%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT117+1 : TPTP v9.3.1. Released v5.2.0.
% 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 12:36:57 PM UTC 2026
% Result : Theorem 2.84s 1.35s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 45
% Syntax : Number of formulae : 282 ( 25 unt; 43 def)
% Number of atoms : 1190 ( 368 equ)
% Maximal formula atoms : 53 ( 4 avg)
% Number of connectives : 1503 ( 595 ~; 573 |; 269 &)
% ( 27 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 29 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 205 ( 0 sgn 176 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f527,axiom,
( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
=> ! [X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f528,conjecture,
( ! [X0,X1] :
( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
=> ! [X2] :
( ( ( X1 = v_x
& X2 = v_y )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) )
& ( ( X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) ) ) )
& ( ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
=> ! [X2] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
& ( ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
=> ! [X2] :
( ( X1 = v_x
=> X2 != v_y )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X2),v_L) )
& ( X2 = v_y
=> ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) ) ) ) )
& ! [X0,X1] :
( X0 != X1
=> ( ( X0 = v_x
& X1 = v_y )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
| ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
| ( X1 = v_x
& X0 = v_y )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X1 != v_y
& X0 != v_y )
| ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& X1 != v_y )
| ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
& X0 != v_y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f529,negated_conjecture,
~ ( ! [X0,X1] :
( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
=> ! [X2] :
( ( ( X1 = v_x
& X2 = v_y )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) )
& ( ( X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) ) ) )
& ( ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
=> ! [X2] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
& ( ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
=> ! [X2] :
( ( X1 = v_x
=> X2 != v_y )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X2),v_L) )
& ( X2 = v_y
=> ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) ) ) ) )
& ! [X0,X1] :
( X0 != X1
=> ( ( X0 = v_x
& X1 = v_y )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
| ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
| ( X1 = v_x
& X0 = v_y )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X1 != v_y
& X0 != v_y )
| ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& X1 != v_y )
| ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
& X0 != v_y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f528]) ).
fof(f530,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
=> ! [X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( X4 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L) ) ) ),
inference(rectify,[],[f527]) ).
fof(f531,plain,
~ ( ! [X0,X1] :
( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
=> ! [X2] :
( ( ( X1 = v_x
& X2 = v_y )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) )
& ( ( X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) )
=> ( X0 = v_x
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L) ) ) ) )
& ( ( X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
=> ! [X3] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X3),v_L)
& v_y != X3 )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X3),v_L) ) )
& ( ( X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
=> ! [X4] :
( ( X1 = v_x
=> v_y != X4 )
& ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X4),v_L)
& v_y != X4 )
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X4),v_L) )
& ( v_y = X4
=> ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) ) ) ) )
& ! [X5,X6] :
( X5 != X6
=> ( ( v_x = X5
& v_y = X6 )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X6),v_L)
& v_y != X5
& v_y != X6 )
| ( v_y = X6
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,v_x),v_L)
& v_y != X5 )
| ( v_y = X5
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X6),v_L)
& v_y != X6 )
| ( v_x = X6
& v_y = X5 )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,X5),v_L)
& v_y != X6
& v_y != X5 )
| ( v_y = X5
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,v_x),v_L)
& v_y != X6 )
| ( v_y = X6
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X5),v_L)
& v_y != X5 ) ) ) ),
inference(rectify,[],[f529]) ).
fof(f532,plain,
( ! [X0,X1] :
( ! [X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L) )
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| X4 = X5 ) ),
inference(ennf_transformation,[],[f530]) ).
fof(f533,plain,
( ! [X0,X1] :
( ! [X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L) )
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| X4 = X5 ) ),
inference(flattening,[],[f532]) ).
fof(f534,plain,
( ? [X0,X1] :
( ( ? [X2] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X1 = v_x
& X2 = v_y )
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
| ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) ) )
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
| ( ? [X3] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X3),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X3),v_L)
& v_y != X3 )
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ( ? [X4] :
( ( v_y = X4
& X1 = v_x )
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X4),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X4),v_L)
& v_y != X4 )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& v_y = X4 ) )
& X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y ) )
| ? [X5,X6] :
( ( v_x != X5
| v_y != X6 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X6),v_L)
| v_y = X5
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,v_x),v_L)
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X6),v_L)
| v_y = X6 )
& ( v_x != X6
| v_y != X5 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,X5),v_L)
| v_y = X6
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,v_x),v_L)
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X5),v_L)
| v_y = X5 )
& X5 != X6 ) ),
inference(ennf_transformation,[],[f531]) ).
fof(f535,plain,
( ? [X0,X1] :
( ( ? [X2] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X1 = v_x
& X2 = v_y )
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
| ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) ) )
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
| ( ? [X3] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X3),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X3),v_L)
& v_y != X3 )
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ( ? [X4] :
( ( v_y = X4
& X1 = v_x )
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X4),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X4),v_L)
& v_y != X4 )
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& v_y = X4 ) )
& X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y ) )
| ? [X5,X6] :
( ( v_x != X5
| v_y != X6 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X6),v_L)
| v_y = X5
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,v_x),v_L)
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X6),v_L)
| v_y = X6 )
& ( v_x != X6
| v_y != X5 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,X5),v_L)
| v_y = X6
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,v_x),v_L)
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X5),v_L)
| v_y = X5 )
& X5 != X6 ) ),
inference(flattening,[],[f534]) ).
fof(f543,definition,
! [X4,X1] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X4),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X4),v_L)
& v_y != X4 )
| ~ sP0(X4,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f544,definition,
! [X0,X2,X1] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) )
| ~ sP1(X0,X2,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f545,definition,
! [X0,X1,X2] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X1 = v_x
& X2 = v_y )
| ~ sP2(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f546,definition,
! [X1,X0] :
( ( ? [X4] :
( ( v_y = X4
& X1 = v_x )
| sP0(X4,X1)
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& v_y = X4 ) )
& X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f547,definition,
! [X0,X1] :
( ( ? [X3] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X3),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X3),v_L)
& v_y != X3 )
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ~ sP4(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f548,definition,
( ? [X5,X6] :
( ( v_x != X5
| v_y != X6 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X6),v_L)
| v_y = X5
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,v_x),v_L)
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X6),v_L)
| v_y = X6 )
& ( v_x != X6
| v_y != X5 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,X5),v_L)
| v_y = X6
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,v_x),v_L)
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X5),v_L)
| v_y = X5 )
& X5 != X6 )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f549,plain,
( ? [X0,X1] :
( ( ? [X2] :
( sP2(X0,X1,X2)
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
& X2 != v_y )
| sP1(X0,X2,X1) )
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != v_y
& X1 != v_y )
| sP4(X0,X1)
| sP3(X1,X0) )
| sP5 ),
inference(definition_folding,[],[f535,f548,f547,f546,f545,f544,f543]) ).
