%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV886-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:36:17 AM UTC 2025
% Result : Unsatisfiable 0.37s 0.59s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 31
% Syntax : Number of formulae : 71 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 201 ( 95 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 209 ( 85 ~; 100 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 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 : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 131 ( 117 !; 0 ?; 131 :)
% 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_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $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(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(1,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(2,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,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)],[2,1]) ).
tff(4,plain,
^ [V_i: $i,V_j: $i] :
refl(( ( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) )
<=> ( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) )
<=> ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) )
<=> ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
tff(8,plain,
! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,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_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(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(v_na),tc_nat) ) )
<=> ( ~ ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,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_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(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(v_na),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,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_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(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(v_na),tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_i: $i,V_j: $i] :
( ~ c_lessequals(V_i,V_j,tc_nat)
| ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,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_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(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(v_na),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(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(v_na),tc_nat),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_HOL_Oplus__class_Oplus(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(v_na),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat),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(monotonicity,[status(thm)],[15]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
tff(21,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)],[20,19]) ).
tff(22,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)],[21]) ).
tff(23,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)],[22,18]) ).
tff(24,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_HOL_Oplus__class_Oplus(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(v_na),tc_nat)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat),v_na,tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat),v_na,tc_nat),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)) = c_Suc(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat)),
inference(monotonicity,[status(thm)],[14]) ).
tff(27,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_Suc(c_HOL_Oplus__class_Oplus(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(v_na),tc_nat)),c_Suc(v_na),tc_nat),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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(32,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)],[31]) ).
tff(33,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/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
tff(34,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)],[33,32]) ).
tff(35,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)],[34,30]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,29]) ).
tff(38,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(39,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(40,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)],[39,38]) ).
tff(41,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)],[40,37,3]) ).
tff(42,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)],[41]) ).
tff(43,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(44,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(45,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)],[44,43]) ).
tff(46,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(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( c_Finite__Set_Ofinite(v_G,t_a)
<=> c_Finite__Set_Ofinite(v_G,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
c_Finite__Set_Ofinite(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(49,plain,
c_Finite__Set_Ofinite(v_G,t_a),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,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(51,axiom,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(52,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
refl(( ( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(54,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[53]) ).
tff(55,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(56,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_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(57,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_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[56]) ).
tff(58,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/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
tff(59,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[58,57]) ).
tff(60,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[59,55]) ).
tff(61,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[60]) ).
tff(62,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[61,54]) ).
tff(63,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(64,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(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)],[64,63]) ).
tff(66,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)],[65,62,52,49]) ).
tff(67,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)],[66,46,42,27,25,16]) ).
tff(68,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(69,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(70,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)],[69,68]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV886-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 11:01:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.37/0.59 % SZS status Unsatisfiable
% 0.37/0.59 % SZS output start Proof
% See solution above
% 0.37/0.62 % E exiting
%------------------------------------------------------------------------------