%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV578-1 : 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 05:35:45 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.77s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 38 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 46 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 118 ( 55 ~; 51 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 88 ( 78 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(v_m_type,type,
v_m: $i ).
tff(v_f_type,type,
v_f: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(c_Suc_type,type,
c_Suc: $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i ) > $i ).
tff(1,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_a)
<=> class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n))
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less_0) ).
tff(6,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
refl(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
<=> ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
<=> ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
rewrite(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n)) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n)) )
<=> ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
tff(13,plain,
! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n))
| ( c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) ) )
<=> ( ~ ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n))
| ( c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n))
| ( c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_n: $i,V_f: $i,T_a: $i,V_m: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ( c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a)) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n))
| ( c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) = c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [V_l: $i,V_u: $i] :
refl(( ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) )
<=> ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) )
<=> ! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) )
<=> ! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
tff(26,plain,
! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [V_l: $i,V_u: $i] : ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat) )
| ( c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a) = c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) = c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(transitivity,[status(thm)],[33,21]) ).
tff(35,plain,
( ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) )
<=> ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(37,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV578-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 10:25:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.61/0.77 % SZS status Unsatisfiable
% 0.61/0.77 % SZS output start Proof
% See solution above
% 0.61/0.84 % E exiting
%------------------------------------------------------------------------------