%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT105+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:29 AM UTC 2025
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 36 equ)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 202 ( 52 ~; 53 |; 50 &)
% ( 26 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 86 ( 82 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_member_type,type,
c_member: ( $i * $i * $i ) > $o ).
tff(v_L_type,type,
v_L: $i ).
tff(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: ( $i * $i * $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_Relation_Otrans_type,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(3,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [B_x: $i,B_y: $i] :
trans(monotonicity(rewrite(( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_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,B_y,B_x),v_L) )
<=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_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,B_y,B_x),v_L) ) )),
( ( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) )),
rewrite(( ( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )),
( ( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ),
inference(monotonicity,[status(thm)],[6,5]) ).
tff(8,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ),
inference(transitivity,[status(thm)],[7,3]) ).
tff(9,plain,
^ [B_x: $i,B_y: $i] :
rewrite(( ( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) )
<=> ( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) )
<=> ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ),
inference(monotonicity,[status(thm)],[6,10]) ).
tff(12,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ),
inference(transitivity,[status(thm)],[11,3]) ).
tff(13,plain,
( ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) )
<=> ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x = B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) ),
inference(monotonicity,[status(thm)],[12,8]) ).
tff(14,plain,
( ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,plain,
( ~ ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,axiom,
~ ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_y,B_x),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_x,B_y),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [B_x: $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,B_x,B_x),v_L)
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_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,B_x,B_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,B_y,B_x),v_L) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(18,plain,
$false,
inference(modus_ponens,[status(thm)],[17,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT105+1 : TPTP v9.0.0. Released v5.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:46:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start Proof
% See solution above
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------