%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV580-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:35:46 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 164 ( 78 ~; 74 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 2 ( 2 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; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% 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(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(1,plain,
( class_Orderings_Olinorder(tc_nat)
<=> class_Orderings_Olinorder(tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
tff(3,plain,
class_Orderings_Olinorder(tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_l: $i,V_u: $i,T_a: $i] :
refl(( ( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
<=> ( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
<=> ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
<=> ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_l: $i,V_u: $i,T_a: $i] :
rewrite(( ( ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) )
| ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a) )
<=> ( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) )
| ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a) )
<=> ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_l: $i,V_u: $i,T_a: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) )
| ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I3_J_0) ).
tff(10,plain,
! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
<=> c_HOL_Oord__class_Oless(v_m,v_n,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less_0) ).
tff(16,plain,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) )
<=> ( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_l,V_u,T_a)
| ~ class_Orderings_Olinorder(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,T_a),tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a) ) )
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),
inference(unit_resolution,[status(thm)],[22,16,13,3]) ).
tff(24,plain,
c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),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)],[25]) ).
tff(27,plain,
( ( c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),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) )
<=> ( c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),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(28,axiom,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),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(29,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),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)],[28,27]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV580-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:25:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.19/0.55 % E exiting
%------------------------------------------------------------------------------