TSTP Solution File: DAT001_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT001_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Fri Sep 16 14:36:19 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 98 ( 33 unt; 3 typ; 0 def)
% Number of atoms : 446 ( 16 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 523 ( 196 ~; 229 |; 32 &)
% ( 60 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number arithmetic : 1131 ( 116 atm; 210 fun; 681 num; 124 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 11 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 2 usr; 14 con; 0-2 aty)
% Number of variables : 181 ( 165 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
tff(sorted_type,type,
sorted: list > $o ).
tff(mycons_type,type,
mycons: ( $int * list ) > list ).
tff(nil_type,type,
nil: list ).
tff(1,plain,
^ [X: $int] :
refl(
( sorted(mycons(X,nil))
<=> sorted(mycons(X,nil)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $int] : sorted(mycons(X,nil))
<=> ! [X: $int] : sorted(mycons(X,nil)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $int] : sorted(mycons(X,nil))
<=> ! [X: $int] : sorted(mycons(X,nil)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $int] : sorted(mycons(X,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_is_sorted) ).
tff(5,plain,
! [X: $int] : sorted(mycons(X,nil)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $int] : sorted(mycons(X,nil)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $int] : sorted(mycons(X,nil)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $int] : sorted(mycons(X,nil))
| sorted(mycons(100,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
sorted(mycons(100,nil)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $int,Y: $int,R: list] :
refl(
( ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $int,Y: $int,R: list] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) )
<=> ~ ( $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
( ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) )
<=> ~ ~ ( $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
rewrite(
( ~ ~ ( $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
<=> ( $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
( ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) )
<=> ( $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
( ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
rewrite(
( ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
( ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $int,Y: $int,R: list] :
rewrite(
( ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq($sum(Y,$product(-1,X)),0)
& sorted(mycons(Y,R)) ) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq($sum(Y,$product(-1,X)),0)
& sorted(mycons(Y,R)) ) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [X: $int,Y: $int,R: list] :
rewrite(
( ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq($sum(Y,$product(-1,X)),0)
& sorted(mycons(Y,R)) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq($sum(Y,$product(-1,X)),0)
& sorted(mycons(Y,R)) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [X: $int,Y: $int,R: list] :
trans(
monotonicity(
rewrite(
( ( $less(X,Y)
& sorted(mycons(Y,R)) )
<=> ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) )),
( ( ( $less(X,Y)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) )
<=> ( ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) ) )),
rewrite(
( ( ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ) )),
( ( ( $less(X,Y)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) )
<=> ( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $int,Y: $int,R: list] :
( ( $less(X,Y)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) )
<=> ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [X: $int,Y: $int,R: list] :
( ( $less(X,Y)
& sorted(mycons(Y,R)) )
=> sorted(mycons(X,mycons(Y,R))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursive_sort) ).
tff(22,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq(Y,X)
& sorted(mycons(Y,R)) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $lesseq($sum(Y,$product(-1,X)),0)
& sorted(mycons(Y,R)) ) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) ),
inference(modus_ponens,[status(thm)],[24,15]) ).
tff(26,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| ~ ( ~ $greatereq($sum(X,$product(-1,Y)),0)
& sorted(mycons(Y,R)) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ),
inference(modus_ponens,[status(thm)],[26,13]) ).
tff(28,plain,
! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) ),
inference(modus_ponens,[status(thm)],[27,11]) ).
tff(29,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( sorted(mycons(7,mycons(100,nil)))
| $false
| ~ sorted(mycons(100,nil)) )
<=> ( sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( $greatereq(-93,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
$sum(7,-100) = -93,
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
$product(-1,100) = -100,
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
$sum(7,$product(-1,100)) = $sum(7,-100),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
$sum(7,$product(-1,100)) = -93,
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( $greatereq($sum(7,$product(-1,100)),0)
<=> $greatereq(-93,0) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( $greatereq($sum(7,$product(-1,100)),0)
<=> $false ),
inference(transitivity,[status(thm)],[36,31]) ).
tff(38,plain,
( ( sorted(mycons(7,mycons(100,nil)))
| $greatereq($sum(7,$product(-1,100)),0)
| ~ sorted(mycons(100,nil)) )
<=> ( sorted(mycons(7,mycons(100,nil)))
| $false
| ~ sorted(mycons(100,nil)) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( sorted(mycons(7,mycons(100,nil)))
| $greatereq($sum(7,$product(-1,100)),0)
| ~ sorted(mycons(100,nil)) )
<=> ( sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ) ),
inference(transitivity,[status(thm)],[38,30]) ).