fof(f550,plain,
( ? [X5,X6] :
( ( v_x != X5
| v_y != X6 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X6),v_L)
| v_y = X5
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,v_x),v_L)
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X6),v_L)
| v_y = X6 )
& ( v_x != X6
| v_y != X5 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,X5),v_L)
| v_y = X6
| v_y = X5 )
& ( v_y != X5
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X6,v_x),v_L)
| v_y = X6 )
& ( v_y != X6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X5),v_L)
| v_y = X5 )
& X5 != X6 )
| ~ sP5 ),
inference(nnf_transformation,[],[f548]) ).
fof(f551,plain,
( ? [X0,X1] :
( ( v_x != X0
| v_y != X1 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| v_y = X0
| v_y = X1 )
& ( v_y != X1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| v_y = X0 )
& ( v_y != X0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
| v_y = X1 )
& ( v_x != X1
| v_y != X0 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| v_y = X1
| v_y = X0 )
& ( v_y != X0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
| v_y = X1 )
& ( v_y != X1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
| v_y = X0 )
& X0 != X1 )
| ~ sP5 ),
inference(rectify,[],[f550]) ).
fof(f552,plain,
( ( ( v_x != sK6
| v_y != sK7 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK7),v_L)
| v_y = sK6
| v_y = sK7 )
& ( v_y != sK7
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,v_x),v_L)
| v_y = sK6 )
& ( v_y != sK6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| v_y = sK7 )
& ( v_x != sK7
| v_y != sK6 )
& ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK6),v_L)
| v_y = sK7
| v_y = sK6 )
& ( v_y != sK6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_x),v_L)
| v_y = sK7 )
& ( v_y != sK7
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| v_y = sK6 )
& sK6 != sK7 )
| ~ sP5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f551]) ).
fof(f553,plain,
! [X0,X1] :
( ( ? [X3] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X3),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X3),v_L)
& v_y != X3 )
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f547]) ).
fof(f554,plain,
! [X0,X1] :
( ( ? [X2] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X2),v_L)
& v_y != X2 )
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f553]) ).
fof(f555,plain,
! [X0,X1] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK8(X0)),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK8(X0)),v_L)
& v_y != sK8(X0)
& X1 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X0 != v_y )
| ~ sP4(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0))],[f554]) ).
fof(f556,plain,
! [X1,X0] :
( ( ? [X4] :
( ( v_y = X4
& X1 = v_x )
| sP0(X4,X1)
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L)
& v_y = X4 ) )
& X0 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X1),v_L)
& X1 != v_y )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f546]) ).
fof(f557,plain,
! [X0,X1] :
( ( ? [X2] :
( ( v_y = X2
& v_x = X0 )
| sP0(X2,X0)
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& v_y = X2 ) )
& v_y = X1
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
& v_y != X0 )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f556]) ).
fof(f558,plain,
! [X0,X1] :
( ( ( ( v_y = sK9(X0)
& v_x = X0 )
| sP0(sK9(X0),X0)
| ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& v_y = sK9(X0) ) )
& v_y = X1
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
& v_y != X0 )
| ~ sP3(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f557]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X1 = v_x
& X2 = v_y )
| ~ sP2(X0,X1,X2) ),
inference(nnf_transformation,[],[f545]) ).
fof(f560,plain,
! [X0,X2,X1] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& X2 = v_y
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_x),v_L) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f544]) ).
fof(f561,plain,
! [X0,X1,X2] :
( ( v_x != X0
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
& v_y = X1
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_x),v_L) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f560]) ).
fof(f562,plain,
! [X4,X1] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X4),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X4),v_L)
& v_y != X4 )
| ~ sP0(X4,X1) ),
inference(nnf_transformation,[],[f543]) ).
fof(f563,plain,
! [X0,X1] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& v_y != X0 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f562]) ).
fof(f564,plain,
( ( ( sP2(sK10,sK11,sK12)
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK12),v_L)
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK12),v_L)
& v_y != sK12 )
| sP1(sK10,sK12,sK11) )
& c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK11),v_L)
& v_y != sK10
& v_y != sK11 )
| sP4(sK10,sK11)
| sP3(sK11,sK10)
| sP5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f549]) ).
fof(f570,plain,
! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| X4 = X5 ),
inference(cnf_transformation,[],[f533]) ).
fof(f571,plain,
! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L),
inference(cnf_transformation,[],[f533]) ).
fof(f572,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) ),
inference(cnf_transformation,[],[f533]) ).
fof(f573,plain,
( sK6 != sK7
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f574,plain,
( v_y != sK7
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| v_y = sK6
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f575,plain,
( v_y != sK6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_x),v_L)
| v_y = sK7
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f576,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK6),v_L)
| v_y = sK7
| v_y = sK6
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f577,plain,
( v_x != sK7
| v_y != sK6
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f578,plain,
( v_y != sK6
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| v_y = sK7
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f579,plain,
( v_y != sK7
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,v_x),v_L)
| v_y = sK6
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f580,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK7),v_L)
| v_y = sK6
| v_y = sK7
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f581,plain,
( v_x != sK6
| v_y != sK7
| ~ sP5 ),
inference(cnf_transformation,[],[f552]) ).
fof(f583,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f555]) ).
fof(f586,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK8(X0)),v_L)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f555]) ).
fof(f587,plain,
! [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK8(X0)),v_L)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f555]) ).
fof(f589,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f558]) ).
