TSTP Solution File: NUM299+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM299+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:03:27 EDT 2022
% Result : Theorem 16.35s 10.77s
% Output : Proof 16.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 44
% Syntax : Number of formulae : 84 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 474 ( 23 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 622 ( 260 ~; 218 |; 67 &)
% ( 68 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 203 ( 178 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(rdn_positive_less_type,type,
rdn_positive_less: ( $i * $i ) > $o ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(n4_type,type,
n4: $i ).
tff(n2_type,type,
n2: $i ).
tff(n3_type,type,
n3: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(nn2_type,type,
nn2: $i ).
tff(nn4_type,type,
nn4: $i ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_neg_type,type,
rdn_neg: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ~ ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ~ ~ ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
rewrite(
( ~ ~ ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
<=> ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
( ( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ) )),
rewrite(
( ( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
( ( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
tff(9,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ),
inference(modus_ponens,[status(thm)],[11,4]) ).
tff(13,plain,
! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( rdn_positive_less(rdnn(n3),rdnn(n4))
<=> rdn_positive_less(rdnn(n3),rdnn(n4)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
tff(16,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(modus_ponens,[status(thm)],[15,14]) ).
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,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4)) )
<=> ( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(unit_resolution,[status(thm)],[25,19,16,13]) ).
tff(27,plain,
^ [X: $i,Y: $i] :
refl(
( ( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) )
<=> ( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) )
<=> ! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) )
<=> ! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,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(32,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_property) ).
tff(33,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ( ~ less(Y,X)
& ( Y != X ) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ~ ! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) )
| ( less(nn4,nn2)
<=> ~ ( ( nn2 = nn4 )
| less(nn2,nn4) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( less(nn4,nn2)
<=> ~ ( ( nn2 = nn4 )
| less(nn2,nn4) ) ),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( less(nn2,nn4)
<=> less(nn2,nn4) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ~ less(nn2,nn4)
<=> less(nn2,nn4) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
~ ~ less(nn2,nn4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nn2_not_less_nn4) ).
tff(42,plain,
less(nn2,nn4),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
less(nn2,nn4),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
( ( nn2 = nn4 )
| less(nn2,nn4)
| ~ less(nn2,nn4) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
( ( nn2 = nn4 )
| less(nn2,nn4) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ( less(nn4,nn2)
<=> ~ ( ( nn2 = nn4 )
| less(nn2,nn4) ) )
| ~ less(nn4,nn2)
| ~ ( ( nn2 = nn4 )
| less(nn2,nn4) ) ),
inference(tautology,[status(thm)],]) ).
tff(47,plain,
( ~ ( less(nn4,nn2)
<=> ~ ( ( nn2 = nn4 )
| less(nn2,nn4) ) )
| ~ less(nn4,nn2) ),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
~ less(nn4,nn2),
inference(unit_resolution,[status(thm)],[47,38]) ).
tff(49,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
refl(
( ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,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_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
<=> ~ ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
<=> ~ ~ ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
rewrite(
( ~ ~ ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
<=> ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
<=> ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
( ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) )
<=> ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| less(X,Y) ) )),
rewrite(
( ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
( ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
trans(
monotonicity(
rewrite(
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
<=> ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) ) )),
( ( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) )
<=> ( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) ) )),
rewrite(
( ( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) )
<=> ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ) )),
( ( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) )
<=> ( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_neg) ).
tff(57,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ~ ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
| less(X,Y) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( rdn_translate(nn4,rdn_neg(rdnn(n4)))
<=> rdn_translate(nn4,rdn_neg(rdnn(n4))) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn4) ).
tff(64,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( rdn_translate(nn2,rdn_neg(rdnn(n2)))
<=> rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
tff(67,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( less(nn4,nn2)
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) )
<=> ( less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X) )
| less(nn4,nn2)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,67,64,61,48,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM299+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n004.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 Sep 2 09:15:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 16.35/10.77 % SZS status Theorem
% 16.35/10.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------