%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT115+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 12:36:56 PM UTC 2026
% Result : Theorem 4.13s 1.54s
% Output : Refutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 34
% Syntax : Number of formulae : 234 ( 12 unt; 32 def)
% Number of atoms : 1010 ( 301 equ)
% Maximal formula atoms : 47 ( 4 avg)
% Number of connectives : 1276 ( 500 ~; 472 |; 244 &)
% ( 27 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 29 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 141 ( 0 sgn 111 !; 30 ?)
% 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_x
& X1 != v_x )
=> ! [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)
& X2 != 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,X2),v_L) )
& ( ( X2 = 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,X1,v_y),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_y),v_L) ) ) )
& ( ( 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,X0,v_y),v_L)
& X0 != v_x )
=> ! [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_y,X2),v_L)
& X2 != 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,X2),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,v_y,X1),v_L)
& X1 != v_x )
=> ! [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)
& X2 != 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,v_y,X2),v_L) ) )
& ( X2 = 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,X1,v_y),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_x
& X1 != v_x )
| ( 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,X0,v_y),v_L)
& X0 != v_x )
| ( 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,v_y,X1),v_L)
& X1 != v_x )
| ( 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_x
& X0 != v_x )
| ( 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,X1,v_y),v_L)
& X1 != v_x )
| ( 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_y,X0),v_L)
& X0 != v_x ) ) ) ),
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_x
& X1 != v_x )
=> ! [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)
& X2 != 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,X2),v_L) )
& ( ( X2 = 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,X1,v_y),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_y),v_L) ) ) )
& ( ( 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,X0,v_y),v_L)
& X0 != v_x )
=> ! [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_y,X2),v_L)
& X2 != 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,X2),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,v_y,X1),v_L)
& X1 != v_x )
=> ! [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)
& X2 != 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,v_y,X2),v_L) ) )
& ( X2 = 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,X1,v_y),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_x
& X1 != v_x )
| ( 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,X0,v_y),v_L)
& X0 != v_x )
| ( 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,v_y,X1),v_L)
& X1 != v_x )
| ( 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_x
& X0 != v_x )
| ( 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,X1,v_y),v_L)
& X1 != v_x )
| ( 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_y,X0),v_L)
& X0 != v_x ) ) ) ),
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_x
& X1 != v_x )
=> ! [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)
& X2 != 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,X2),v_L) )
& ( ( X2 = 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,X1,v_y),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_y),v_L) ) ) )
& ( ( 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,X0,v_y),v_L)
& X0 != v_x )
=> ! [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_y,X3),v_L)
& v_x != 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_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_y,X1),v_L)
& X1 != v_x )
=> ! [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_x != X4 )
=> ( 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_y,X4),v_L) ) )
& ( v_x = 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_y),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_x != X5
& v_x != X6 )
| ( v_x = 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_y),v_L)
& v_x != X5 )
| ( v_x = 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_y,X6),v_L)
& v_x != 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_x != X6
& v_x != X5 )
| ( v_x = 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_y),v_L)
& v_x != X6 )
| ( v_x = 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_y,X5),v_L)
& v_x != 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] :
( ( ~ 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_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_y),v_L)
& X2 = 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,X1,v_y),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_x
& X1 != v_x )
| ( ? [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_y,X3),v_L)
& v_x != X3 )
& 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,X0,v_y),v_L)
& X0 != v_x )
| ( ? [X4] :
( ( 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_y,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_x != 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_y),v_L)
& v_x = X4 ) )
& 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,v_y,X1),v_L)
& X1 != v_x ) )
| ? [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_x = X5
| v_x = X6 )
& ( v_x != 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_y),v_L)
| v_x = X5 )
& ( v_x != 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_y,X6),v_L)
| v_x = 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_x = X6
| v_x = X5 )
& ( v_x != 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_y),v_L)
| v_x = X6 )
& ( v_x != 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_y,X5),v_L)
| v_x = X5 )
& X5 != X6 ) ),
inference(ennf_transformation,[],[f531]) ).
fof(f535,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)
& X2 != 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_y),v_L)
& X2 = 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,X1,v_y),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_x
& X1 != v_x )
| ( ? [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_y,X3),v_L)
& v_x != X3 )
& 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,X0,v_y),v_L)
& X0 != v_x )
| ( ? [X4] :
( ( 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_y,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_x != 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_y),v_L)
& v_x = X4 ) )
& 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,v_y,X1),v_L)
& X1 != v_x ) )
| ? [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_x = X5
| v_x = X6 )
& ( v_x != 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_y),v_L)
| v_x = X5 )
& ( v_x != 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_y,X6),v_L)
| v_x = 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_x = X6
| v_x = X5 )
& ( v_x != 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_y),v_L)
| v_x = X6 )
& ( v_x != 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_y,X5),v_L)
| v_x = X5 )
& X5 != X6 ) ),
inference(flattening,[],[f534]) ).
