sK0)
| ~ ne(sK1)
| ~ ne(sK2)
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1097,f108]) ).
fof(f1099,plain,
( ~ ne(sK0)
| ~ ne(sK1)
| ~ ne(sK2)
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1098,f102]) ).
fof(f1100,plain,
( ~ ne(sK1)
| ~ ne(sK2)
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1099,f99]) ).
fof(f1101,plain,
( ~ ne(sK2)
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1100,f100]) ).
fof(f1102,plain,
( $false
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f1101,f101]) ).
fof(f1103,plain,
spl14_25,
inference(avatar_contradiction_clause,[],[f1102]) ).
fof(f1105,plain,
( ! [X0] :
( ~ mem(ap(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),sK5),arr(X0,arr(arr(sK2,sK3),arr(sK0,sK1))))
| ~ mem(sK9,X0) )
| spl14_26 ),
inference(resolution,[],[f624,f187]) ).
fof(f1106,plain,
( ! [X0,X1] :
( ~ mem(c_2Equotient_2E_2D_2D_3E(sK0,sK3,sK2,sK1),arr(X1,arr(X0,arr(arr(sK2,sK3),arr(sK0,sK1)))))
| ~ mem(sK5,X1)
| ~ mem(sK9,X0) )
| spl14_26 ),
inference(resolution,[],[f1105,f187]) ).
fof(f1140,plain,
( ~ mem(sK5,arr(sK0,sK2))
| ~ mem(sK9,arr(sK3,sK1))
| ~ ne(sK1)
| ~ ne(sK2)
| ~ ne(sK3)
| ~ ne(sK0)
| spl14_26 ),
inference(resolution,[],[f1106,f184]) ).
fof(f1141,plain,
( ~ mem(sK9,arr(sK3,sK1))
| ~ ne(sK1)
| ~ ne(sK2)
| ~ ne(sK3)
| ~ ne(sK0)
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1140,f104]) ).
fof(f1142,plain,
( ~ ne(sK1)
| ~ ne(sK2)
| ~ ne(sK3)
| ~ ne(sK0)
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1141,f109]) ).
fof(f1143,plain,
( ~ ne(sK2)
| ~ ne(sK3)
| ~ ne(sK0)
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1142,f100]) ).
fof(f1144,plain,
( ~ ne(sK3)
| ~ ne(sK0)
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1143,f101]) ).
fof(f1145,plain,
( ~ ne(sK0)
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1144,f102]) ).
fof(f1146,plain,
( $false
| spl14_26 ),
inference(forward_subsumption_resolution,[],[f1145,f99]) ).
fof(f1147,plain,
spl14_26,
inference(avatar_contradiction_clause,[],[f1146]) ).
fof(f1194,plain,
( ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10) = ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK10)
| ~ spl14_5
| ~ spl14_24 ),
inference(resolution,[],[f996,f111]) ).
fof(f1195,plain,
( ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11) = ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11)
| ~ spl14_5
| ~ spl14_24 ),
inference(resolution,[],[f996,f112]) ).
fof(f1206,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK10))
| ~ spl14_5
| ~ spl14_7
| ~ spl14_24 ),
inference(superposition,[],[f239,f1194]) ).
fof(f1212,plain,
( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| ~ spl14_5
| ~ spl14_6
| ~ spl14_24 ),
inference(superposition,[],[f234,f1195]) ).
fof(f1342,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK10))
| ~ mem(sK10,arr(sK0,sK1))
| ~ mem(sK11,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| spl14_1
| ~ spl14_30 ),
inference(resolution,[],[f641,f203]) ).
fof(f1344,plain,
( ~ mem(sK10,arr(sK0,sK1))
| ~ mem(sK11,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| spl14_1
| ~ spl14_5
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1342,f1206]) ).
fof(f1345,plain,
( ~ mem(sK11,arr(sK0,sK1))
| ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| spl14_1
| ~ spl14_5
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1344,f111]) ).
fof(f1346,plain,
( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) != ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| spl14_1
| ~ spl14_5
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1345,f112]) ).
