%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT009+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 04:57:39 AM UTC 2025
% Result : Theorem 0.92s 1.11s
% Output : Proof 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 74
% Syntax : Number of formulae : 166 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 1267 ( 0 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 1743 ( 734 ~; 564 |; 226 &)
% ( 204 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 92 ( 92 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 400 ( 347 !; 0 ?; 400 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(n25_type,type,
n25: $i ).
tff(n24_type,type,
n24: $i ).
tff(accept_population_type,type,
accept_population: ( $i * $i * $i ) > $o ).
tff(christian_type,type,
christian: $i ).
tff(muslimcountrybhumanitarianorganization_type,type,
muslimcountrybhumanitarianorganization: $i ).
tff(n0_type,type,
n0: $i ).
tff(other_type,type,
other: $i ).
tff(native_type,type,
native: $i ).
tff(n1_type,type,
n1: $i ).
tff(muslim_type,type,
muslim: $i ).
tff(n75_type,type,
n75: $i ).
tff(atheist_type,type,
atheist: $i ).
tff(accept_city_type,type,
accept_city: ( $i * $i ) > $o ).
tff(towna_type,type,
towna: $i ).
tff(citya_type,type,
citya: $i ).
tff(accept_number_type,type,
accept_number: ( $i * $i ) > $o ).
tff(n2_type,type,
n2: $i ).
tff(accept_leader_type,type,
accept_leader: ( $i * $i ) > $o ).
tff(countrybhumanitarianorganization_type,type,
countrybhumanitarianorganization: $i ).
tff(accept_team_type,type,
accept_team: ( $i * $i * $i * $i ) > $o ).
tff(rdn_positive_less_type,type,
rdn_positive_less: ( $i * $i ) > $o ).
tff(rdn_type,type,
rdn: ( $i * $i ) > $i ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(n5_type,type,
n5: $i ).
tff(n4_type,type,
n4: $i ).
tff(rdn_non_zero_type,type,
rdn_non_zero: $i > $o ).
tff(rdn_non_zero_digit_type,type,
rdn_non_zero_digit: $i > $o ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_pos_type,type,
rdn_pos: $i > $i ).
tff(1,plain,
^ [A: $i] :
refl(( ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A: $i] :
trans(trans(monotonicity(rewrite(( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ( ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
rewrite(( ( ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
rewrite(( ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
^ [A: $i] :
rewrite(( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) )
<=> ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,axiom,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax',a2_9) ).
tff(9,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
inference(modus_ponens,[status(thm)],[11,4]) ).
tff(13,plain,
! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( ~ ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,towna) )
| ~ ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,towna) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ accept_city(muslimcountrybhumanitarianorganization,towna)
<=> ~ accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax',deduced_366) ).
tff(18,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,towna) )
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
( ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,towna) )
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
^ [A: $i] :
refl(( ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [A: $i] :
trans(trans(monotonicity(rewrite(( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ( ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
rewrite(( ( ~ ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
rewrite(( ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [A: $i] :
rewrite(( ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) )
<=> ! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax',a2_10) ).
tff(30,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [A: $i] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n25)
& accept_population(A,muslim,n0)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) ),
inference(modus_ponens,[status(thm)],[33,23]) ).
tff(35,plain,
( ~ ! [A: $i] :
~ ( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n25)
| ~ accept_population(A,muslim,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0) )
<=> accept_city(A,citya) )
| ~ ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,citya) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
~ ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,citya) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [A: $i,C: $i,N: $i,L: $i] :
refl(( ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) )
<=> ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) )
<=> ! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [A: $i,C: $i,N: $i,L: $i] :
trans(trans(monotonicity(rewrite(( ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) )
<=> ~ ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) ) )),
( ( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ( accept_team(A,L,C,N)
<=> ~ ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) ) ) )),
rewrite(( ( accept_team(A,L,C,N)
<=> ~ ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) ) )
<=> ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) )),
( ( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) )),
rewrite(( ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) )
<=> ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) )),
( ( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [A: $i,C: $i,N: $i,L: $i] :
rewrite(( ( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) )
<=> ! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax',a1_1) ).
