%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM290+1 : TPTP v9.0.0. Released 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 05:19:00 AM UTC 2025
% Result : Theorem 30.98s 31.17s
% Output : Proof 31.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 32 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 243 ( 0 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 322 ( 132 ~; 116 |; 44 &)
% ( 24 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 100 ( 88 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i ).
tff(n2_type,type,
n2: $i ).
tff(rdn_positive_less_type,type,
rdn_positive_less: ( $i * $i ) > $o ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_pos_type,type,
rdn_pos: $i > $i ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(1,plain,
( ~ less(n2,n3)
<=> ~ less(n2,n3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ less(n2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n2_less_n3) ).
tff(3,plain,
~ less(n2,n3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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)],[6]) ).
tff(8,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(9,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(10,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)],[9]) ).
tff(11,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(12,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)],[11,10]) ).
tff(13,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)],[12,8]) ).
tff(14,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)],[13]) ).
tff(15,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)],[14,7]) ).
tff(16,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)],[15,5]) ).
tff(17,plain,
( rdn_positive_less(rdnn(n2),rdnn(n3))
<=> rdn_positive_less(rdnn(n2),rdnn(n3)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
tff(19,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( rdn_translate(n3,rdn_pos(rdnn(n3)))
<=> rdn_translate(n3,rdn_pos(rdnn(n3))) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
tff(22,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( rdn_translate(n2,rdn_pos(rdnn(n2)))
<=> rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
tff(25,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) )
<=> ( ~ ! [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,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( less(n2,n3)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) )
<=> ( less(n2,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,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,n3)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) )
<=> ( ~ ! [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,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,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,n3)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) )
<=> ( ~ ! [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,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,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,n3)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,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,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,25,22,19,16,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM290+1 : TPTP v9.0.0. Released v3.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 00:46:02 EDT 2025
% 0.14/0.36 % CPUTime :
% 30.98/31.17 % SZS status Theorem
% 30.98/31.17 % SZS output start Proof
% See solution above
% 31.15/31.36 % E exiting
%------------------------------------------------------------------------------