%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 : Fri Sep 25 02:40:45 PM UTC 2026
% Result : Theorem 10.44s 2.27s
% Output : CNFRefutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 69 ( 4 unt; 1 def)
% Number of atoms : 305 ( 51 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 382 ( 146 ~; 159 |; 64 &)
% ( 4 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 98 ( 0 sgn 80 !; 18 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f523,conjecture,
( ( ! [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) ) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,X1,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,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f524,negated_conjecture,
~ ( ( ! [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) ) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,X1,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,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(negated_conjecture,[status(cth)],[f523]) ).
fof(f525,plain,
~ ( ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,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) ) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(rectify,[],[f524]) ).
fof(f527,plain,
( ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(ennf_transformation,[],[f525]) ).
fof(f528,plain,
( ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(flattening,[],[f527]) ).
fof(f759,plain,
( ( sP0
| ( ! [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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ~ sP0
| ? [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,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) )
| ? [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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(nnf_transformation,[],[f752]) ).
fof(f760,plain,
( ( sP0
| ( ! [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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ~ sP0
| ? [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,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) )
| ? [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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(flattening,[],[f759]) ).
fof(f761,plain,
( ( sP0
| ( ! [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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ~ sP0
| ? [X1,X2] :
( 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,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,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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(rectify,[],[f760]) ).
fof(f762,plain,
( ( sP0
| ( ! [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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ~ sP0
| ( sK6 != 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,sK7,sK6),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,sK6,sK7),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,sK5,sK5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f761]) ).
fof(f871,plain,
! [X4,X5] :
( sP0
| 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) ),
inference(cnf_transformation,[],[f762]) ).
fof(f872,plain,
! [X3] :
( sP0
| ~ c_member(tc_prod(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,[],[f762]) ).
fof(f873,plain,
( sP0
| c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f762]) ).
fof(f874,plain,
( ~ sP0
| sK6 != 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,sK5,sK5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f762]) ).
fof(f875,plain,
( ~ sP0
| ~ c_member(tc_prod(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)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f762]) ).
fof(f876,plain,
( ~ sP0
| ~ c_member(tc_prod(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)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f762]) ).
tcf(c_56,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK6,sK7),v_L) ),
inference(cnf_transformation,[],[f876]) ).
tcf(c_57,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK7,sK6),v_L) ),
inference(cnf_transformation,[],[f875]) ).
tcf(c_58,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ( sK6 != sK7 ) ),
inference(cnf_transformation,[],[f874]) ).
tcf(c_59,negated_conjecture,
( sP0
| c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f873]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( sP0
| ~ c_member(tc_prod(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) ),
inference(cnf_transformation,[],[f872]) ).
tcf(c_61,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| c_member(tc_prod(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)
| c_member(tc_prod(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 = X1 ) ),
inference(cnf_transformation,[],[f871]) ).
fof(f751,definition,
( sP0
<=> ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f752,plain,
( sP0
<~> ( ! [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,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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(definition_folding,[],[f528,f751]) ).
fof(f755,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ? [X1,X2] :
( 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,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,X2,X1),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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ) ),
inference(nnf_transformation,[],[f751]) ).
fof(f756,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( 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,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,X2,X1),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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ? [X1,X2] :
( 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,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,X2,X1),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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ) ),
inference(flattening,[],[f755]) ).
fof(f757,plain,
( ( ~ sP0
| ( ! [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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ? [X1,X2] :
( 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,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,X2,X1),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)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ) ),
inference(rectify,[],[f756]) ).
fof(f758,plain,
( ( ~ sP0
| ( ! [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) )
& ! [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)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) )
& ( ( sK3 != sK4
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK4),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,sK4,sK3),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,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f757]) ).
fof(f865,plain,
! [X4,X5] :
( ~ sP0
| 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(cnf_transformation,[],[f758]) ).
fof(f866,plain,
! [X3] :
( ~ sP0
| ~ c_member(tc_prod(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,[],[f758]) ).
fof(f867,plain,
( ~ sP0
| c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f758]) ).
fof(f868,plain,
( sK3 != sK4
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ),
inference(cnf_transformation,[],[f758]) ).
fof(f869,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,sK3,sK4),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,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ),
inference(cnf_transformation,[],[f758]) ).
fof(f870,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,sK4,sK3),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,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP0 ),
inference(cnf_transformation,[],[f758]) ).
tcf(c_50,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK4,sK3),v_L) ),
inference(cnf_transformation,[],[f870]) ).
tcf(c_51,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK3,sK4),v_L) ),
inference(cnf_transformation,[],[f869]) ).
tcf(c_52,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ( sK4 != sK3 ) ),
inference(cnf_transformation,[],[f868]) ).
tcf(c_53,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ sP0 ),
inference(cnf_transformation,[],[f867]) ).
tcf(c_54,plain,
! [X0: $i] :
( ~ sP0
| ~ c_member(tc_prod(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) ),
inference(cnf_transformation,[],[f866]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( c_member(tc_prod(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)
| c_member(tc_prod(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 = X1 )
| ~ sP0 ),
inference(cnf_transformation,[],[f865]) ).
tcf(c_652,negated_conjecture,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_53]) ).
tcf(c_656,negated_conjecture,
! [X0: $i] : ~ c_member(tc_prod(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),
inference(global_subsumption_just,[status(thm)],[c_60,c_60,c_54]) ).
tcf(c_659,plain,
! [X0: $i] : ~ c_member(tc_prod(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),
inference(global_subsumption_just,[status(thm)],[c_54,c_656]) ).
tcf(c_667,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),v_L)
| ( sK4 != sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_52,c_652]) ).