fof(f555,definition,
! [X1] :
( ? [X4] :
( ( 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_y,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_x != 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_y),v_L)
& v_x = X4 ) )
| ~ sP0(X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f556,definition,
! [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,v_y),v_L)
& X2 = 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,X1,v_y),v_L) )
| ~ sP1(X0,X2,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f557,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_y,X3),v_L)
& v_x != X3 )
& 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,X0,v_y),v_L)
& X0 != v_x )
| ~ sP2(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f558,definition,
! [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_x )
| 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_x
& X1 != v_x )
| ~ sP3(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f559,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_x = X5
| v_x = X6 )
& ( v_x != 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_y),v_L)
| v_x = X5 )
& ( v_x != 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_y,X6),v_L)
| v_x = 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_x = X6
| v_x = X5 )
& ( v_x != 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_y),v_L)
| v_x = X6 )
& ( v_x != 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_y,X5),v_L)
| v_x = X5 )
& X5 != X6 )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f560,plain,
( ? [X0,X1] :
( sP3(X0,X1)
| sP2(X0,X1)
| ( sP0(X1)
& 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,v_y,X1),v_L)
& X1 != v_x ) )
| sP4 ),
inference(definition_folding,[],[f535,f559,f558,f557,f556,f555]) ).
fof(f565,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_x = X5
| v_x = X6 )
& ( v_x != 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_y),v_L)
| v_x = X5 )
& ( v_x != 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_y,X6),v_L)
| v_x = 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_x = X6
| v_x = X5 )
& ( v_x != 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_y),v_L)
| v_x = X6 )
& ( v_x != 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_y,X5),v_L)
| v_x = X5 )
& X5 != X6 )
| ~ sP4 ),
inference(nnf_transformation,[],[f559]) ).
fof(f566,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_x = X0
| v_x = X1 )
& ( v_x != 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_y),v_L)
| v_x = X0 )
& ( 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,v_y,X1),v_L)
| v_x = 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_x = X1
| v_x = X0 )
& ( 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,X1,v_y),v_L)
| v_x = X1 )
& ( v_x != 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_y,X0),v_L)
| v_x = X0 )
& X0 != X1 )
| ~ sP4 ),
inference(rectify,[],[f565]) ).
fof(f567,plain,
( ( ( v_x != sK7
| v_y != sK8 )
& ( ~ 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,sK8),v_L)
| v_x = sK7
| v_x = sK8 )
& ( v_x != sK8
| ~ 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_y),v_L)
| v_x = sK7 )
& ( v_x != 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_y,sK8),v_L)
| v_x = sK8 )
& ( v_x != sK8
| 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,sK8,sK7),v_L)
| v_x = sK8
| v_x = sK7 )
& ( v_x != 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,sK8,v_y),v_L)
| v_x = sK8 )
& ( v_x != sK8
| ~ 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_y,sK7),v_L)
| v_x = sK7 )
& sK7 != sK8 )
| ~ sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f566]) ).
fof(f568,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)
& X2 != v_x )
| 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_x
& X1 != v_x )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f558]) ).
fof(f569,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,sK9(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,sK9(X0,X1)),v_L)
& v_x != sK9(X0,X1) )
| sP1(X0,sK9(X0,X1),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_x
& X1 != v_x )
| ~ sP3(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f568]) ).
fof(f570,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_y,X3),v_L)
& v_x != X3 )
& 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,X0,v_y),v_L)
& X0 != v_x )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f557]) ).
fof(f571,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_y,X2),v_L)
& v_x != X2 )
& 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,X0,v_y),v_L)
& X0 != v_x )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f570]) ).
fof(f572,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,sK10(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_y,sK10(X0)),v_L)
& v_x != sK10(X0)
& 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,X0,v_y),v_L)
& X0 != v_x )
| ~ sP2(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f571]) ).
fof(f573,plain,
! [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,v_y),v_L)
& X2 = 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,X1,v_y),v_L) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f556]) ).
fof(f574,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,v_y),v_L)
& v_x = 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_y),v_L) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f573]) ).
fof(f575,plain,
! [X1] :
( ? [X4] :
( ( 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_y,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_x != 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_y),v_L)
& v_x = X4 ) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f555]) ).
fof(f576,plain,
! [X0] :
( ? [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_y,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,X1),v_L)
& v_x != 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_y),v_L)
& v_x = X1 ) )
| ~ sP0(X0) ),
inference(rectify,[],[f575]) ).
fof(f577,plain,
! [X0] :
( ( v_y != sK11(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_y,sK11(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,X0,sK11(X0)),v_L)
& v_x != sK11(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_y),v_L)
& v_x = sK11(X0) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f576]) ).
fof(f578,plain,
( sP3(sK12,sK13)
| sP2(sK12,sK13)
| ( sP0(sK13)
& v_x = 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,v_y,sK13),v_L)
& v_x != sK13 )
| sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f560]) ).
fof(f601,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,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(cnf_transformation,[],[f533]) ).
fof(f602,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(f603,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,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) ),
inference(cnf_transformation,[],[f533]) ).