fof(f592,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| sP0(sK9(X0),X0)
| v_x = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f558]) ).
fof(f596,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| v_x = X1 ),
inference(cnf_transformation,[],[f559]) ).
fof(f597,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f598,plain,
! [X2,X0,X1] :
( v_x != X0
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f559]) ).
fof(f599,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_x),v_L)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f561]) ).
fof(f601,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f561]) ).
fof(f604,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f563]) ).
fof(f605,plain,
! [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f563]) ).
fof(f608,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK11),v_L)
| sP4(sK10,sK11)
| sP3(sK11,sK10)
| sP5 ),
inference(cnf_transformation,[],[f564]) ).
fof(f610,plain,
( sP2(sK10,sK11,sK12)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK12),v_L)
| sP1(sK10,sK12,sK11)
| sP4(sK10,sK11)
| sP3(sK11,sK10)
| sP5 ),
inference(cnf_transformation,[],[f564]) ).
fof(f611,plain,
( sP2(sK10,sK11,sK12)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK12),v_L)
| sP1(sK10,sK12,sK11)
| sP4(sK10,sK11)
| sP3(sK11,sK10)
| sP5 ),
inference(cnf_transformation,[],[f564]) ).
fof(f628,definition,
~ sP14(v_x),
introduced(definition,[new_symbols(definition,[sP14])],[inequality_splitting_name_introduction]) ).
fof(f629,definition,
~ sP15(v_y),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f630,plain,
( sP15(sK7)
| sP14(sK6)
| ~ sP5 ),
inference(inequality_splitting,[],[f581,f629,f628]) ).
fof(f631,definition,
~ sP16(v_y),
introduced(definition,[new_symbols(definition,[sP16])],[inequality_splitting_name_introduction]) ).
fof(f632,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,v_x),v_L)
| sP16(sK7)
| v_y = sK6
| ~ sP5 ),
inference(inequality_splitting,[],[f579,f631]) ).
fof(f633,definition,
~ sP17(v_y),
introduced(definition,[new_symbols(definition,[sP17])],[inequality_splitting_name_introduction]) ).
fof(f634,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| sP17(sK6)
| v_y = sK7
| ~ sP5 ),
inference(inequality_splitting,[],[f578,f633]) ).
fof(f635,definition,
~ sP18(v_x),
introduced(definition,[new_symbols(definition,[sP18])],[inequality_splitting_name_introduction]) ).
fof(f636,definition,
~ sP19(v_y),
introduced(definition,[new_symbols(definition,[sP19])],[inequality_splitting_name_introduction]) ).
fof(f637,plain,
( sP19(sK6)
| sP18(sK7)
| ~ sP5 ),
inference(inequality_splitting,[],[f577,f636,f635]) ).
fof(f638,definition,
~ sP20(v_y),
introduced(definition,[new_symbols(definition,[sP20])],[inequality_splitting_name_introduction]) ).
fof(f639,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_x),v_L)
| sP20(sK6)
| v_y = sK7
| ~ sP5 ),
inference(inequality_splitting,[],[f575,f638]) ).
fof(f640,definition,
~ sP21(v_y),
introduced(definition,[new_symbols(definition,[sP21])],[inequality_splitting_name_introduction]) ).
fof(f641,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| sP21(sK7)
| v_y = sK6
| ~ sP5 ),
inference(inequality_splitting,[],[f574,f640]) ).
fof(f642,definition,
~ sP22(sK6),
introduced(definition,[new_symbols(definition,[sP22])],[inequality_splitting_name_introduction]) ).
fof(f643,plain,
( sP22(sK7)
| ~ sP5 ),
inference(inequality_splitting,[],[f573,f642]) ).
fof(f650,definition,
~ sP26(v_x),
introduced(definition,[new_symbols(definition,[sP26])],[inequality_splitting_name_introduction]) ).
fof(f651,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| sP26(X0) ),
inference(inequality_splitting,[],[f598,f650]) ).
fof(f675,definition,
( spl32_1
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f677,plain,
( sP5
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f679,definition,
( spl32_2
<=> sP3(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f681,plain,
( sP3(sK11,sK10)
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f683,definition,
( spl32_3
<=> sP4(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
fof(f685,plain,
( sP4(sK10,sK11)
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f697,definition,
( spl32_6
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK11),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_6])],[avatar_definition]) ).
fof(f699,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK11),v_L)
| ~ spl32_6 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f700,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_6 ),
inference(avatar_split_clause,[],[f608,f697,f683,f679,f675]) ).
fof(f702,definition,
( spl32_7
<=> sP1(sK10,sK12,sK11) ),
introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition]) ).
fof(f704,plain,
( sP1(sK10,sK12,sK11)
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f710,definition,
( spl32_9
<=> sP2(sK10,sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl32_9])],[avatar_definition]) ).
fof(f712,plain,
( sP2(sK10,sK11,sK12)
| ~ spl32_9 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f715,definition,
( spl32_10
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK12),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_10])],[avatar_definition]) ).
fof(f717,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK12),v_L)
| ~ spl32_10 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f718,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_7
| spl32_10
| spl32_9 ),
inference(avatar_split_clause,[],[f610,f710,f715,f702,f683,f679,f675]) ).
fof(f720,definition,
( spl32_11
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK12),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_11])],[avatar_definition]) ).
fof(f722,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK12),v_L)
| spl32_11 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f723,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_7
| ~ spl32_11
| spl32_9 ),
inference(avatar_split_clause,[],[f611,f710,f720,f702,f683,f679,f675]) ).
fof(f749,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
| v_x = X0
| ~ sP2(X0,X1,X2) ),
inference(resolution,[],[f570,f597]) ).
fof(f754,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK6),v_L)
| sK6 = sK7
| v_y = sK6
| v_y = sK7
| ~ sP5 ),
inference(resolution,[],[f570,f580]) ).
fof(f755,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| v_x = sK6
| sP16(sK7)
| v_y = sK6
| ~ sP5 ),
inference(resolution,[],[f570,f632]) ).
fof(f757,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| v_x = sK7
| sP20(sK6)
| v_y = sK7
| ~ sP5 ),
inference(resolution,[],[f570,f639]) ).
