%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL121-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:00:52 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 57
% Syntax : Number of formulae : 128 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 754 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1151 ( 555 ~; 528 |; 0 &)
% ( 68 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 485 ( 447 !; 0 ?; 485 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(c_Comb_Odiamond__strip__lemmaE__1_type,type,
c_Comb_Odiamond__strip__lemmaE__1: ( $i * $i * $i * $i ) > $i ).
tff(v_z_type,type,
v_z: $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(v_xaa_type,type,
v_xaa: $i ).
tff(v_ya_type,type,
v_ya: $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_Comb_Odiamond_type,type,
c_Comb_Odiamond: ( $i * $i ) > $o ).
tff(1,plain,
^ [V_U: $i] :
refl(( ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_U: $i] :
rewrite(( ( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_U: $i] :
( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_U: $i] :
( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(7,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(13,plain,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
( ( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
rewrite(( ( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
( ( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
tff(24,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[33,27,13,17]) ).
tff(35,plain,
^ [V_U: $i] :
refl(( ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V_U: $i] :
rewrite(( ( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V_U: $i] :
( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V_U: $i] :
( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(41,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[47,44,34]) ).
tff(49,plain,
( c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(51,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( c_Comb_Odiamond(v_r,t_a)
<=> c_Comb_Odiamond(v_r,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(54,plain,
c_Comb_Odiamond(v_r,t_a),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
refl(( ( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
<=> ( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) )),
( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
rewrite(( ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) )),
( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
tff(61,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) )
<=> ( ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[70,64,54,51,48]) ).
tff(72,plain,
^ [V_U: $i] :
refl(( ( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(76,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[81,78,71]) ).
tff(83,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[88,27,17,82]) ).
tff(90,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_y,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[92,10,34]) ).
tff(94,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_xaa),v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[99,27,93,89]) ).
tff(101,plain,
^ [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
refl(( ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) )),
( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) )),
rewrite(( ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) )),
( ( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
tff(107,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ( ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [V_x: $i,V_y_H: $i,V_r: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a)
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) )
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_x(v_x(v_xaa)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[116,110,54,51,48]) ).
tff(118,plain,
^ [V_r: $i,T_a: $i,V_p: $i] :
refl(( ( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
<=> ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
tff(122,plain,
! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ( ~ ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [V_r: $i,T_a: $i,V_p: $i] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(v_x(v_xaa)),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_x(v_xaa)),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,124,117,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL121-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 12:18:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------