fof(f604,plain,
( sK7 != sK8
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f605,plain,
( v_x != sK8
| ~ 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_y,sK7),v_L)
| v_x = sK7
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f606,plain,
( v_x != 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,sK8,v_y),v_L)
| v_x = sK8
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f607,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,sK8,sK7),v_L)
| v_x = sK8
| v_x = sK7
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f608,plain,
( v_x != sK8
| v_y != sK7
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f609,plain,
( v_x != 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_y,sK8),v_L)
| v_x = sK8
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f610,plain,
( v_x != sK8
| ~ 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_y),v_L)
| v_x = sK7
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f611,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,sK8),v_L)
| v_x = sK7
| v_x = sK8
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f612,plain,
( v_x != sK7
| v_y != sK8
| ~ sP4 ),
inference(cnf_transformation,[],[f567]) ).
fof(f615,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)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f569]) ).
fof(f617,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,sK9(X0,X1)),v_L)
| sP1(X0,sK9(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f569]) ).
fof(f618,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP1(X0,sK9(X0,X1),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,sK9(X0,X1)),v_L) ),
inference(cnf_transformation,[],[f569]) ).
fof(f620,plain,
! [X0,X1] :
( ~ sP2(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_y),v_L) ),
inference(cnf_transformation,[],[f572]) ).
fof(f621,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| v_x = X1 ),
inference(cnf_transformation,[],[f572]) ).
fof(f623,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_y,sK10(X0)),v_L)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f572]) ).
fof(f624,plain,
! [X0,X1] :
( ~ sP2(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,sK10(X0)),v_L) ),
inference(cnf_transformation,[],[f572]) ).
fof(f625,plain,
! [X2,X0,X1] :
( ~ sP1(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,X2,v_y),v_L) ),
inference(cnf_transformation,[],[f574]) ).
fof(f627,plain,
! [X2,X0,X1] :
( ~ sP1(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,v_y),v_L) ),
inference(cnf_transformation,[],[f574]) ).
fof(f631,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(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,X0,v_y),v_L)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f577]) ).
fof(f633,plain,
! [X0] :
( ~ sP0(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_y),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_y,sK11(X0)),v_L) ),
inference(cnf_transformation,[],[f577]) ).
fof(f637,plain,
( sP3(sK12,sK13)
| sP2(sK12,sK13)
| 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_y,sK13),v_L)
| sP4 ),
inference(cnf_transformation,[],[f578]) ).
fof(f639,plain,
( sP3(sK12,sK13)
| sP2(sK12,sK13)
| sP0(sK13)
| sP4 ),
inference(cnf_transformation,[],[f578]) ).
fof(f749,definition,
( spl15_1
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f753,definition,
( spl15_2
<=> v_x = sK13 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f754,plain,
( v_x = sK13
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f757,definition,
( spl15_3
<=> sP2(sK12,sK13) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f759,plain,
( sP2(sK12,sK13)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f761,definition,
( spl15_4
<=> sP3(sK12,sK13) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f763,plain,
( sP3(sK12,sK13)
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f766,definition,
( spl15_5
<=> 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_y,sK13),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f767,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_y,sK13),v_L)
| spl15_5 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f768,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_y,sK13),v_L)
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f769,plain,
( spl15_1
| spl15_5
| spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f637,f761,f757,f766,f749]) ).
fof(f776,definition,
( spl15_7
<=> sP0(sK13) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f778,plain,
( sP0(sK13)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f779,plain,
( spl15_1
| spl15_7
| spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f639,f761,f757,f776,f749]) ).
fof(f781,definition,
( spl15_8
<=> sK7 = sK8 ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f783,plain,
( sK7 != sK8
| spl15_8 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f784,plain,
( ~ spl15_1
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f604,f781,f749]) ).
fof(f786,definition,
( spl15_9
<=> v_x = sK7 ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f790,definition,
( spl15_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,v_y,sK7),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f792,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_y,sK7),v_L)
| spl15_10 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f794,definition,
( spl15_11
<=> v_x = sK8 ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f795,plain,
( v_x = sK8
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f797,plain,
( ~ spl15_1
| spl15_9
| ~ spl15_10
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f605,f794,f790,f786,f749]) ).
fof(f799,definition,
( spl15_12
<=> 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,sK8,v_y),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f801,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,sK8,v_y),v_L)
| spl15_12 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f802,plain,
( ~ spl15_1
| spl15_11
| ~ spl15_12
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f606,f786,f799,f794,f749]) ).
fof(f804,definition,
( spl15_13
<=> 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,sK8,sK7),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
fof(f806,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,sK8,sK7),v_L)
| spl15_13 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f807,plain,
( ~ spl15_1
| spl15_9
| spl15_11
| ~ spl15_13 ),
inference(avatar_split_clause,[],[f607,f804,f794,f786,f749]) ).
fof(f809,definition,
( spl15_14
<=> v_y = sK7 ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f811,plain,
( v_y != sK7
| spl15_14 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f812,plain,
( ~ spl15_1
| ~ spl15_14
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f608,f794,f809,f749]) ).
fof(f814,definition,
( spl15_15
<=> 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_y,sK8),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
fof(f816,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_y,sK8),v_L)
| spl15_15 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f817,plain,
( ~ spl15_1
| spl15_11
| ~ spl15_15
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f609,f786,f814,f794,f749]) ).
fof(f819,definition,
( spl15_16
<=> 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_y),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f821,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_y),v_L)
| spl15_16 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f822,plain,
( ~ spl15_1
| spl15_9
| ~ spl15_16
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f610,f794,f819,f786,f749]) ).
