%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM292+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:19:00 AM UTC 2025
% Result : Theorem 55.32s 55.57s
% Output : Proof 55.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 57 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 365 ( 146 ~; 130 |; 44 &)
% ( 33 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 152 ( 132 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
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(n1_type,type,
n1: $i ).
tff(n3_type,type,
n3: $i ).
tff(n2_type,type,
n2: $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(less_type,type,
less: ( $i * $i ) > $o ).
tff(n13_type,type,
n13: $i ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_pos_type,type,
rdn_pos: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,axiom,
! [X: $i] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_non_zero_by_digit) ).
tff(7,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( rdn_non_zero_digit(rdnn(n1))
<=> rdn_non_zero_digit(rdnn(n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_digit1) ).
tff(13,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero_digit(rdnn(n1)) )
<=> ( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero_digit(rdnn(n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero_digit(rdnn(n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) )
| rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero_digit(rdnn(n1)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
rdn_non_zero(rdnn(n1)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [D: $i,Db: $i,Ob: $i] :
refl(( ( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
<=> ( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
<=> ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
<=> ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [D: $i,Db: $i,Ob: $i] :
rewrite(( ( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
<=> ( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [D: $i,Db: $i,Ob: $i] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
<=> ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [D: $i,Db: $i,Ob: $i] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_extra_digits_positive_less) ).
tff(24,plain,
! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
| ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) )
<=> ( ~ ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
| ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
| ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [D: $i,Db: $i,Ob: $i] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) )
| ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
( ~ less(n2,n13)
<=> ~ less(n2,n13) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
~ less(n2,n13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n2_less_n13) ).
tff(34,plain,
~ less(n2,n13),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,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(41,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)],[40]) ).
tff(42,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/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
tff(43,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)],[42,41]) ).
tff(44,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)],[43,39]) ).
tff(45,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)],[44]) ).
tff(46,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)],[45,38]) ).
tff(47,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)],[46,36]) ).
tff(48,plain,
( rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
<=> rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn13) ).
tff(50,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( rdn_translate(n2,rdn_pos(rdnn(n2)))
<=> rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
tff(53,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,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(n2,n13)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) )
<=> ( ~ ! [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(n2,n13)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,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(n2,n13)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,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(n2,n13)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,53,50,47,34,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : NUM292+1 : TPTP v9.0.0. Released v3.1.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 00:45:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 55.32/55.57 % SZS status Theorem
% 55.32/55.57 % SZS output start Proof
% See solution above
% 55.55/55.75 % E exiting
%------------------------------------------------------------------------------