%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM298+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:19:01 AM UTC 2025
% Result : Theorem 56.55s 56.79s
% Output : Proof 56.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 48 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 272 ( 33 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 338 ( 141 ~; 109 |; 26 &)
% ( 59 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 128 ( 112 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(n2_type,type,
n2: $i ).
tff(nn2_type,type,
nn2: $i ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_neg_type,type,
rdn_neg: $i > $i ).
tff(rdn_pos_type,type,
rdn_pos: $i > $i ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) )
<=> ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) )
<=> ! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Y: $i] :
trans(trans(monotonicity(rewrite(( ( ~ less(Y,X)
& ( Y != X ) )
<=> ~ ( ( Y = X )
| less(Y,X) ) )),
( ( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ) )),
rewrite(( ( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) )
<=> ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) )),
( ( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) )),
rewrite(( ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) )
<=> ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) )),
( ( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_property) ).
tff(7,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,Y: $i] :
~ ( ( ( Y = X )
| less(Y,X) )
<=> less(X,Y) )
| ~ ( ( ( n2 = nn2 )
| less(n2,nn2) )
<=> less(nn2,n2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ( n2 = nn2 )
| less(n2,nn2) )
<=> less(nn2,n2) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( less(n2,nn2)
<=> less(n2,nn2) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( ~ ~ less(n2,nn2)
<=> less(n2,nn2) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ ~ less(n2,nn2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n2_not_less_nn2) ).
tff(16,plain,
less(n2,nn2),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
less(n2,nn2),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( ( n2 = nn2 )
| less(n2,nn2)
| ~ less(n2,nn2) ),
inference(tautology,[status(thm)],[]) ).
tff(19,plain,
( ( n2 = nn2 )
| less(n2,nn2) ),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ( ( n2 = nn2 )
| less(n2,nn2) )
<=> less(nn2,n2) )
| ~ ( ( n2 = nn2 )
| less(n2,nn2) )
| ~ less(nn2,n2) ),
inference(tautology,[status(thm)],[]) ).
tff(21,plain,
( ( ( ( n2 = nn2 )
| less(n2,nn2) )
<=> less(nn2,n2) )
| ~ less(nn2,n2) ),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
~ less(nn2,n2),
inference(unit_resolution,[status(thm)],[21,12]) ).
tff(23,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
refl(( ( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
<=> ( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
<=> ~ ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
<=> ~ ~ ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
rewrite(( ~ ~ ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
<=> ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
<=> ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
( ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) )
<=> ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X))
| less(X,Y) ) )),
rewrite(( ( ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X))
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
( ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
rewrite(( ( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
=> less(X,Y) )
<=> ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
=> less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_pos) ).
tff(31,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
| less(X,Y) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( rdn_translate(nn2,rdn_neg(rdnn(n2)))
<=> rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
tff(38,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( rdn_translate(n2,rdn_pos(rdnn(n2)))
<=> rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
tff(41,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( less(nn2,n2)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2))) )
<=> ( less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) )
| less(nn2,n2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,41,38,35,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM298+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 00:47:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 56.55/56.79 % SZS status Theorem
% 56.55/56.79 % SZS output start Proof
% See solution above
% 56.71/56.96 % E exiting
%------------------------------------------------------------------------------