fof(f762,plain,
( sK6 = sK7
| v_y = sK6
| v_y = sK7
| ~ sP5 ),
inference(forward_subsumption_resolution,[],[f754,f576]) ).
fof(f766,definition,
( spl32_12
<=> sP20(sK6) ),
introduced(definition,[new_symbols(definition,[spl32_12])],[avatar_definition]) ).
fof(f768,plain,
( sP20(sK6)
| ~ spl32_12 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f770,definition,
( spl32_13
<=> v_x = sK7 ),
introduced(definition,[new_symbols(definition,[spl32_13])],[avatar_definition]) ).
fof(f772,plain,
( v_x = sK7
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f774,definition,
( spl32_14
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_14])],[avatar_definition]) ).
fof(f776,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| ~ spl32_14 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f784,definition,
( spl32_16
<=> sP16(sK7) ),
introduced(definition,[new_symbols(definition,[spl32_16])],[avatar_definition]) ).
fof(f788,definition,
( spl32_17
<=> v_x = sK6 ),
introduced(definition,[new_symbols(definition,[spl32_17])],[avatar_definition]) ).
fof(f790,plain,
( v_x = sK6
| ~ spl32_17 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f792,definition,
( spl32_18
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_18])],[avatar_definition]) ).
fof(f794,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| ~ spl32_18 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f802,definition,
( spl32_20
<=> sP21(sK7) ),
introduced(definition,[new_symbols(definition,[spl32_20])],[avatar_definition]) ).
fof(f803,plain,
( ~ sP21(sK7)
| spl32_20 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f811,definition,
( spl32_22
<=> sP17(sK6) ),
introduced(definition,[new_symbols(definition,[spl32_22])],[avatar_definition]) ).
fof(f812,plain,
( ~ sP17(sK6)
| spl32_22 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f813,plain,
( sP17(sK6)
| ~ spl32_22 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f822,definition,
( spl32_24
<=> sK6 = sK7 ),
introduced(definition,[new_symbols(definition,[spl32_24])],[avatar_definition]) ).
fof(f823,plain,
( sK6 != sK7
| spl32_24 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f824,plain,
( sK6 = sK7
| ~ spl32_24 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f827,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK8(X1)),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP4(X1,X2) ),
inference(resolution,[],[f572,f586]) ).
fof(f829,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP1(X2,X3,X1) ),
inference(resolution,[],[f572,f599]) ).
fof(f830,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| sP0(sK9(X1),X1)
| v_x = X1
| ~ sP3(X1,X2) ),
inference(resolution,[],[f572,f592]) ).
fof(f834,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| ~ sP0(X1,X2) ),
inference(resolution,[],[f572,f604]) ).
fof(f891,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,X0),v_L)
| ~ sP0(X0,X1)
| ~ sP3(X1,X2) ),
inference(resolution,[],[f834,f589]) ).
fof(f900,plain,
! [X2,X0,X1] :
( ~ sP3(X1,X2)
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f891,f605]) ).
fof(f905,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_x),v_L)
| ~ sP4(X0,X1)
| ~ sP4(X0,X2) ),
inference(resolution,[],[f827,f587]) ).
fof(f911,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X2)
| ~ sP4(X0,X1) ),
inference(forward_subsumption_resolution,[],[f905,f583]) ).
fof(f917,definition,
( spl32_25
<=> ! [X0] : ~ sP3(sK11,X0) ),
introduced(definition,[new_symbols(definition,[spl32_25])],[avatar_definition]) ).
fof(f918,plain,
( ! [X0] : ~ sP3(sK11,X0)
| ~ spl32_25 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f925,definition,
( spl32_27
<=> v_x = sK11 ),
introduced(definition,[new_symbols(definition,[spl32_27])],[avatar_definition]) ).
fof(f926,plain,
( v_x != sK11
| spl32_27 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f927,plain,
( v_x = sK11
| ~ spl32_27 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f929,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK7),v_L)
| v_x = sK7
| sP20(sK6)
| v_y = sK7
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f757,f677]) ).
fof(f930,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK6),v_L)
| v_x = sK6
| sP16(sK7)
| v_y = sK6
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f755,f677]) ).
fof(f934,plain,
( sK6 = sK7
| v_y = sK6
| v_y = sK7
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f762,f677]) ).
fof(f942,definition,
( spl32_28
<=> v_y = sK7 ),
introduced(definition,[new_symbols(definition,[spl32_28])],[avatar_definition]) ).
fof(f944,plain,
( v_y = sK7
| ~ spl32_28 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f945,plain,
( spl32_28
| spl32_12
| spl32_13
| spl32_14
| ~ spl32_1 ),
inference(avatar_split_clause,[],[f929,f675,f774,f770,f766,f942]) ).
fof(f947,definition,
( spl32_29
<=> v_y = sK6 ),
introduced(definition,[new_symbols(definition,[spl32_29])],[avatar_definition]) ).
fof(f949,plain,
( v_y = sK6
| ~ spl32_29 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f950,plain,
( spl32_29
| spl32_16
| spl32_17
| spl32_18
| ~ spl32_1 ),
inference(avatar_split_clause,[],[f930,f675,f792,f788,f784,f947]) ).
fof(f954,plain,
( spl32_28
| spl32_29
| spl32_24
| ~ spl32_1 ),
inference(avatar_split_clause,[],[f934,f675,f822,f947,f942]) ).
fof(f993,plain,
( ~ sP18(sK7)
| ~ spl32_13 ),
inference(superposition,[],[f635,f772]) ).
fof(f1015,plain,
( ~ sP22(sK7)
| ~ spl32_24 ),
inference(superposition,[],[f642,f824]) ).
fof(f1110,plain,
( ~ sP5
| ~ spl32_24 ),
inference(resolution,[],[f1015,f643]) ).
fof(f1111,plain,
( $false
| ~ spl32_1
| ~ spl32_24 ),
inference(forward_subsumption_resolution,[],[f1110,f677]) ).
fof(f1112,plain,
( ~ spl32_1
| ~ spl32_24 ),
inference(avatar_contradiction_clause,[],[f1111]) ).