tff(40,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| $greatereq($sum(7,$product(-1,100)),0)
| ~ sorted(mycons(100,nil)) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| $greatereq($sum(7,$product(-1,100)),0)
| ~ sorted(mycons(100,nil)) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ) ),
inference(transitivity,[status(thm)],[40,29]) ).
tff(42,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| $greatereq($sum(7,$product(-1,100)),0)
| ~ sorted(mycons(100,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(7,mycons(100,nil)))
| ~ sorted(mycons(100,nil)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
sorted(mycons(7,mycons(100,nil))),
inference(unit_resolution,[status(thm)],[43,28,9]) ).
tff(45,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| $false
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( $greatereq(-3,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
$sum(4,-7) = -3,
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
$product(-1,7) = -7,
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
$sum(4,$product(-1,7)) = $sum(4,-7),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
$sum(4,$product(-1,7)) = -3,
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( $greatereq($sum(4,$product(-1,7)),0)
<=> $greatereq(-3,0) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( $greatereq($sum(4,$product(-1,7)),0)
<=> $false ),
inference(transitivity,[status(thm)],[52,47]) ).
tff(54,plain,
( ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| $greatereq($sum(4,$product(-1,7)),0)
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| $false
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| $greatereq($sum(4,$product(-1,7)),0)
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(transitivity,[status(thm)],[54,46]) ).
tff(56,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| $greatereq($sum(4,$product(-1,7)),0)
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| $greatereq($sum(4,$product(-1,7)),0)
| ~ sorted(mycons(7,mycons(100,nil))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ) ),
inference(transitivity,[status(thm)],[56,45]) ).
tff(58,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| $greatereq($sum(4,$product(-1,7)),0)
| ~ sorted(mycons(7,mycons(100,nil))) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ sorted(mycons(7,mycons(100,nil))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
sorted(mycons(4,mycons(7,mycons(100,nil)))),
inference(unit_resolution,[status(thm)],[59,28,44]) ).
tff(61,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $false
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( $greatereq(-2,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
$sum(2,-4) = -2,
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
$product(-1,4) = -4,
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
$sum(2,$product(-1,4)) = $sum(2,-4),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
$sum(2,$product(-1,4)) = -2,
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( $greatereq($sum(2,$product(-1,4)),0)
<=> $greatereq(-2,0) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( $greatereq($sum(2,$product(-1,4)),0)
<=> $false ),
inference(transitivity,[status(thm)],[68,63]) ).
tff(70,plain,
( ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $greatereq($sum(2,$product(-1,4)),0)
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $false
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $greatereq($sum(2,$product(-1,4)),0)
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(transitivity,[status(thm)],[70,62]) ).
tff(72,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $greatereq($sum(2,$product(-1,4)),0)
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $greatereq($sum(2,$product(-1,4)),0)
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ) ),
inference(transitivity,[status(thm)],[72,61]) ).
tff(74,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| $greatereq($sum(2,$product(-1,4)),0)
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ sorted(mycons(4,mycons(7,mycons(100,nil)))) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))),
inference(unit_resolution,[status(thm)],[75,28,60]) ).
tff(77,plain,
( ~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
<=> ~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',check_list) ).
tff(79,plain,
~ sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $false
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( $greatereq(-1,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
$sum(1,-2) = -1,
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
$product(-1,2) = -2,
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
$sum(1,$product(-1,2)) = $sum(1,-2),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
$sum(1,$product(-1,2)) = -1,
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( $greatereq($sum(1,$product(-1,2)),0)
<=> $greatereq(-1,0) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( $greatereq($sum(1,$product(-1,2)),0)
<=> $false ),
inference(transitivity,[status(thm)],[87,82]) ).
tff(89,plain,
( ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $greatereq($sum(1,$product(-1,2)),0)
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $false
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $greatereq($sum(1,$product(-1,2)),0)
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(transitivity,[status(thm)],[89,81]) ).
tff(91,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $greatereq($sum(1,$product(-1,2)),0)
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $greatereq($sum(1,$product(-1,2)),0)
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) )
<=> ( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ) ),
inference(transitivity,[status(thm)],[91,80]) ).
tff(93,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| $greatereq($sum(1,$product(-1,2)),0)
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X: $int,Y: $int,R: list] :
( sorted(mycons(X,mycons(Y,R)))
| $greatereq($sum(X,$product(-1,Y)),0)
| ~ sorted(mycons(Y,R)) )
| sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil))))))
| ~ sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
$false,
inference(unit_resolution,[status(thm)],[94,28,79,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT001_1 : TPTP v8.1.0. Released v5.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Aug 31 01:37:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------