TSTP Solution File: SWV693-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV693-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Thu Sep 29 15:24:05 EDT 2022
% Result : Unsatisfiable 0.92s 0.97s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 38
% Syntax : Number of formulae : 54 ( 12 unt; 25 typ; 0 def)
% Number of atoms : 117 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 164 ( 78 ~; 74 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 19 >; 21 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-5 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $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(tc_nat_type,type,
tc_nat: $i ).
tff(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(v_i_type,type,
v_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(c_COMBS_type,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
tff(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: ( $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $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_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(
( ( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) ) )
<=> ( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u)) )
<=> ( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u)) )
<=> ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u)) ),
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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
tff(16,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) )
<=> ( ~ class_Orderings_Olinorder(tc_nat)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) ) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) ) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) )
<=> ( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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) ) )
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ~ class_Orderings_Olinorder(tc_nat)
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_l: $i,V_u: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_l,T_a),V_u))
| ~ 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat),
inference(unit_resolution,[status(thm)],[22,16,13,3]) ).
tff(24,plain,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))) )
<=> ( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(28,plain,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV693-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 07:03:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.92/0.97 % SZS status Unsatisfiable
% 0.92/0.97 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------