fof(f1632,plain,
( ! [X0] : ~ sP4(sK10,X0)
| ~ spl32_3 ),
inference(resolution,[],[f911,f685]) ).
fof(f1633,plain,
( $false
| ~ spl32_3 ),
inference(resolution,[],[f1632,f685]) ).
fof(f1634,plain,
~ spl32_3,
inference(avatar_contradiction_clause,[],[f1633]) ).
fof(f1636,plain,
( v_x = sK11
| ~ spl32_9 ),
inference(resolution,[],[f712,f596]) ).
fof(f1660,plain,
( spl32_27
| ~ spl32_9 ),
inference(avatar_split_clause,[],[f1636,f710,f925]) ).
fof(f1665,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,v_x),v_L)
| ~ sP1(X0,X1,sK11) )
| ~ spl32_6 ),
inference(resolution,[],[f699,f829]) ).
fof(f1668,plain,
( ! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK10),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK11),v_L) )
| ~ spl32_6 ),
inference(resolution,[],[f699,f572]) ).
fof(f1681,definition,
( spl32_42
<=> ! [X0,X1] : ~ sP1(X0,X1,sK11) ),
introduced(definition,[new_symbols(definition,[spl32_42])],[avatar_definition]) ).
fof(f1682,plain,
( ! [X0,X1] : ~ sP1(X0,X1,sK11)
| ~ spl32_42 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f1724,definition,
( spl32_49
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,v_x),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_49])],[avatar_definition]) ).
fof(f1726,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,v_x),v_L)
| ~ spl32_49 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f1728,plain,
( spl32_42
| spl32_49
| ~ spl32_6 ),
inference(avatar_split_clause,[],[f1665,f697,f1724,f1681]) ).
fof(f1759,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK11),v_L)
| v_x = sK10
| ~ sP2(sK10,X0,X1) )
| ~ spl32_6 ),
inference(resolution,[],[f1668,f749]) ).
fof(f1776,definition,
( spl32_57
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK11),v_L) ),
introduced(definition,[new_symbols(definition,[spl32_57])],[avatar_definition]) ).
fof(f1777,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK11),v_L)
| spl32_57 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f1778,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,sK11),v_L)
| ~ spl32_57 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f1781,definition,
( spl32_58
<=> ! [X0,X1] : ~ sP1(sK10,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl32_58])],[avatar_definition]) ).
fof(f1782,plain,
( ! [X0,X1] : ~ sP1(sK10,X0,X1)
| ~ spl32_58 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f1784,definition,
( spl32_59
<=> v_x = sK10 ),
introduced(definition,[new_symbols(definition,[spl32_59])],[avatar_definition]) ).
fof(f1786,plain,
( v_x = sK10
| ~ spl32_59 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f1789,definition,
( spl32_60
<=> ! [X0,X1] : ~ sP2(sK10,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl32_60])],[avatar_definition]) ).
fof(f1790,plain,
( ! [X0,X1] : ~ sP2(sK10,X0,X1)
| ~ spl32_60 ),
inference(avatar_component_clause,[],[f1789]) ).
fof(f1791,plain,
( spl32_60
| spl32_59
| spl32_57
| ~ spl32_6 ),
inference(avatar_split_clause,[],[f1759,f697,f1776,f1784,f1789]) ).
fof(f1906,plain,
( $false
| ~ spl32_2
| ~ spl32_25 ),
inference(resolution,[],[f918,f681]) ).
fof(f1907,plain,
( ~ spl32_2
| ~ spl32_25 ),
inference(avatar_contradiction_clause,[],[f1906]) ).
fof(f1910,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,v_x),v_L)
| ~ spl32_27
| ~ spl32_57 ),
inference(forward_demodulation,[],[f1778,f927]) ).
fof(f1917,plain,
( $false
| ~ spl32_27
| ~ spl32_57 ),
inference(forward_subsumption_resolution,[],[f1910,f571]) ).
fof(f1918,plain,
( ~ spl32_27
| ~ spl32_57 ),
inference(avatar_contradiction_clause,[],[f1917]) ).
fof(f1932,plain,
( ! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK11),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK12),v_L) )
| ~ spl32_10 ),
inference(resolution,[],[f717,f572]) ).
fof(f1984,plain,
( ! [X0,X1] : ~ sP1(sK10,X0,X1)
| ~ spl32_49 ),
inference(resolution,[],[f1726,f601]) ).
fof(f1993,plain,
( spl32_58
| ~ spl32_49 ),
inference(avatar_split_clause,[],[f1984,f1724,f1781]) ).
fof(f2006,plain,
( ! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_x,v_x),v_L)
| sP0(sK9(sK11),sK11)
| v_x = sK11
| ~ sP3(sK11,X0) )
| ~ spl32_57 ),
inference(resolution,[],[f1778,f830]) ).
fof(f2012,plain,
( ! [X0] :
( sP0(sK9(sK11),sK11)
| v_x = sK11
| ~ sP3(sK11,X0) )
| ~ spl32_57 ),
inference(forward_subsumption_resolution,[],[f2006,f571]) ).
fof(f2014,plain,
( ! [X0] :
( v_x = sK11
| ~ sP3(sK11,X0) )
| ~ spl32_57 ),
inference(forward_subsumption_resolution,[],[f2012,f900]) ).
fof(f2015,plain,
( ! [X0] : ~ sP3(sK11,X0)
| spl32_27
| ~ spl32_57 ),
inference(forward_subsumption_resolution,[],[f2014,f926]) ).
fof(f2016,plain,
( spl32_25
| spl32_27
| ~ spl32_57 ),
inference(avatar_split_clause,[],[f2015,f1776,f925,f917]) ).
fof(f2019,plain,
( ! [X0] : ~ sP3(sK11,X0)
| spl32_57 ),
inference(resolution,[],[f1777,f589]) ).
fof(f2022,plain,
( spl32_25
| spl32_57 ),
inference(avatar_split_clause,[],[f2019,f1776,f917]) ).
fof(f2023,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK10,sK12),v_L)
| ~ spl32_6
| ~ spl32_10 ),
inference(resolution,[],[f699,f1932]) ).
