%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW358+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:36:52 AM UTC 2025
% Result : Theorem 16.46s 16.64s
% Output : Proof 16.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 61 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 304 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 375 ( 156 ~; 151 |; 0 &)
% ( 33 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 170 ( 150 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i ) > $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
tff(1,plain,
( ( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) )
<=> ( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(3,plain,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) = hAPP(c_Finite__Set_Ocard(t_a),v_G),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G)) = hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(monotonicity,[status(thm)],[5,3]) ).
tff(7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(11,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
^ [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
refl(( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
<=> ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
<=> ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
^ [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
rewrite(( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) )
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) )
<=> ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
tff(18,plain,
! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) )
<=> ( ~ ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_h_2: $i,T_c: $i,V_F_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(unit_resolution,[status(thm)],[24,21,11]) ).
tff(26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(28,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [V_A_2: $i,V_B_2: $i,T_b: $i] :
refl(( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [V_A_2: $i,V_B_2: $i,T_b: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) )
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )),
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) )
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) )),
rewrite(( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )),
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) )
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
tff(35,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) )
<=> ( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
inference(unit_resolution,[status(thm)],[41,38,28,25]) ).
tff(43,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))),
inference(modus_ponens,[status(thm)],[42,8]) ).
tff(44,plain,
( ( v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) )
<=> ( v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(46,plain,
v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [V_A_2: $i,V_B_2: $i,T_b: $i] :
refl(( ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
<=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [V_A_2: $i,V_B_2: $i,T_b: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ( V_A_2 = V_B_2 ) ) )),
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) )
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ( V_A_2 = V_B_2 ) ) ) )),
rewrite(( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ( V_A_2 = V_B_2 ) ) )
<=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )),
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) )
<=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )),
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) ) )
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) )),
rewrite(( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )
<=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )),
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) ) )
<=> ( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) ) )
<=> ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> ( V_A_2 = V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
tff(53,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
| ( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) )
<=> ( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
| ( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
| ( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( V_A_2 = V_B_2 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) )
| ( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))),
inference(unit_resolution,[status(thm)],[59,56,28,46,25]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW358+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:32:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 16.46/16.64 % SZS status Theorem
% 16.46/16.64 % SZS output start Proof
% See solution above
% 16.94/17.10 % E exiting
%------------------------------------------------------------------------------