fof(f824,definition,
( spl15_17
<=> 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,sK8),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f826,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,sK8),v_L)
| spl15_17 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f827,plain,
( ~ spl15_1
| spl15_11
| spl15_9
| ~ spl15_17 ),
inference(avatar_split_clause,[],[f611,f824,f786,f794,f749]) ).
fof(f829,definition,
( spl15_18
<=> v_y = sK8 ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
fof(f831,plain,
( v_y != sK8
| spl15_18 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f832,plain,
( ~ spl15_1
| ~ spl15_18
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f612,f786,f829,f749]) ).
fof(f833,plain,
( v_x = sK13
| ~ spl15_3 ),
inference(resolution,[],[f621,f759]) ).
fof(f834,plain,
( spl15_2
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f833,f757,f753]) ).
fof(f843,plain,
( sP1(sK12,sK9(sK12,sK13),sK13)
| ~ 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,sK12,sK9(sK12,sK13)),v_L)
| ~ spl15_4 ),
inference(resolution,[],[f618,f763]) ).
fof(f845,definition,
( spl15_19
<=> 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,sK12,sK9(sK12,sK13)),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
fof(f847,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,sK12,sK9(sK12,sK13)),v_L)
| spl15_19 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f849,definition,
( spl15_20
<=> sP1(sK12,sK9(sK12,sK13),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_20])],[avatar_definition]) ).
fof(f850,plain,
( ~ sP1(sK12,sK9(sK12,sK13),sK13)
| spl15_20 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f851,plain,
( sP1(sK12,sK9(sK12,sK13),sK13)
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f852,plain,
( ~ spl15_19
| spl15_20
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f843,f761,f849,f845]) ).
fof(f888,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,sK8),v_L)
| sK7 = sK8
| spl15_13 ),
inference(resolution,[],[f806,f601]) ).
fof(f890,plain,
( sK7 = sK8
| spl15_13
| spl15_17 ),
inference(forward_subsumption_resolution,[],[f888,f826]) ).
fof(f891,plain,
( $false
| spl15_8
| spl15_13
| spl15_17 ),
inference(forward_subsumption_resolution,[],[f890,f783]) ).
fof(f892,plain,
( spl15_8
| spl15_13
| spl15_17 ),
inference(avatar_contradiction_clause,[],[f891]) ).
fof(f894,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_y,sK8),v_L)
| v_y = sK8
| spl15_12 ),
inference(resolution,[],[f801,f601]) ).
fof(f896,plain,
( v_y = sK8
| spl15_12
| spl15_15 ),
inference(forward_subsumption_resolution,[],[f894,f816]) ).
fof(f897,plain,
( $false
| spl15_12
| spl15_15
| spl15_18 ),
inference(forward_subsumption_resolution,[],[f896,f831]) ).
fof(f898,plain,
( spl15_12
| spl15_15
| spl15_18 ),
inference(avatar_contradiction_clause,[],[f897]) ).
fof(f902,plain,
( v_x != sK7
| spl15_8
| ~ spl15_11 ),
inference(superposition,[],[f783,f795]) ).
fof(f905,plain,
( sP2(sK12,v_x)
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_demodulation,[],[f759,f754]) ).
fof(f909,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,sK12,sK10(sK12)),v_L)
| ~ spl15_2
| ~ spl15_3 ),
inference(resolution,[],[f905,f624]) ).
fof(f910,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,sK12,v_y),v_L)
| ~ spl15_2
| ~ spl15_3 ),
inference(resolution,[],[f905,f620]) ).
fof(f926,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),sK12),v_L)
| sK12 = sK10(sK12)
| ~ spl15_2
| ~ spl15_3 ),
inference(resolution,[],[f909,f601]) ).
fof(f929,definition,
( spl15_23
<=> sK12 = sK10(sK12) ),
introduced(definition,[new_symbols(definition,[spl15_23])],[avatar_definition]) ).
fof(f931,plain,
( sK12 = sK10(sK12)
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f933,definition,
( spl15_24
<=> 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),sK12),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_24])],[avatar_definition]) ).
fof(f935,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),sK12),v_L)
| ~ spl15_24 ),
inference(avatar_component_clause,[],[f933]) ).
fof(f936,plain,
( spl15_23
| spl15_24
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f926,f757,f753,f933,f929]) ).
fof(f949,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_y,sK12),v_L)
| ~ sP2(sK12,X0) )
| ~ spl15_23 ),
inference(superposition,[],[f623,f931]) ).
fof(f952,definition,
( spl15_25
<=> ! [X0] : ~ sP2(sK12,X0) ),
introduced(definition,[new_symbols(definition,[spl15_25])],[avatar_definition]) ).
fof(f953,plain,
( ! [X0] : ~ sP2(sK12,X0)
| ~ spl15_25 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f956,definition,
( spl15_26
<=> 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_y,sK12),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_26])],[avatar_definition]) ).
fof(f957,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_y,sK12),v_L)
| spl15_26 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f958,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_y,sK12),v_L)
| ~ spl15_26 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f959,plain,
( spl15_25
| spl15_26
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f949,f929,f956,f952]) ).