fof(f2030,plain,
( $false
| ~ spl32_6
| ~ spl32_10
| spl32_11 ),
inference(forward_subsumption_resolution,[],[f2023,f722]) ).
fof(f2031,plain,
( ~ spl32_6
| ~ spl32_10
| spl32_11 ),
inference(avatar_contradiction_clause,[],[f2030]) ).
fof(f2032,plain,
( $false
| ~ spl32_7
| ~ spl32_42 ),
inference(forward_subsumption_resolution,[],[f704,f1682]) ).
fof(f2033,plain,
( ~ spl32_7
| ~ spl32_42 ),
inference(avatar_contradiction_clause,[],[f2032]) ).
fof(f2034,plain,
( $false
| ~ spl32_7
| ~ spl32_58 ),
inference(forward_subsumption_resolution,[],[f704,f1782]) ).
fof(f2035,plain,
( ~ spl32_7
| ~ spl32_58 ),
inference(avatar_contradiction_clause,[],[f2034]) ).
fof(f2036,plain,
( $false
| ~ spl32_9
| ~ spl32_60 ),
inference(forward_subsumption_resolution,[],[f712,f1790]) ).
fof(f2037,plain,
( ~ spl32_9
| ~ spl32_60 ),
inference(avatar_contradiction_clause,[],[f2036]) ).
fof(f2039,plain,
( sP2(sK10,v_x,sK12)
| ~ spl32_9
| ~ spl32_27 ),
inference(forward_demodulation,[],[f712,f927]) ).
fof(f2044,plain,
( sP2(v_x,v_x,sK12)
| ~ spl32_9
| ~ spl32_27
| ~ spl32_59 ),
inference(forward_demodulation,[],[f2039,f1786]) ).
fof(f2050,plain,
( sP26(v_x)
| ~ spl32_9
| ~ spl32_27
| ~ spl32_59 ),
inference(resolution,[],[f2044,f651]) ).
fof(f2051,plain,
( $false
| ~ spl32_9
| ~ spl32_27
| ~ spl32_59 ),
inference(forward_subsumption_resolution,[],[f2050,f650]) ).
fof(f2052,plain,
( ~ spl32_9
| ~ spl32_27
| ~ spl32_59 ),
inference(avatar_contradiction_clause,[],[f2051]) ).
fof(f2059,plain,
( ~ sP17(sK6)
| ~ spl32_29 ),
inference(superposition,[],[f633,f949]) ).
fof(f2060,plain,
( ~ sP19(sK6)
| ~ spl32_29 ),
inference(superposition,[],[f636,f949]) ).
fof(f2061,plain,
( ~ sP20(sK6)
| ~ spl32_29 ),
inference(superposition,[],[f638,f949]) ).
fof(f2070,plain,
( $false
| ~ spl32_12
| ~ spl32_29 ),
inference(forward_subsumption_resolution,[],[f2061,f768]) ).
fof(f2071,plain,
( ~ spl32_12
| ~ spl32_29 ),
inference(avatar_contradiction_clause,[],[f2070]) ).
fof(f2072,plain,
( $false
| ~ spl32_22
| ~ spl32_29 ),
inference(forward_subsumption_resolution,[],[f2059,f813]) ).
fof(f2073,plain,
( ~ spl32_22
| ~ spl32_29 ),
inference(avatar_contradiction_clause,[],[f2072]) ).
fof(f2138,plain,
( sP18(sK7)
| ~ sP5
| ~ spl32_29 ),
inference(resolution,[],[f2060,f637]) ).
fof(f2139,plain,
( ~ sP5
| ~ spl32_13
| ~ spl32_29 ),
inference(forward_subsumption_resolution,[],[f2138,f993]) ).
fof(f2140,plain,
( $false
| ~ spl32_1
| ~ spl32_13
| ~ spl32_29 ),
inference(forward_subsumption_resolution,[],[f2139,f677]) ).
fof(f2141,plain,
( ~ spl32_1
| ~ spl32_13
| ~ spl32_29 ),
inference(avatar_contradiction_clause,[],[f2140]) ).
fof(f2145,plain,
( sP17(sK6)
| v_y = sK7
| ~ sP5
| ~ spl32_14 ),
inference(resolution,[],[f776,f634]) ).
fof(f2154,plain,
( v_y = sK7
| ~ sP5
| ~ spl32_14
| spl32_22 ),
inference(forward_subsumption_resolution,[],[f2145,f812]) ).
fof(f2155,plain,
( v_y = sK7
| ~ spl32_1
| ~ spl32_14
| spl32_22 ),
inference(forward_subsumption_resolution,[],[f2154,f677]) ).
fof(f2156,plain,
( spl32_28
| ~ spl32_1
| ~ spl32_14
| spl32_22 ),
inference(avatar_split_clause,[],[f2155,f811,f774,f675,f942]) ).
fof(f2157,plain,
( sK6 = sK7
| ~ spl32_28
| ~ spl32_29 ),
inference(superposition,[],[f944,f949]) ).
fof(f2159,plain,
( ~ sP15(sK7)
| ~ spl32_28 ),
inference(superposition,[],[f629,f944]) ).
fof(f2160,plain,
( ~ sP16(sK7)
| ~ spl32_28 ),
inference(superposition,[],[f631,f944]) ).
fof(f2164,plain,
( ~ sP21(sK7)
| ~ spl32_28 ),
inference(superposition,[],[f640,f944]) ).
fof(f2175,plain,
( ~ spl32_20
| ~ spl32_28 ),
inference(avatar_split_clause,[],[f2164,f942,f802]) ).
fof(f2176,plain,
( ~ spl32_16
| ~ spl32_28 ),
inference(avatar_split_clause,[],[f2160,f942,f784]) ).
fof(f2177,plain,
( $false
| spl32_24
| ~ spl32_28
| ~ spl32_29 ),
inference(forward_subsumption_resolution,[],[f2157,f823]) ).
fof(f2178,plain,
( spl32_24
| ~ spl32_28
| ~ spl32_29 ),
inference(avatar_contradiction_clause,[],[f2177]) ).