tff(45,plain,
! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [A: $i,C: $i,N: $i,L: $i] :
( accept_team(A,L,C,N)
<=> ( accept_city(A,C)
& accept_leader(A,L)
& accept_number(A,N) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
( ~ ! [A: $i,C: $i,N: $i,L: $i] :
~ ( ( ~ accept_city(A,C)
| ~ accept_leader(A,L)
| ~ accept_number(A,N) )
<=> accept_team(A,L,C,N) )
| ~ ( ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) )
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
~ ( ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) )
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2)
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ~ accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2)
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
~ ~ accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query_9) ).
tff(55,plain,
accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,plain,
( ( ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) )
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) )
| ~ ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) )
| ~ accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
( ( ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) )
<=> accept_team(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization,citya,n2) )
| ~ ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
~ ( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2) ),
inference(unit_resolution,[status(thm)],[58,51]) ).
tff(60,plain,
( ~ accept_city(muslimcountrybhumanitarianorganization,citya)
| ~ accept_leader(muslimcountrybhumanitarianorganization,countrybhumanitarianorganization)
| ~ accept_number(muslimcountrybhumanitarianorganization,n2)
| accept_city(muslimcountrybhumanitarianorganization,citya) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
accept_city(muslimcountrybhumanitarianorganization,citya),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ( ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
<=> accept_city(muslimcountrybhumanitarianorganization,citya) )
| ~ ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
| ~ accept_city(muslimcountrybhumanitarianorganization,citya) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
~ ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(unit_resolution,[status(thm)],[62,61,36]) ).
tff(64,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
accept_population(muslimcountrybhumanitarianorganization,atheist,n75),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
<=> accept_population(muslimcountrybhumanitarianorganization,muslim,n1) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax',deduced_204) ).
tff(68,plain,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( accept_population(muslimcountrybhumanitarianorganization,native,n0)
<=> accept_population(muslimcountrybhumanitarianorganization,native,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax',deduced_203) ).
tff(71,plain,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( accept_population(muslimcountrybhumanitarianorganization,other,n0)
<=> accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax',deduced_93) ).
tff(74,plain,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
( ~ ( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) )
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
inference(unit_resolution,[status(thm)],[75,74,71,68]) ).
tff(77,plain,
~ accept_population(muslimcountrybhumanitarianorganization,christian,n24),
inference(unit_resolution,[status(thm)],[76,65,21]) ).
tff(78,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_population(muslimcountrybhumanitarianorganization,christian,n25) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
accept_population(muslimcountrybhumanitarianorganization,christian,n25),
inference(unit_resolution,[status(thm)],[78,63]) ).
tff(80,plain,
^ [A: $i,N: $i,M: $i,P: $i] :
refl(( ( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
<=> ( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
<=> ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [A: $i,N: $i,M: $i,P: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( accept_population(A,P,N)
& less(M,N) )
<=> ~ ( ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
( ~ ( accept_population(A,P,N)
& less(M,N) )
<=> ~ ~ ( ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
rewrite(( ~ ~ ( ~ accept_population(A,P,N)
| ~ less(M,N) )
<=> ( ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
( ~ ( accept_population(A,P,N)
& less(M,N) )
<=> ( ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
( ( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) )
<=> ( ~ accept_population(A,P,N)
| ~ less(M,N)
| accept_population(A,P,M) ) )),
rewrite(( ( ~ accept_population(A,P,N)
| ~ less(M,N)
| accept_population(A,P,M) )
<=> ( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
( ( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) )
<=> ( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) )
<=> ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) )
<=> ! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [A: $i,N: $i,M: $i,P: $i] :
rewrite(( ( ( accept_population(A,P,N)
& less(M,N) )
=> accept_population(A,P,M) )
<=> ( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [A: $i,N: $i,M: $i,P: $i] :
( ( accept_population(A,P,N)
& less(M,N) )
=> accept_population(A,P,M) )
<=> ! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [A: $i,N: $i,M: $i,P: $i] :
( ( accept_population(A,P,N)
& less(M,N) )
=> accept_population(A,P,M) ),
file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax',a1_3) ).
tff(88,plain,
! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [A: $i,N: $i,M: $i,P: $i] :
( ~ ( accept_population(A,P,N)
& less(M,N) )
| accept_population(A,P,M) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) ),
inference(modus_ponens,[status(thm)],[91,81]) ).