fof(f990,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)
| ~ 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) ),
inference(resolution,[],[f603,f602]) ).
fof(f1007,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,sK12,v_y),v_L)
| ~ spl15_26 ),
inference(resolution,[],[f990,f958]) ).
fof(f1014,plain,
( $false
| ~ spl15_2
| ~ spl15_3
| ~ spl15_26 ),
inference(forward_subsumption_resolution,[],[f1007,f910]) ).
fof(f1015,plain,
( ~ spl15_2
| ~ spl15_3
| ~ spl15_26 ),
inference(avatar_contradiction_clause,[],[f1014]) ).
fof(f1016,plain,
( $false
| ~ spl15_2
| ~ spl15_3
| ~ spl15_25 ),
inference(resolution,[],[f953,f905]) ).
fof(f1017,plain,
( ~ spl15_2
| ~ spl15_3
| ~ spl15_25 ),
inference(avatar_contradiction_clause,[],[f1016]) ).
fof(f1022,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,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,v_y,X0),v_L) )
| spl15_26 ),
inference(resolution,[],[f957,f603]) ).
fof(f1023,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,sK12,v_y),v_L)
| v_y = sK12
| spl15_26 ),
inference(resolution,[],[f957,f601]) ).
fof(f1050,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_y,sK10(sK12)),v_L)
| ~ spl15_24
| spl15_26 ),
inference(resolution,[],[f1022,f935]) ).
fof(f1057,plain,
( ! [X0] : ~ sP2(sK12,X0)
| ~ spl15_24
| spl15_26 ),
inference(resolution,[],[f1050,f623]) ).
fof(f1070,plain,
( spl15_25
| ~ spl15_24
| spl15_26 ),
inference(avatar_split_clause,[],[f1057,f956,f933,f952]) ).
fof(f1075,definition,
( spl15_29
<=> v_y = sK12 ),
introduced(definition,[new_symbols(definition,[spl15_29])],[avatar_definition]) ).
fof(f1077,plain,
( v_y = sK12
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f1079,definition,
( spl15_30
<=> 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,sK12,v_y),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_30])],[avatar_definition]) ).
fof(f1081,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,sK12,v_y),v_L)
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f1082,plain,
( spl15_29
| spl15_30
| spl15_26 ),
inference(avatar_split_clause,[],[f1023,f956,f1079,f1075]) ).
fof(f1087,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,sK12,v_y),v_L)
| ~ spl15_20 ),
inference(resolution,[],[f851,f627]) ).
fof(f1090,plain,
( $false
| ~ spl15_20
| ~ spl15_30 ),
inference(forward_subsumption_resolution,[],[f1087,f1081]) ).
fof(f1091,plain,
( ~ spl15_20
| ~ spl15_30 ),
inference(avatar_contradiction_clause,[],[f1090]) ).
fof(f1092,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,sK9(sK12,sK13)),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,sK12,X0),v_L) )
| spl15_19 ),
inference(resolution,[],[f847,f603]) ).
fof(f1148,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,sK12,sK13),v_L)
| sP1(sK12,sK9(sK12,sK13),sK13)
| ~ sP3(sK12,sK13)
| spl15_19 ),
inference(resolution,[],[f1092,f617]) ).
fof(f1152,plain,
( sP1(sK12,sK9(sK12,sK13),sK13)
| ~ sP3(sK12,sK13)
| spl15_19 ),
inference(forward_subsumption_resolution,[],[f1148,f615]) ).
fof(f1153,plain,
( ~ sP3(sK12,sK13)
| spl15_19
| spl15_20 ),
inference(forward_subsumption_resolution,[],[f1152,f850]) ).
fof(f1154,plain,
( $false
| ~ spl15_4
| spl15_19
| spl15_20 ),
inference(forward_subsumption_resolution,[],[f1153,f763]) ).
fof(f1155,plain,
( ~ spl15_4
| spl15_19
| spl15_20 ),
inference(avatar_contradiction_clause,[],[f1154]) ).
fof(f1158,plain,
( sP3(v_y,sK13)
| ~ spl15_4
| ~ spl15_29 ),
inference(superposition,[],[f763,f1077]) ).
fof(f1174,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,sK13,v_y),v_L)
| ~ spl15_20 ),
inference(resolution,[],[f851,f625]) ).
fof(f1198,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_y,sK13),v_L)
| ~ spl15_20 ),
inference(resolution,[],[f1174,f990]) ).
fof(f1199,plain,
( ~ spl15_5
| ~ spl15_20 ),
inference(avatar_split_clause,[],[f1198,f849,f766]) ).
fof(f1203,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,sK13),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_y,X0),v_L) )
| spl15_5 ),
inference(resolution,[],[f767,f603]) ).
fof(f1205,plain,
( ~ sP3(v_y,sK13)
| spl15_5 ),
inference(resolution,[],[f767,f615]) ).
fof(f1206,plain,
( $false
| ~ spl15_4
| spl15_5
| ~ spl15_29 ),
inference(forward_subsumption_resolution,[],[f1205,f1158]) ).
fof(f1207,plain,
( ~ spl15_4
| spl15_5
| ~ spl15_29 ),
inference(avatar_contradiction_clause,[],[f1206]) ).