fof(f2200,plain,
( sP14(sK6)
| ~ sP5
| ~ spl32_28 ),
inference(resolution,[],[f2159,f630]) ).
fof(f2201,plain,
( sP14(sK6)
| ~ spl32_1
| ~ spl32_28 ),
inference(forward_subsumption_resolution,[],[f2200,f677]) ).
fof(f2202,plain,
( sP14(v_x)
| ~ spl32_1
| ~ spl32_17
| ~ spl32_28 ),
inference(forward_demodulation,[],[f2201,f790]) ).
fof(f2203,plain,
( $false
| ~ spl32_1
| ~ spl32_17
| ~ spl32_28 ),
inference(forward_subsumption_resolution,[],[f2202,f628]) ).
fof(f2204,plain,
( ~ spl32_1
| ~ spl32_17
| ~ spl32_28 ),
inference(avatar_contradiction_clause,[],[f2203]) ).
fof(f2206,plain,
( sP21(sK7)
| v_y = sK6
| ~ sP5
| ~ spl32_18 ),
inference(resolution,[],[f794,f641]) ).
fof(f2218,plain,
( v_y = sK6
| ~ sP5
| ~ spl32_18
| spl32_20 ),
inference(forward_subsumption_resolution,[],[f2206,f803]) ).
fof(f2220,plain,
( v_y = sK6
| ~ spl32_1
| ~ spl32_18
| spl32_20 ),
inference(forward_subsumption_resolution,[],[f2218,f677]) ).
fof(f2222,plain,
( sK6 = sK7
| ~ spl32_1
| ~ spl32_18
| spl32_20
| ~ spl32_28 ),
inference(forward_demodulation,[],[f2220,f944]) ).
fof(f2223,plain,
( $false
| ~ spl32_1
| ~ spl32_18
| spl32_20
| spl32_24
| ~ spl32_28 ),
inference(forward_subsumption_resolution,[],[f2222,f823]) ).
fof(f2224,plain,
( ~ spl32_1
| ~ spl32_18
| spl32_20
| spl32_24
| ~ spl32_28 ),
inference(avatar_contradiction_clause,[],[f2223]) ).
cnf(s3,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_6 ),
inference(sat_conversion,[],[f700]) ).
cnf(s5,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_7
| spl32_9
| spl32_10 ),
inference(sat_conversion,[],[f718]) ).
cnf(s6,plain,
( spl32_1
| spl32_2
| spl32_3
| spl32_7
| spl32_9
| ~ spl32_11 ),
inference(sat_conversion,[],[f723]) ).
cnf(s16,plain,
( ~ spl32_1
| spl32_12
| spl32_13
| spl32_14
| spl32_28 ),
inference(sat_conversion,[],[f945]) ).
cnf(s17,plain,
( ~ spl32_1
| spl32_16
| spl32_17
| spl32_18
| spl32_29 ),
inference(sat_conversion,[],[f950]) ).
cnf(s21,plain,
( ~ spl32_1
| spl32_24
| spl32_28
| spl32_29 ),
inference(sat_conversion,[],[f954]) ).
cnf(s28,plain,
( ~ spl32_1
| ~ spl32_24 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s33,plain,
~ spl32_3,
inference(sat_conversion,[],[f1634]) ).
cnf(s37,plain,
( ~ spl32_9
| spl32_27 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s46,plain,
( ~ spl32_6
| spl32_42
| spl32_49 ),
inference(sat_conversion,[],[f1728]) ).
cnf(s55,plain,
( ~ spl32_6
| spl32_57
| spl32_59
| spl32_60 ),
inference(sat_conversion,[],[f1791]) ).
cnf(s69,plain,
( ~ spl32_2
| ~ spl32_25 ),
inference(sat_conversion,[],[f1907]) ).
cnf(s72,plain,
( ~ spl32_27
| ~ spl32_57 ),
inference(sat_conversion,[],[f1918]) ).
cnf(s79,plain,
( ~ spl32_49
| spl32_58 ),
inference(sat_conversion,[],[f1993]) ).
cnf(s81,plain,
( spl32_25
| spl32_27
| ~ spl32_57 ),
inference(sat_conversion,[],[f2016]) ).
cnf(s82,plain,
( spl32_25
| spl32_57 ),
inference(sat_conversion,[],[f2022]) ).
cnf(s84,plain,
( ~ spl32_6
| ~ spl32_10
| spl32_11 ),
inference(sat_conversion,[],[f2031]) ).
cnf(s85,plain,
( ~ spl32_7
| ~ spl32_42 ),
inference(sat_conversion,[],[f2033]) ).
cnf(s86,plain,
( ~ spl32_7
| ~ spl32_58 ),
inference(sat_conversion,[],[f2035]) ).
cnf(s87,plain,
( ~ spl32_9
| ~ spl32_60 ),
inference(sat_conversion,[],[f2037]) ).
cnf(s89,plain,
( ~ spl32_9
| ~ spl32_27
| ~ spl32_59 ),
inference(sat_conversion,[],[f2052]) ).
cnf(s90,plain,
( ~ spl32_12
| ~ spl32_29 ),
inference(sat_conversion,[],[f2071]) ).
cnf(s91,plain,
( ~ spl32_22
| ~ spl32_29 ),
inference(sat_conversion,[],[f2073]) ).
cnf(s93,plain,
( ~ spl32_1
| ~ spl32_13
| ~ spl32_29 ),
inference(sat_conversion,[],[f2141]) ).
cnf(s94,plain,
( ~ spl32_1
| ~ spl32_14
| spl32_22
| spl32_28 ),
inference(sat_conversion,[],[f2156]) ).
cnf(s96,plain,
( ~ spl32_20
| ~ spl32_28 ),
inference(sat_conversion,[],[f2175]) ).
cnf(s97,plain,
( ~ spl32_16
| ~ spl32_28 ),
inference(sat_conversion,[],[f2176]) ).
cnf(s98,plain,
( spl32_24
| ~ spl32_28
| ~ spl32_29 ),
inference(sat_conversion,[],[f2178]) ).
cnf(s100,plain,
( ~ spl32_1
| ~ spl32_17
| ~ spl32_28 ),
inference(sat_conversion,[],[f2204]) ).