fof(f1347,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1346,f208]) ).
fof(f1348,plain,
( $false
| spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_6
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1347,f1212]) ).
fof(f1349,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_6
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(avatar_contradiction_clause,[],[f1348]) ).
fof(f1350,plain,
( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK10) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(sK2,sK1,sK0,sK3),sK6),sK8),sK11)
| ~ mem(sK10,arr(sK0,sK1))
| ~ mem(sK11,arr(sK0,sK1))
| ~ spl14_1
| ~ spl14_33 ),
inference(resolution,[],[f204,f653]) ).
fof(f1351,plain,
( ~ p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK11))
| ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| spl14_3 ),
inference(superposition,[],[f212,f117]) ).
fof(f1352,plain,
( ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| spl14_3
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f1351,f234]) ).
fof(f1353,plain,
( ~ ne(arr(sK0,sK1))
| spl14_3
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f1352,f181]) ).
fof(f1354,plain,
( $false
| spl14_3
| ~ spl14_5
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f1353,f229]) ).
fof(f1355,plain,
( spl14_3
| ~ spl14_5
| ~ spl14_6 ),
inference(avatar_contradiction_clause,[],[f1354]) ).
fof(f1356,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK11),sK11))
| ~ spl14_5
| spl14_6
| ~ spl14_24 ),
inference(forward_demodulation,[],[f233,f1195]) ).
fof(f1360,plain,
( ! [X0] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),sK11))
| ~ mem(X0,arr(sK0,sK1))
| ~ mem(sK11,arr(sK0,sK1)) )
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(resolution,[],[f1356,f649]) ).
fof(f1366,plain,
( ! [X0] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),X0),sK11))
| ~ mem(X0,arr(sK0,sK1)) )
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(forward_subsumption_resolution,[],[f1360,f112]) ).
fof(f1380,plain,
( ~ mem(sK10,arr(sK0,sK1))
| ~ spl14_1
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(resolution,[],[f1366,f204]) ).
fof(f1384,plain,
( $false
| ~ spl14_1
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(forward_subsumption_resolution,[],[f1380,f111]) ).
fof(f1385,plain,
( ~ spl14_1
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(avatar_contradiction_clause,[],[f1384]) ).
fof(f1394,plain,
( ~ p(ap(ap(c_2Ecombin_2EW(arr(sK0,sK1),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7)),sK10))
| ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| spl14_4 ),
inference(superposition,[],[f217,f117]) ).
fof(f1395,plain,
( ~ ne(bool)
| ~ ne(arr(sK0,sK1))
| spl14_4
| ~ spl14_7 ),
inference(forward_subsumption_resolution,[],[f1394,f239]) ).
fof(f1396,plain,
( ~ ne(arr(sK0,sK1))
| spl14_4
| ~ spl14_7 ),
inference(forward_subsumption_resolution,[],[f1395,f181]) ).
fof(f1397,plain,
( $false
| spl14_4
| ~ spl14_5
| ~ spl14_7 ),
inference(forward_subsumption_resolution,[],[f1396,f229]) ).
fof(f1398,plain,
( spl14_4
| ~ spl14_5
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f1397]) ).
fof(f1399,plain,
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),sK10))
| ~ spl14_5
| spl14_7
| ~ spl14_24 ),
inference(forward_demodulation,[],[f238,f1194]) ).
fof(f1404,plain,
( ! [X0] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),X0))
| ~ mem(sK10,arr(sK0,sK1))
| ~ mem(X0,arr(sK0,sK1)) )
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(resolution,[],[f1399,f645]) ).
fof(f1408,plain,
( ! [X0] :
( ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(sK0,sK1),sK4),sK7),sK10),X0))
| ~ mem(X0,arr(sK0,sK1)) )
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(forward_subsumption_resolution,[],[f1404,f111]) ).
fof(f2091,plain,
( ~ mem(sK11,arr(sK0,sK1))
| ~ spl14_1
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(resolution,[],[f1408,f204]) ).