fof(f1211,plain,
( ! [X0] :
( ~ sP3(X0,sK13)
| ~ 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_y,X0),v_L) )
| spl15_5 ),
inference(resolution,[],[f1203,f615]) ).
fof(f1212,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_y,sK12),v_L)
| ~ spl15_4
| spl15_5 ),
inference(resolution,[],[f1211,f763]) ).
fof(f1213,plain,
( $false
| ~ spl15_4
| spl15_5
| ~ spl15_26 ),
inference(forward_subsumption_resolution,[],[f1212,f958]) ).
fof(f1214,plain,
( ~ spl15_4
| spl15_5
| ~ spl15_26 ),
inference(avatar_contradiction_clause,[],[f1213]) ).
fof(f1222,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,sK13,v_y),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_y,sK11(sK13)),v_L)
| ~ spl15_7 ),
inference(resolution,[],[f778,f633]) ).
fof(f1225,definition,
( spl15_33
<=> 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_y,sK11(sK13)),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_33])],[avatar_definition]) ).
fof(f1227,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_y,sK11(sK13)),v_L)
| spl15_33 ),
inference(avatar_component_clause,[],[f1225]) ).
fof(f1234,definition,
( spl15_35
<=> 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,sK13,v_y),v_L) ),
introduced(definition,[new_symbols(definition,[spl15_35])],[avatar_definition]) ).
fof(f1237,plain,
( ~ spl15_33
| spl15_35
| ~ spl15_7 ),
inference(avatar_split_clause,[],[f1222,f776,f1234,f1225]) ).
fof(f1250,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,sK13,v_y),v_L)
| ~ spl15_5 ),
inference(resolution,[],[f768,f990]) ).
fof(f1251,plain,
( ~ spl15_35
| ~ spl15_5 ),
inference(avatar_split_clause,[],[f1250,f766,f1234]) ).
fof(f1255,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(sK13)),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_y,X0),v_L) )
| spl15_33 ),
inference(resolution,[],[f1227,f603]) ).
fof(f1306,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_y,sK13),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,sK13,v_y),v_L)
| ~ sP0(sK13)
| spl15_33 ),
inference(resolution,[],[f1255,f631]) ).
fof(f1312,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_y,sK13),v_L)
| ~ sP0(sK13)
| spl15_33 ),
inference(forward_subsumption_resolution,[],[f1306,f990]) ).
fof(f1314,plain,
( ~ sP0(sK13)
| ~ spl15_5
| spl15_33 ),
inference(forward_subsumption_resolution,[],[f1312,f768]) ).
fof(f1316,plain,
( $false
| ~ spl15_5
| ~ spl15_7
| spl15_33 ),
inference(forward_subsumption_resolution,[],[f1314,f778]) ).
fof(f1317,plain,
( ~ spl15_5
| ~ spl15_7
| spl15_33 ),
inference(avatar_contradiction_clause,[],[f1316]) ).
fof(f1319,plain,
( ~ spl15_9
| spl15_8
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f902,f794,f781,f786]) ).
fof(f1330,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_y),v_L)
| v_y = sK7
| spl15_10 ),
inference(resolution,[],[f792,f601]) ).
fof(f1332,plain,
( v_y = sK7
| spl15_10
| spl15_16 ),
inference(forward_subsumption_resolution,[],[f1330,f821]) ).
fof(f1333,plain,
( $false
| spl15_10
| spl15_14
| spl15_16 ),
inference(forward_subsumption_resolution,[],[f1332,f811]) ).
fof(f1334,plain,
( spl15_10
| spl15_14
| spl15_16 ),
inference(avatar_contradiction_clause,[],[f1333]) ).
cnf(s2,plain,
( spl15_1
| spl15_3
| spl15_4
| spl15_5 ),
inference(sat_conversion,[],[f769]) ).
cnf(s4,plain,
( spl15_1
| spl15_3
| spl15_4
| spl15_7 ),
inference(sat_conversion,[],[f779]) ).
cnf(s5,plain,
( ~ spl15_1
| ~ spl15_8 ),
inference(sat_conversion,[],[f784]) ).
cnf(s6,plain,
( ~ spl15_1
| spl15_9
| ~ spl15_10
| ~ spl15_11 ),
inference(sat_conversion,[],[f797]) ).
cnf(s7,plain,
( ~ spl15_1
| ~ spl15_9
| spl15_11
| ~ spl15_12 ),
inference(sat_conversion,[],[f802]) ).
cnf(s8,plain,
( ~ spl15_1
| spl15_9
| spl15_11
| ~ spl15_13 ),
inference(sat_conversion,[],[f807]) ).
cnf(s9,plain,
( ~ spl15_1
| ~ spl15_11
| ~ spl15_14 ),
inference(sat_conversion,[],[f812]) ).
cnf(s10,plain,
( ~ spl15_1
| ~ spl15_9
| spl15_11
| ~ spl15_15 ),
inference(sat_conversion,[],[f817]) ).
cnf(s11,plain,
( ~ spl15_1
| spl15_9
| ~ spl15_11
| ~ spl15_16 ),
inference(sat_conversion,[],[f822]) ).