tcf(c_669,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ( sK6 != sK7 ) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_59,c_53,c_58]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i] :
( ( 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(global_subsumption_just,[status(thm)],[c_61,c_61,c_55]) ).
tcf(c_672,negated_conjecture,
! [X0: $i,X1: $i] :
( c_member(tc_prod(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)
| c_member(tc_prod(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 = X1 ) ),
inference(renaming,[status(thm)],[c_671]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i] :
( c_member(tc_prod(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)
| c_member(tc_prod(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 = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_672]) ).
tcf(c_680,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),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,sK3,sK4),v_L) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_59,c_53,c_51]) ).
tcf(c_682,plain,
( sP0
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK2),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,sK4,sK3),v_L) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_59,c_53,c_50]) ).
tcf(c_684,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ~ c_member(tc_prod(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) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_59,c_53,c_57]) ).
tcf(c_686,negated_conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK5),v_L)
| ~ sP0
| ~ c_member(tc_prod(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) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_59,c_53,c_56]) ).
tcf(c_1544,plain,
( sP0
| ( sK4 != sK3 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_667,c_659]) ).
tcf(c_1545,plain,
( sP0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK3),v_L) ),
inference(backward_subsumption_resolution,[status(thm)],[c_682,c_659]) ).
tcf(c_1546,plain,
( sP0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK4),v_L) ),
inference(backward_subsumption_resolution,[status(thm)],[c_680,c_659]) ).
tcf(c_1547,plain,
( ~ sP0
| ( sK6 != sK7 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_669,c_659]) ).
tcf(c_1548,plain,
( ~ sP0
| ~ c_member(tc_prod(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) ),
inference(backward_subsumption_resolution,[status(thm)],[c_686,c_659]) ).
tcf(c_1549,plain,
( ~ sP0
| ~ c_member(tc_prod(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) ),
inference(backward_subsumption_resolution,[status(thm)],[c_684,c_659]) ).
tcf(c_3750,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)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK4),v_L) ),
inference(resolution,[status(thm)],[c_1546,c_1549]) ).
tcf(c_3757,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)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK4),v_L) ),
inference(resolution,[status(thm)],[c_1546,c_1548]) ).
tcf(c_3764,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,sK3,sK4),v_L)
| ( sK6 != sK7 ) ),
inference(resolution,[status(thm)],[c_1546,c_1547]) ).
tcf(c_3771,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)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK3),v_L) ),
inference(resolution,[status(thm)],[c_1545,c_1549]) ).
tcf(c_3778,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)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK3),v_L) ),
inference(resolution,[status(thm)],[c_1545,c_1548]) ).
tcf(c_3785,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,sK4,sK3),v_L)
| ( sK6 != sK7 ) ),
inference(resolution,[status(thm)],[c_1545,c_1547]) ).
tcf(c_3792,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)
| ( sK4 != sK3 ) ),
inference(resolution,[status(thm)],[c_1544,c_1549]) ).
tcf(c_3799,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)
| ( sK4 != sK3 ) ),
inference(resolution,[status(thm)],[c_1544,c_1548]) ).
tcf(c_3806,plain,
( ( sK6 != sK7 )
| ( sK4 != sK3 ) ),
inference(resolution,[status(thm)],[c_1544,c_1547]) ).
tcf(c_12955,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,sK3,sK4),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,sK4,sK3),v_L)
| ( sK4 = sK3 ) ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_16025,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)
| c_member(tc_prod(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)
| ( sK6 = sK7 ) ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_16029,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16025,c_12955,c_3806,c_3799,c_3792,c_3785,c_3778,c_3771,c_3764,c_3757,c_3750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:45:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 10.44/2.27 % SZS status Started for theBenchmark.p
% 10.44/2.27 % SZS status Theorem for theBenchmark.p
% 10.44/2.27
% 10.44/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.44/2.27
% 10.44/2.27 % ------ iProver source info
% 10.44/2.27
% 10.44/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.44/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.44/2.27 % git: non_committed_changes: false
% 10.44/2.27
% 10.44/2.27 % ------ Parsing...
% 10.44/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.44/2.27
% 10.44/2.27 % ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.44/2.27
% 10.44/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.44/2.27
% 10.44/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.44/2.27 % ------ Proving...
% 10.44/2.27 % ------ Problem Properties
% 10.44/2.27
% 10.44/2.27 %
% 10.44/2.27 % clauses 276
% 10.44/2.27 % conjectures 0
% 10.44/2.27 % EPR 11
% 10.44/2.27 % Horn 220
% 10.44/2.27 % unary 78
% 10.44/2.27 % binary 104
% 10.44/2.27 % lits 584
% 10.44/2.27 % lits eq 129
% 10.44/2.27 % fd_pure 0
% 10.44/2.27 % fd_pseudo 0
% 10.44/2.27 % fd_cond 0
% 10.44/2.27 % fd_pseudo_cond 37
% 10.44/2.27 % AC symbols 0
% 10.44/2.27
% 10.44/2.27 % ------ Schedule dynamic 5 is on
% 10.44/2.27
% 10.44/2.27 % ------ no conjectures: strip conj schedule
% 10.44/2.27
% 10.44/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.44/2.27
% 10.44/2.27
% 10.44/2.27 % ------
% 10.44/2.27 % Current options:
% 10.44/2.27 % ------
% 10.44/2.27
% 10.44/2.27
% 10.44/2.27 %
% 10.44/2.27
% 10.44/2.27 % ------ Proving...
% 10.44/2.27 %
% 10.44/2.27
% 10.44/2.27 % SZS status Theorem for theBenchmark.p
% 10.44/2.27
% 10.44/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.44/2.27
% 10.44/2.27
%------------------------------------------------------------------------------