%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT071-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:25 AM UTC 2025
% Result : Unsatisfiable 0.54s 0.69s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 62 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 246 ( 53 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 317 ( 147 ~; 141 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 221 ( 195 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1_type,type,
c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1: ( $i * $i ) > $i ).
tff(c_Fun_Obij__betw_type,type,
c_Fun_Obij__betw: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)
<=> c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__indi_0) ).
tff(3,plain,
c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_a: $i,V_M: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
<=> ( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
<=> ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
<=> ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [T_a: $i,V_M: $i] :
rewrite(( ( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat)
| ~ c_Finite__Set_Ofinite(V_M,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T_a: $i,V_M: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat)
| ~ c_Finite__Set_Ofinite(V_M,T_a) )
<=> ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T_a: $i,V_M: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat)
| ~ c_Finite__Set_Ofinite(V_M,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__bij__betw__finite__nat_0) ).
tff(10,plain,
! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) )
<=> ( ~ ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T_a: $i,V_M: $i] :
( ~ c_Finite__Set_Ofinite(V_M,T_a)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M,T_a),V_M,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_M,T_a),tc_nat),T_a,tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
<=> ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B )
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) )
<=> ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B )
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B )
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
tff(24,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
<=> ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) )
<=> ( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
tff(38,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) )
| ~ c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat),
inference(unit_resolution,[status(thm)],[44,41,17]) ).
tff(46,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(48,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [V_h: $i] :
refl(( ( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
<=> ( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
<=> ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
<=> ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [V_h: $i] :
trans(monotonicity(rewrite(( ( ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) )
<=> ( ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) )),
( ( ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| v_thesis____ )
<=> ( ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| v_thesis____ ) )),
rewrite(( ( ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| v_thesis____ )
<=> ( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) )),
( ( ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| v_thesis____ )
<=> ( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_h: $i] :
( ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| v_thesis____ )
<=> ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [V_h: $i] :
( ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) )
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
tff(55,plain,
! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
| v_thesis____
| ~ c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
<=> ( ~ ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
| v_thesis____
| ~ c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
| v_thesis____
| ~ c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [V_h: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(V_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) )
| v_thesis____
| ~ c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,58,48,45,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SCT071-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 03:45:49 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.54/0.69 % SZS status Unsatisfiable
% 0.54/0.69 % SZS output start Proof
% See solution above
% 0.54/0.74 % E exiting
%------------------------------------------------------------------------------