fof(f2098,plain,
( $false
| ~ spl14_1
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(forward_subsumption_resolution,[],[f2091,f112]) ).
fof(f2099,plain,
( ~ spl14_1
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(avatar_contradiction_clause,[],[f2098]) ).
fof(f2102,plain,
( ~ mem(sK10,arr(sK0,sK1))
| ~ mem(sK11,arr(sK0,sK1))
| ~ spl14_1
| spl14_2
| ~ spl14_33 ),
inference(forward_subsumption_resolution,[],[f1350,f207]) ).
fof(f2103,plain,
( ~ mem(sK11,arr(sK0,sK1))
| ~ spl14_1
| spl14_2
| ~ spl14_33 ),
inference(forward_subsumption_resolution,[],[f2102,f111]) ).
fof(f2104,plain,
( $false
| ~ spl14_1
| spl14_2
| ~ spl14_33 ),
inference(forward_subsumption_resolution,[],[f2103,f112]) ).
fof(f2105,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_33 ),
inference(avatar_contradiction_clause,[],[f2104]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f209]) ).
cnf(s2,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f214]) ).
cnf(s3,plain,
( spl14_1
| spl14_4 ),
inference(sat_conversion,[],[f219]) ).
cnf(s4,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f220]) ).
cnf(s5,plain,
( ~ spl14_3
| ~ spl14_5
| spl14_6 ),
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
( ~ spl14_4
| ~ spl14_5
| spl14_7 ),
inference(sat_conversion,[],[f240]) ).
cnf(s7,plain,
spl14_5,
inference(sat_conversion,[],[f244]) ).
cnf(s23,plain,
( ~ spl14_5
| ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_30 ),
inference(sat_conversion,[],[f642]) ).
cnf(s24,plain,
( ~ spl14_5
| ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_31 ),
inference(sat_conversion,[],[f646]) ).
cnf(s25,plain,
( ~ spl14_5
| ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_32 ),
inference(sat_conversion,[],[f650]) ).
cnf(s26,plain,
( ~ spl14_5
| ~ spl14_23
| ~ spl14_24
| ~ spl14_25
| ~ spl14_26
| spl14_33 ),
inference(sat_conversion,[],[f654]) ).
cnf(s27,plain,
spl14_23,
inference(sat_conversion,[],[f658]) ).
cnf(s54,plain,
spl14_24,
inference(sat_conversion,[],[f987]) ).
cnf(s58,plain,
spl14_25,
inference(sat_conversion,[],[f1103]) ).
cnf(s61,plain,
spl14_26,
inference(sat_conversion,[],[f1147]) ).
cnf(s65,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_6
| ~ spl14_7
| ~ spl14_24
| ~ spl14_30 ),
inference(sat_conversion,[],[f1349]) ).
cnf(s66,plain,
( spl14_3
| ~ spl14_5
| ~ spl14_6 ),
inference(sat_conversion,[],[f1355]) ).
cnf(s67,plain,
( ~ spl14_1
| ~ spl14_5
| spl14_6
| ~ spl14_24
| ~ spl14_32 ),
inference(sat_conversion,[],[f1385]) ).
cnf(s68,plain,
( spl14_4
| ~ spl14_5
| ~ spl14_7 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s144,plain,
( ~ spl14_1
| ~ spl14_5
| spl14_7
| ~ spl14_24
| ~ spl14_31 ),
inference(sat_conversion,[],[f2099]) ).
cnf(s145,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_33 ),
inference(sat_conversion,[],[f2105]) ).
cnf(s170,plain,
( ~ spl14_5
| spl14_33 ),
inference(rat,[],[s26,s61,s58,s54,s27]) ).
cnf(s171,plain,
( ~ spl14_5
| spl14_32 ),
inference(rat,[],[s25,s61,s58,s54,s27]) ).
cnf(s172,plain,
( ~ spl14_5
| spl14_31 ),
inference(rat,[],[s24,s61,s58,s54,s27]) ).