cnf(s12,plain,
( ~ spl15_1
| spl15_9
| spl15_11
| ~ spl15_17 ),
inference(sat_conversion,[],[f827]) ).
cnf(s13,plain,
( ~ spl15_1
| ~ spl15_9
| ~ spl15_18 ),
inference(sat_conversion,[],[f832]) ).
cnf(s14,plain,
( spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f834]) ).
cnf(s15,plain,
( ~ spl15_4
| ~ spl15_19
| spl15_20 ),
inference(sat_conversion,[],[f852]) ).
cnf(s17,plain,
( spl15_8
| spl15_13
| spl15_17 ),
inference(sat_conversion,[],[f892]) ).
cnf(s18,plain,
( spl15_12
| spl15_15
| spl15_18 ),
inference(sat_conversion,[],[f898]) ).
cnf(s20,plain,
( ~ spl15_2
| ~ spl15_3
| spl15_23
| spl15_24 ),
inference(sat_conversion,[],[f936]) ).
cnf(s23,plain,
( ~ spl15_23
| spl15_25
| spl15_26 ),
inference(sat_conversion,[],[f959]) ).
cnf(s25,plain,
( ~ spl15_2
| ~ spl15_3
| ~ spl15_26 ),
inference(sat_conversion,[],[f1015]) ).
cnf(s26,plain,
( ~ spl15_2
| ~ spl15_3
| ~ spl15_25 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s28,plain,
( ~ spl15_24
| spl15_25
| spl15_26 ),
inference(sat_conversion,[],[f1070]) ).
cnf(s29,plain,
( spl15_26
| spl15_29
| spl15_30 ),
inference(sat_conversion,[],[f1082]) ).
cnf(s32,plain,
( ~ spl15_20
| ~ spl15_30 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s35,plain,
( ~ spl15_4
| spl15_19
| spl15_20 ),
inference(sat_conversion,[],[f1155]) ).
cnf(s36,plain,
( ~ spl15_5
| ~ spl15_20 ),
inference(sat_conversion,[],[f1199]) ).
cnf(s37,plain,
( ~ spl15_4
| spl15_5
| ~ spl15_29 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s39,plain,
( ~ spl15_4
| spl15_5
| ~ spl15_26 ),
inference(sat_conversion,[],[f1214]) ).
cnf(s41,plain,
( ~ spl15_7
| ~ spl15_33
| spl15_35 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s42,plain,
( ~ spl15_5
| ~ spl15_35 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s49,plain,
( ~ spl15_5
| ~ spl15_7
| spl15_33 ),
inference(sat_conversion,[],[f1317]) ).
cnf(s50,plain,
( spl15_8
| ~ spl15_9
| ~ spl15_11 ),
inference(sat_conversion,[],[f1319]) ).
cnf(s52,plain,
( spl15_10
| spl15_14
| spl15_16 ),
inference(sat_conversion,[],[f1334]) ).
cnf(s53,plain,
( ~ spl15_5
| ~ spl15_7 ),
inference(rat,[],[s41,s42,s49]) ).
cnf(s54,plain,
( spl15_4
| spl15_3
| spl15_1 ),
inference(rat,[],[s53,s2,s4]) ).
cnf(s55,plain,
( spl15_20
| ~ spl15_4 ),
inference(rat,[],[s15,s35]) ).
cnf(s56,plain,
~ spl15_4,
inference(rat,[],[s29,s37,s39,s32,s36,s55]) ).
cnf(s57,plain,
( ~ spl15_2
| ~ spl15_3 ),
inference(rat,[],[s20,s23,s28,s26,s25]) ).
cnf(s58,plain,
~ spl15_3,
inference(rat,[],[s57,s14]) ).
cnf(s59,plain,
spl15_1,
inference(rat,[],[s54,s56,s58]) ).
cnf(s60,plain,
~ spl15_8,
inference(rat,[],[s5,s59]) ).
cnf(s61,plain,
( spl15_11
| spl15_9 ),
inference(rat,[],[s17,s8,s12,s59,s60]) ).
cnf(s62,plain,
spl15_9,
inference(rat,[],[s6,s52,s11,s9,s61,s59]) ).
cnf(s63,plain,
~ spl15_11,
inference(rat,[],[s50,s60,s62]) ).
cnf(s64,plain,
~ spl15_18,
inference(rat,[],[s13,s59,s62]) ).
cnf(s65,plain,
~ spl15_15,
inference(rat,[],[s10,s62,s59,s63]) ).
cnf(s66,plain,
~ spl15_12,
inference(rat,[],[s7,s62,s59,s63]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s18,s64,s65,s66]) ).
fof(f1335,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT115+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 23:46:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 4.13/1.54 % (2858692)Detected formulas, will run a generic FOF schedule.
% 4.13/1.54 % (2858703)dis-21_1_sil=8000:lcm=predicate:random_seed=1678470392: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)
% 4.13/1.54 % (2858697)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=831201191:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.13/1.54 % (2858698)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=108118260:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.13/1.54 % (2858703)Instruction limit reached!
