TSTP Solution File: NUM343+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 13:03:34 EDT 2022
% Result : Theorem 114.62s 73.04s
% Output : Proof 114.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 84 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 452 ( 23 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 636 ( 285 ~; 217 |; 68 &)
% ( 58 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 158 ( 127 !; 12 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(nn2_type,type,
nn2: $i ).
tff(nn1_type,type,
nn1: $i ).
tff(n1_type,type,
n1: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(n21_type,type,
n21: $i ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_neg_type,type,
rdn_neg: $i > $i ).
tff(rdn_positive_less_type,type,
rdn_positive_less: ( $i * $i ) > $o ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(n2_type,type,
n2: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[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/sandbox/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] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,Y: $i] :
( less(X,Y)
<=> ~ ( ( Y = X )
| less(Y,X) ) )
| ( less(nn1,nn2)
<=> ~ ( ( nn2 = nn1 )
| less(nn2,nn1) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( less(nn1,nn2)
<=> ~ ( ( nn2 = nn1 )
| less(nn2,nn1) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
refl(
( ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
<=> ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,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_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_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_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ) )),
rewrite(
( ~ ~ ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
<=> ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_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_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_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_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| less(X,Y) ) )),
rewrite(
( ( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| less(X,Y) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_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) )
<=> ( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ) )),
inference(bind,[status(th)],]) ).
tff(16,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_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,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(21,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)],[20,19]) ).
tff(22,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)],[21,17]) ).
tff(23,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)],[22]) ).
tff(24,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
( rdn_positive_less(rdnn(n1),rdnn(n2))
<=> rdn_positive_less(rdnn(n1),rdnn(n2)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
rdn_positive_less(rdnn(n1),rdnn(n2)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less12) ).
tff(28,plain,
rdn_positive_less(rdnn(n1),rdnn(n2)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( rdn_translate(nn2,rdn_neg(rdnn(n2)))
<=> rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
tff(31,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( rdn_translate(nn1,rdn_neg(rdnn(n1)))
<=> rdn_translate(nn1,rdn_neg(rdnn(n1))) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn1) ).
tff(34,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( less(nn2,nn1)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1))) )
<=> ( ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| less(nn2,nn1)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| less(nn2,nn1)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1))) )
<=> ( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| less(nn2,nn1)
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1))) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( less(X,Y)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y)) )
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n1),rdnn(n2))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn2,nn1) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
less(nn2,nn1),
inference(unit_resolution,[status(thm)],[40,34,31,28,25]) ).
tff(42,plain,
( ( nn2 = nn1 )
| less(nn2,nn1)
| ~ less(nn2,nn1) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( ( nn2 = nn1 )
| less(nn2,nn1) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ ( less(nn1,nn2)
<=> ~ ( ( nn2 = nn1 )
| less(nn2,nn1) ) )
| ~ less(nn1,nn2)
| ~ ( ( nn2 = nn1 )
| less(nn2,nn1) ) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
( ~ ( less(nn1,nn2)
<=> ~ ( ( nn2 = nn1 )
| less(nn2,nn1) ) )
| ~ less(nn1,nn2) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
~ less(nn1,nn2),
inference(unit_resolution,[status(thm)],[45,12]) ).
tff(47,plain,
( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2)
| less(nn1,nn2) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X: $i] :
refl(
( ~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
<=> ~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
<=> ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) )
<=> ~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] :
~ ( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) )
<=> ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) )
<=> ~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ? [X: $i] :
( ( less(nn1,X)
& less(X,n1) )
=> sum(n21,X,n21) )
<=> ~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
~ ? [X: $i] :
( ( less(nn1,X)
& less(X,n1) )
=> sum(n21,X,n21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_something_n0_samething) ).
tff(56,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[58,53]) ).
tff(60,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
~ ? [X: $i] :
( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(modus_ponens,[status(thm)],[61,53]) ).
tff(63,plain,
^ [X: $i] :
refl(
$oeq(
~ ( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
~ ( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ))),
inference(bind,[status(th)],]) ).
tff(64,plain,
! [X: $i] :
~ ( ~ ( less(nn1,X)
& less(X,n1) )
| sum(n21,X,n21) ),
inference(nnf-neg,[status(sab)],[62,63]) ).
tff(65,plain,
! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ),
inference(modus_ponens,[status(thm)],[64,52]) ).
tff(66,plain,
! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) ),
inference(modus_ponens,[status(thm)],[65,50]) ).
tff(67,plain,
( ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) )
<=> ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ( sum(n21,nn2,n21)
| ~ less(nn1,nn2)
| ~ less(nn2,n1) )
<=> ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn1,nn2)
| ~ less(nn2,n1) ) )
<=> ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn1,nn2)
| ~ less(nn2,n1) ) )
<=> ( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn1,nn2)
| ~ less(nn2,n1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X: $i] :
~ ( sum(n21,X,n21)
| ~ less(nn1,X)
| ~ less(X,n1) )
| ~ ( sum(n21,nn2,n21)
| ~ less(nn2,n1)
| ~ less(nn1,nn2) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,66,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 09:34:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 114.62/73.04 % SZS status Theorem
% 114.62/73.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------