cnf(s101,plain,
( ~ spl32_1
| ~ spl32_18
| spl32_20
| spl32_24
| ~ spl32_28 ),
inference(sat_conversion,[],[f2224]) ).
cnf(s102,plain,
( spl32_1
| spl32_2
| spl32_7
| spl32_9
| ~ spl32_11 ),
inference(rat,[],[s6,s33]) ).
cnf(s103,plain,
( spl32_1
| spl32_2
| spl32_7
| spl32_9
| spl32_10 ),
inference(rat,[],[s5,s33]) ).
cnf(s105,plain,
( spl32_1
| spl32_2
| spl32_6 ),
inference(rat,[],[s3,s33]) ).
cnf(s108,plain,
( ~ spl32_9
| ~ spl32_6 ),
inference(rat,[],[s55,s72,s89,s37,s87]) ).
cnf(s109,plain,
( spl32_7
| spl32_2
| spl32_1 ),
inference(rat,[],[s84,s103,s102,s108,s105]) ).
cnf(s110,plain,
( spl32_2
| spl32_1 ),
inference(rat,[],[s46,s79,s85,s86,s109,s105]) ).
cnf(s111,plain,
( spl32_25
| ~ spl32_57 ),
inference(rat,[],[s72,s81]) ).
cnf(s112,plain,
spl32_25,
inference(rat,[],[s111,s82]) ).
cnf(s113,plain,
~ spl32_2,
inference(rat,[],[s69,s112]) ).
cnf(s114,plain,
spl32_1,
inference(rat,[],[s110,s113]) ).
cnf(s115,plain,
~ spl32_24,
inference(rat,[],[s28,s114]) ).
cnf(s116,plain,
~ spl32_28,
inference(rat,[],[s101,s17,s100,s96,s97,s98,s114,s115]) ).
cnf(s117,plain,
spl32_29,
inference(rat,[],[s21,s115,s114,s116]) ).
cnf(s118,plain,
~ spl32_22,
inference(rat,[],[s91,s117]) ).
cnf(s119,plain,
~ spl32_12,
inference(rat,[],[s90,s117]) ).
cnf(s120,plain,
~ spl32_13,
inference(rat,[],[s93,s114,s117]) ).
cnf(s121,plain,
~ spl32_14,
inference(rat,[],[s94,s116,s114,s118]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s16,s116,s119,s114,s120,s121]) ).
fof(f2225,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT117+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.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 23:46:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.84/1.35 % (2858270)Detected formulas, will run a generic FOF schedule.
% 2.84/1.35 % (2858280)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1371579344:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.35 % (2858280)Instruction limit reached!
% 2.84/1.35 % (2858280)------------------------------
% 2.84/1.35 % (2858280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.35 % (2858280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.35 % (2858280)CaDiCaL version: 2.1.3
% 2.84/1.35 % (2858280)Termination reason: Instruction limit
% 2.84/1.35 % (2858280)Time elapsed: 0.037 s
% 2.84/1.35 % (2858280)Peak memory usage: 89 MB
% 2.84/1.35 % (2858280)Instructions burned: 120 (million)
% 2.84/1.35 % (2858281)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2868996506:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.35 % (2858279)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3080598644:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.35 % (2858276)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=4009984634:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.35 % (2858282)dis-21_1_sil=8000:lcm=predicate:random_seed=1499128827: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)
% 2.84/1.35 % (2858277)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=321609283:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.35 % (2858278)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=2231828044:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.35 % (2858279)First to succeed.
% 2.84/1.35 % (2858279)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2858270"
% 2.84/1.35 % (2858282)Instruction limit reached!
% 2.84/1.35 % (2858282)------------------------------
% 2.84/1.35 % (2858282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.35 % (2858282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.35 % (2858282)CaDiCaL version: 2.1.3
% 2.84/1.35 % (2858282)Termination reason: Instruction limit
% 2.84/1.35 % (2858282)Termination phase: Saturation
% 2.84/1.35 % (2858282)Time elapsed: 0.072 s
% 2.84/1.35 % (2858282)Peak memory usage: 90 MB
% 2.84/1.35 % (2858282)Instructions burned: 130 (million)
% 2.84/1.35 % (2858281)Instruction limit reached!
% 2.84/1.35 % (2858281)------------------------------
% 2.84/1.35 % (2858281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.35 % (2858281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.35 % (2858281)CaDiCaL version: 2.1.3
% 2.84/1.35 % (2858281)Termination reason: Instruction limit
% 2.84/1.35 % (2858281)Termination phase: Saturation
% 2.84/1.35 % (2858281)Time elapsed: 0.093 s
% 2.84/1.35 % (2858281)Peak memory usage: 90 MB
% 2.84/1.35 % (2858281)Instructions burned: 140 (million)
% 2.84/1.35 % (2858284)lrs+10_1_sil=8000:sp=occurrence:random_seed=4027193926:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.84/1.35 % (2858284)Also succeeded, but the first one will report.
% 2.84/1.35 % (2858291)lrs+10_1_sil=32000:urr=on:br=off:random_seed=987567664:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.84/1.35 % (2858292)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2245816391:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.84/1.35 % (2858292)Also succeeded, but the first one will report.
% 2.84/1.35 % (2858279)Refutation found. Thanks to Tanya!
% 2.84/1.35 % SZS status Theorem for theBenchmark
% 2.84/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.55 % (2858279)------------------------------
% 3.94/1.55 % (2858279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.55 % (2858279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.55 % (2858279)CaDiCaL version: 2.1.3
% 3.94/1.55 % (2858279)Termination reason: Refutation
% 3.94/1.55 % (2858279)Time elapsed: 0.048 s
% 3.94/1.55 % (2858279)Peak memory usage: 90 MB
% 3.94/1.55 % (2858279)Instructions burned: 75 (million)
% 3.94/1.55 % (2858279)------------------------------
% 3.94/1.55 % (2858279)------------------------------
% 3.94/1.55 % (2858270)Success in time 0.492 s
% 3.94/1.55 % Vampire exiting
%------------------------------------------------------------------------------