% 4.13/1.54 % (2858703)------------------------------
% 4.13/1.54 % (2858703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858703)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858703)Termination reason: Instruction limit
% 4.13/1.54 % (2858703)Termination phase: Saturation
% 4.13/1.54 % (2858703)Time elapsed: 0.041 s
% 4.13/1.54 % (2858703)Peak memory usage: 90 MB
% 4.13/1.54 % (2858703)Instructions burned: 132 (million)
% 4.13/1.54 % (2858701)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3848153944:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.13/1.54 % (2858702)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2828422259:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.13/1.54 % (2858700)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1999128182:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.13/1.54 % (2858699)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=2582632520:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.13/1.54 % (2858701)Instruction limit reached!
% 4.13/1.54 % (2858701)------------------------------
% 4.13/1.54 % (2858701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858701)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858701)Termination reason: Instruction limit
% 4.13/1.54 % (2858701)Termination phase: Saturation
% 4.13/1.54 % (2858701)Time elapsed: 0.065 s
% 4.13/1.54 % (2858701)Peak memory usage: 88 MB
% 4.13/1.54 % (2858701)Instructions burned: 121 (million)
% 4.13/1.54 % (2858700)Instruction limit reached!
% 4.13/1.54 % (2858700)------------------------------
% 4.13/1.54 % (2858700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858700)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858700)Termination reason: Instruction limit
% 4.13/1.54 % (2858700)Termination phase: Saturation
% 4.13/1.54 % (2858700)Time elapsed: 0.066 s
% 4.13/1.54 % (2858700)Peak memory usage: 89 MB
% 4.13/1.54 % (2858700)Instructions burned: 109 (million)
% 4.13/1.54 % (2858711)lrs+10_1_sil=8000:sp=occurrence:random_seed=1859986026:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.13/1.54 % (2858702)Instruction limit reached!
% 4.13/1.54 % (2858702)------------------------------
% 4.13/1.54 % (2858702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858702)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858702)Termination reason: Instruction limit
% 4.13/1.54 % (2858702)Termination phase: Saturation
% 4.13/1.54 % (2858702)Time elapsed: 0.092 s
% 4.13/1.54 % (2858702)Peak memory usage: 90 MB
% 4.13/1.54 % (2858702)Instructions burned: 140 (million)
% 4.13/1.54 % (2858711)Instruction limit reached!
% 4.13/1.54 % (2858711)------------------------------
% 4.13/1.54 % (2858711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858711)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858711)Termination reason: Instruction limit
% 4.13/1.54 % (2858711)Termination phase: Saturation
% 4.13/1.54 % (2858711)Time elapsed: 0.088 s
% 4.13/1.54 % (2858711)Peak memory usage: 90 MB
% 4.13/1.54 % (2858711)Instructions burned: 286 (million)
% 4.13/1.54 % (2858713)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3665931090:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.13/1.54 % (2858712)lrs+10_1_sil=32000:urr=on:br=off:random_seed=453081721:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.13/1.54 % (2858715)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=1799100226:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.13/1.54 % (2858713)First to succeed.
% 4.13/1.54 % (2858713)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2858692"
% 4.13/1.54 % (2858716)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2589631377:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.13/1.54 % (2858712)Instruction limit reached!
% 4.13/1.54 % (2858712)------------------------------
% 4.13/1.54 % (2858712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858712)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858712)Termination reason: Instruction limit
% 4.13/1.54 % (2858712)Termination phase: Saturation
% 4.13/1.54 % (2858712)Time elapsed: 0.089 s
% 4.13/1.54 % (2858712)Peak memory usage: 91 MB
% 4.13/1.54 % (2858712)Instructions burned: 157 (million)
% 4.13/1.54 % (2858716)Also succeeded, but the first one will report.
% 4.13/1.54 % (2858715)Instruction limit reached!
% 4.13/1.54 % (2858715)------------------------------
% 4.13/1.54 % (2858715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (2858715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (2858715)CaDiCaL version: 2.1.3
% 4.13/1.54 % (2858715)Termination reason: Instruction limit
% 4.13/1.54 % (2858715)Termination phase: Saturation
% 4.13/1.54 % (2858715)Time elapsed: 0.141 s
% 4.13/1.54 % (2858715)Peak memory usage: 91 MB
% 4.13/1.54 % (2858715)Instructions burned: 249 (million)
% 4.13/1.54 % (2858721)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3626951773:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.13/1.54 % (2858713)Refutation found. Thanks to Tanya!
% 4.13/1.54 % SZS status Theorem for theBenchmark
% 4.13/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.11/1.64 % (2858713)------------------------------
% 5.11/1.64 % (2858713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.64 % (2858713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.64 % (2858713)CaDiCaL version: 2.1.3
% 5.11/1.64 % (2858713)Termination reason: Refutation
% 5.11/1.64 % (2858713)Time elapsed: 0.027 s
% 5.11/1.64 % (2858713)Peak memory usage: 90 MB
% 5.11/1.64 % (2858713)Instructions burned: 38 (million)
% 5.11/1.64 % (2858713)------------------------------
% 5.11/1.64 % (2858713)------------------------------
% 5.11/1.64 % (2858692)Success in time 0.671 s
% 5.11/1.64 % Vampire exiting
%------------------------------------------------------------------------------