tff(93,plain,
( ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) )
<=> ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ less(n24,n25) )
<=> ( ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ less(n24,n25) )
<=> ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ less(n24,n25) )
<=> ( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| ~ less(n24,n25) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [A: $i,N: $i,M: $i,P: $i] :
( accept_population(A,P,M)
| ~ accept_population(A,P,N)
| ~ less(M,N) )
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n25)
| accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ less(n24,n25) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
~ less(n24,n25),
inference(unit_resolution,[status(thm)],[98,92,79,77]) ).
tff(100,plain,
^ [X: $i] :
refl(( ( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
<=> ( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
<=> ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
<=> ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
^ [X: $i] :
rewrite(( ( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) )
<=> ( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [X: $i] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) )
<=> ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [X: $i] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_non_zero_by_digit) ).
tff(106,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( rdn_non_zero_digit(rdnn(n2))
<=> rdn_non_zero_digit(rdnn(n2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
rdn_non_zero_digit(rdnn(n2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_digit2) ).
tff(112,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero_digit(rdnn(n2)) )
<=> ( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero_digit(rdnn(n2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero_digit(rdnn(n2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero_digit(rdnn(n2)) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
rdn_non_zero(rdnn(n2)),
inference(unit_resolution,[status(thm)],[115,112,109]) ).
tff(117,plain,
^ [Ds: $i,O: $i,Db: $i] :
refl(( ( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
<=> ( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
<=> ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
^ [Ds: $i,O: $i,Db: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
<=> ~ ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
<=> ~ ~ ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
rewrite(( ~ ~ ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
<=> ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
<=> ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
( ( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O)
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ) )),
rewrite(( ( ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O)
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
( ( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
^ [Ds: $i,O: $i,Db: $i] :
rewrite(( ( ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
=> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [Ds: $i,O: $i,Db: $i] :
( ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
=> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) )
<=> ! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [Ds: $i,O: $i,Db: $i] :
( ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
=> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_multi_digit_low) ).
tff(125,plain,
! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [Ds: $i,O: $i,Db: $i] :
( ~ ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) ),
inference(modus_ponens,[status(thm)],[128,118]) ).
tff(130,plain,
( rdn_positive_less(rdnn(n4),rdnn(n5))
<=> rdn_positive_less(rdnn(n4),rdnn(n5)) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
tff(132,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
( ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) )
<=> ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2)) )
<=> ( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2)) )
<=> ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2)) )
<=> ( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [Ds: $i,O: $i,Db: $i] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| ~ rdn_non_zero(O) )
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ rdn_non_zero(rdnn(n2))
| rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ),
inference(unit_resolution,[status(thm)],[138,132,129]) ).
tff(140,plain,
rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))),
inference(unit_resolution,[status(thm)],[139,116]) ).
tff(141,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
refl(( ( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
<=> ~ ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
<=> ~ ~ ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
rewrite(( ~ ~ ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
<=> ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
<=> ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
( ( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) )
<=> ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y)
| less(X,Y) ) )),
rewrite(( ( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y)
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
( ( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
trans(monotonicity(rewrite(( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
<=> ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) ) )),
( ( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) )
<=> ( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ) )),
rewrite(( ( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) )
<=> ( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ) )),
( ( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) )
<=> ( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
tff(149,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) ),
inference(modus_ponens,[status(thm)],[152,142]) ).
tff(154,plain,
( rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2))))
<=> rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,axiom,
rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn25) ).
tff(156,plain,
rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
<=> rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn24) ).
tff(159,plain,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( less(n24,n25)
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2))))
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) )
<=> ( less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2))))
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ) ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2))))
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ) ),
inference(transitivity,[status(thm)],[162,160]) ).
tff(164,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2))))
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(n24,n25)
| ~ rdn_positive_less(rdn(rdnn(n4),rdnn(n2)),rdn(rdnn(n5),rdnn(n2)))
| ~ rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2))))
| ~ rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
$false,
inference(unit_resolution,[status(thm)],[165,159,156,153,140,99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : AGT009+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 10:43:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.92/1.11 % SZS status Theorem
% 0.92/1.11 % SZS output start Proof
% See solution above
% 0.97/1.15 % E exiting
%------------------------------------------------------------------------------