cnf(s173,plain,
( ~ spl14_5
| spl14_30 ),
inference(rat,[],[s23,s61,s58,s54,s27]) ).
cnf(s190,plain,
spl14_33,
inference(rat,[],[s170,s7]) ).
cnf(s191,plain,
spl14_32,
inference(rat,[],[s171,s7]) ).
cnf(s192,plain,
spl14_31,
inference(rat,[],[s172,s7]) ).
cnf(s193,plain,
spl14_30,
inference(rat,[],[s173,s7]) ).
cnf(s197,plain,
( ~ spl14_4
| spl14_7 ),
inference(rat,[],[s6,s7]) ).
cnf(s198,plain,
( ~ spl14_3
| spl14_6 ),
inference(rat,[],[s5,s7]) ).
cnf(s199,plain,
spl14_1,
inference(rat,[],[s65,s198,s197,s1,s2,s3,s7,s54,s193]) ).
cnf(s200,plain,
spl14_2,
inference(rat,[],[s145,s190,s199]) ).
cnf(s201,plain,
spl14_7,
inference(rat,[],[s144,s192,s54,s7,s199]) ).
cnf(s202,plain,
spl14_6,
inference(rat,[],[s67,s191,s54,s7,s199]) ).
cnf(s203,plain,
spl14_4,
inference(rat,[],[s68,s7,s201]) ).
cnf(s204,plain,
spl14_3,
inference(rat,[],[s66,s7,s202]) ).
cnf(s205,plain,
$false,
inference(rat,[],[s4,s200,s199,s203,s204]) ).
fof(f2106,plain,
$false,
inference(avatar_sat_refutation,[],[s205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP009+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 11:57:09 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.40/2.05 % (2206396)Detected formulas, will run a generic FOF schedule.
% 5.40/2.05 % (2206417)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1761935857:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.40/2.05 % (2206418)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1842865320:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.40/2.05 % (2206417)Instruction limit reached!
% 5.40/2.05 % (2206417)------------------------------
% 5.40/2.05 % (2206417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206417)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206417)Termination reason: Instruction limit
% 5.40/2.05 % (2206417)Termination phase: Saturation
% 5.40/2.05 % (2206417)Time elapsed: 0.057 s
% 5.40/2.05 % (2206417)Peak memory usage: 88 MB
% 5.40/2.05 % (2206417)Instructions burned: 121 (million)
% 5.40/2.05 % (2206413)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=3326172905:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.40/2.05 % (2206414)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=3159600316:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.40/2.05 % (2206416)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2187045154:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.40/2.05 % (2206415)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=151227087:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.40/2.05 % (2206419)dis-21_1_sil=8000:lcm=predicate:random_seed=728774479: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)
% 5.40/2.05 % (2206418)Instruction limit reached!
% 5.40/2.05 % (2206418)------------------------------
% 5.40/2.05 % (2206418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206418)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206418)Termination reason: Instruction limit
% 5.40/2.05 % (2206418)Termination phase: Saturation
% 5.40/2.05 % (2206418)Time elapsed: 0.149 s
% 5.40/2.05 % (2206418)Peak memory usage: 90 MB
% 5.40/2.05 % (2206418)Instructions burned: 139 (million)
% 5.40/2.05 % (2206416)Instruction limit reached!
% 5.40/2.05 % (2206416)------------------------------
% 5.40/2.05 % (2206416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206416)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206416)Termination reason: Instruction limit
% 5.40/2.05 % (2206416)Termination phase: Saturation
% 5.40/2.05 % (2206416)Time elapsed: 0.103 s
% 5.40/2.05 % (2206416)Peak memory usage: 90 MB
% 5.40/2.05 % (2206416)Instructions burned: 110 (million)
% 5.40/2.05 % (2206426)lrs+10_1_sil=8000:sp=occurrence:random_seed=4078192846:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.40/2.05 % (2206419)Instruction limit reached!
