%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV885-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:36:16 AM UTC 2025
% Result : Unsatisfiable 0.52s 0.72s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 41
% Syntax : Number of formulae : 92 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 335 ( 84 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 392 ( 164 ~; 189 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 236 ( 210 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_na_type,type,
v_na: $i ).
tff(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [V_n: $i,V_m: $i] :
refl(( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
tff(5,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
<=> c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(12,plain,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_n: $i,V_m: $i] :
refl(( ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [V_n: $i,V_m: $i] :
rewrite(( ( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
tff(19,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)),
inference(unit_resolution,[status(thm)],[25,22,12]) ).
tff(27,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) )
<=> ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(30,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
c_Suc(c_Finite__Set_Ocard(v_G,t_a)) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
<=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(36,plain,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
rewrite(( ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
tff(43,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(53,plain,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Finite__Set_Ofinite(V_A,T_a) ) )),
( ( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) )),
( ( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
tff(60,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_Finite__Set_Ofinite(v_G,t_a) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_Finite__Set_Ofinite(v_G,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_Finite__Set_Ofinite(v_G,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_Finite__Set_Ofinite(v_G,t_a) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
c_Finite__Set_Ofinite(v_G,t_a),
inference(unit_resolution,[status(thm)],[66,63,53,50]) ).
tff(68,plain,
( ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
<=> ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(70,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
rewrite(( ( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
tff(77,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ~ c_Finite__Set_Ofinite(v_G,t_a)
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) )
<=> ( c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(unit_resolution,[status(thm)],[86,80,70,67]) ).
tff(88,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(transitivity,[status(thm)],[87,33,27,9]) ).
tff(89,plain,
( ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
<=> ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(91,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
$false,
inference(unit_resolution,[status(thm)],[91,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV885-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 10:59:33 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.52/0.72 % SZS status Unsatisfiable
% 0.52/0.72 % SZS output start Proof
% See solution above
% 0.61/0.77 % E exiting
%------------------------------------------------------------------------------