%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT028-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:24:22 AM UTC 2025
% Result : Unsatisfiable 16.24s 16.45s
% Output : Proof 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 59
% Syntax : Number of formulae : 147 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 586 ( 108 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 731 ( 311 ~; 357 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 410 ( 374 !; 0 ?; 410 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
tff(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_b_type,type,
v_b: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(3,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_1: $i,T_2: $i] :
refl(( ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
tff(8,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| ~ class_Lattices_Olattice(tc_bool)
| class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[16,10,3]) ).
tff(18,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
tff(22,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
<=> c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).
tff(32,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).
tff(39,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
tff(53,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_lessequals(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,
inference(unit_resolution,[status(thm)],[59,56,46,17]) ).
tff(61,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(symmetry,[status(thm)],[60]) ).
tff(64,plain,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(transitivity,[status(thm)],[63,62,29]) ).
tff(65,plain,
c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [T_b: $i,V_r: $i,T_a: $i,V_s: $i] :
refl(( ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) )
<=> ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) )
<=> ! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) )
<=> ! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
tff(71,plain,
! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [T_b: $i,V_r: $i,T_a: $i,V_s: $i] : ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) )
| ( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(transitivity,[status(thm)],[76,66]) ).
tff(78,plain,
( c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
<=> c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
<=> c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
^ [V_x: $i] :
refl(( ( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(84,plain,
! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unit_resolution,[status(thm)],[89,32,86]) ).
tff(91,plain,
^ [V_x: $i,V_L: $i,V_y: $i] :
refl(( ( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
^ [V_x: $i,V_L: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_x = V_y ) )
<=> ( ( V_x = V_y )
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
( ( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ( V_x = V_y )
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
rewrite(( ( ( V_x = V_y )
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
( ( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [V_x: $i,V_L: $i,V_y: $i] :
( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,axiom,
! [V_x: $i,V_L: $i,V_y: $i] :
( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
tff(97,plain,
! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( v_a != v_b )
<=> ( v_a != v_b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
v_a != v_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
tff(103,plain,
v_a != v_b,
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ( v_a = v_b )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [V_x: $i,V_L: $i,V_y: $i] :
( ( V_x = V_y )
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_a = v_b )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unit_resolution,[status(thm)],[109,32,103,100,90]) ).
tff(111,plain,
^ [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
<=> ( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
<=> ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
<=> ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
tff(115,plain,
! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ( c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [T_b: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) )
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unit_resolution,[status(thm)],[123,117,110]) ).
tff(125,plain,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(modus_ponens,[status(thm)],[124,79]) ).
tff(126,plain,
( c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
<=> c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(127,plain,
( c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
<=> c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
^ [V_L: $i] :
refl(( ( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
^ [V_L: $i] :
rewrite(( ( c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [V_L: $i] :
( c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [V_L: $i] :
( c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
tff(134,plain,
! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
( ( ~ ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [V_L: $i] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[140,32,137]) ).
tff(142,plain,
c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(modus_ponens,[status(thm)],[141,127]) ).
tff(143,plain,
( ( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [V_x: $i] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(unit_resolution,[status(thm)],[145,86]) ).
tff(147,plain,
$false,
inference(unit_resolution,[status(thm)],[146,142,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SCT028-1 : TPTP v9.0.0. Released v4.1.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:34:40 EDT 2025
% 0.13/0.36 % CPUTime :
% 16.24/16.45 % SZS status Unsatisfiable
% 16.24/16.45 % SZS output start Proof
% See solution above
% 16.33/16.56 % E exiting
%------------------------------------------------------------------------------