% 5.40/2.05 % (2206419)------------------------------
% 5.40/2.05 % (2206419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206419)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206419)Termination reason: Instruction limit
% 5.40/2.05 % (2206419)Termination phase: Saturation
% 5.40/2.05 % (2206419)Time elapsed: 0.127 s
% 5.40/2.05 % (2206419)Peak memory usage: 90 MB
% 5.40/2.05 % (2206419)Instructions burned: 130 (million)
% 5.40/2.05 % (2206430)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2909611472:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.40/2.05 % (2206430)Instruction limit reached!
% 5.40/2.05 % (2206430)------------------------------
% 5.40/2.05 % (2206430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206430)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206430)Termination reason: Instruction limit
% 5.40/2.05 % (2206430)Termination phase: Saturation
% 5.40/2.05 % (2206430)Time elapsed: 0.077 s
% 5.40/2.05 % (2206430)Peak memory usage: 97 MB
% 5.40/2.05 % (2206430)Instructions burned: 158 (million)
% 5.40/2.05 % (2206431)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3383544368:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.40/2.05 % (2206426)Instruction limit reached!
% 5.40/2.05 % (2206426)------------------------------
% 5.40/2.05 % (2206426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206426)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206426)Termination reason: Instruction limit
% 5.40/2.05 % (2206426)Termination phase: Saturation
% 5.40/2.05 % (2206426)Time elapsed: 0.224 s
% 5.40/2.05 % (2206426)Peak memory usage: 92 MB
% 5.40/2.05 % (2206426)Instructions burned: 285 (million)
% 5.40/2.05 % (2206433)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=1830257624:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.40/2.05 % (2206435)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4072448417:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.40/2.05 % (2206431)First to succeed.
% 5.40/2.05 % (2206431)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2206396"
% 5.40/2.05 % (2206435)Instruction limit reached!
% 5.40/2.05 % (2206435)------------------------------
% 5.40/2.05 % (2206435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206435)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206435)Termination reason: Instruction limit
% 5.40/2.05 % (2206435)Termination phase: Saturation
% 5.40/2.05 % (2206435)Time elapsed: 0.113 s
% 5.40/2.05 % (2206435)Peak memory usage: 88 MB
% 5.40/2.05 % (2206435)Instructions burned: 295 (million)
% 5.40/2.05 % (2206433)Instruction limit reached!
% 5.40/2.05 % (2206433)------------------------------
% 5.40/2.05 % (2206433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.40/2.05 % (2206433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.40/2.05 % (2206433)CaDiCaL version: 2.1.3
% 5.40/2.05 % (2206433)Termination reason: Instruction limit
% 5.40/2.05 % (2206433)Termination phase: Saturation
% 5.40/2.05 % (2206433)Time elapsed: 0.216 s
% 5.40/2.05 % (2206433)Peak memory usage: 98 MB
% 5.40/2.05 % (2206433)Instructions burned: 252 (million)
% 5.40/2.05 % (2206438)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=798143887:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.40/2.05 % (2206444)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1395423947:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 5.40/2.05 % (2206441)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1775737904:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 5.40/2.05 % (2206431)Refutation found. Thanks to Tanya!
% 5.40/2.05 % SZS status Theorem for theBenchmark
% 5.40/2.05 % SZS output start Proof for theBenchmark
% See solution above
% 8.05/2.24 % (2206431)------------------------------
% 8.05/2.24 % (2206431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.05/2.24 % (2206431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.05/2.24 % (2206431)CaDiCaL version: 2.1.3
% 8.05/2.24 % (2206431)Termination reason: Refutation
% 8.05/2.24 % (2206431)Time elapsed: 0.212 s
% 8.05/2.24 % (2206431)Peak memory usage: 92 MB
% 8.05/2.24 % (2206431)Instructions burned: 197 (million)
% 8.05/2.24 % (2206431)------------------------------
% 8.05/2.24 % (2206431)------------------------------
% 8.05/2.24 % (2206396)Success in time 1.043 s
% 8.05/2.24 % Vampire exiting
%------------------------------------------------------------------------------