TSTP Solution File: SYO524_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO524_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 30 01:40:48 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 50 ( 20 unt; 1 typ; 0 def)
% Number of atoms : 106 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 34 ~; 26 |; 5 &)
% ( 22 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 1062 ( 98 atm; 402 fun; 520 num; 42 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 1 usr; 10 con; 0-2 aty)
% Number of variables : 42 ( 40 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $int > $int ).
tff(1,plain,
( $lesseq(f(7),3)
<=> $lesseq(f(7),3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ( ! [U: $int] : $lesseq(f($sum(U,1)),f($sum(U,2)))
& $lesseq(f(7),3) )
=> $lesseq(f(4),3) )
<=> ~ ( ~ ( ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U)))
& $lesseq(f(7),3) )
| $lesseq(f(4),3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( ! [U: $int] : $lesseq(f($sum(U,1)),f($sum(U,2)))
& $lesseq(f(7),3) )
=> $lesseq(f(4),3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(4,plain,
~ ( ~ ( ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U)))
& $lesseq(f(7),3) )
| $lesseq(f(4),3) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U)))
& $lesseq(f(7),3) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
$lesseq(f(7),3),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
$lesseq(f(7),3),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
^ [U: $int] :
refl(
( $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
<=> $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
<=> ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [U: $int] :
rewrite(
( $lesseq(f($sum(1,U)),f($sum(2,U)))
<=> $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U)))
<=> ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U)))
<=> ! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U))) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U))),
inference(and_elim,[status(thm)],[5]) ).
tff(14,plain,
! [U: $int] : $lesseq(f($sum(1,U)),f($sum(2,U))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(4),$product(-1,f(5))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(4),$product(-1,f(5))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( $lesseq($sum(f($sum(1,$sum($sum(6,$product(-1,2)),$product(-1,1)))),$product(-1,f($sum(2,$sum($sum(6,$product(-1,2)),$product(-1,1)))))),0)
<=> $lesseq($sum(f(4),$product(-1,f(5))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(6,$product(-1,2)),$product(-1,1)))),$product(-1,f($sum(2,$sum($sum(6,$product(-1,2)),$product(-1,1)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(4),$product(-1,f(5))),0) ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(6,$product(-1,2)),$product(-1,1)))),$product(-1,f($sum(2,$sum($sum(6,$product(-1,2)),$product(-1,1)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(4),$product(-1,f(5))),0) ) ),
inference(transitivity,[status(thm)],[20,18]) ).
tff(22,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(6,$product(-1,2)),$product(-1,1)))),$product(-1,f($sum(2,$sum($sum(6,$product(-1,2)),$product(-1,1)))))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(4),$product(-1,f(5))),0) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$lesseq($sum(f(4),$product(-1,f(5))),0),
inference(unit_resolution,[status(thm)],[23,17]) ).
tff(25,plain,
( ~ $lesseq(f(4),3)
<=> ~ $lesseq(f(4),3) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
~ $lesseq(f(4),3),
inference(or_elim,[status(thm)],[4]) ).
tff(27,plain,
~ $lesseq(f(4),3),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(5),$product(-1,f(6))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(5),$product(-1,f(6))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,2)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,2)),$product(-1,2)))))),0)
<=> $lesseq($sum(f(5),$product(-1,f(6))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,2)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,2)),$product(-1,2)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(5),$product(-1,f(6))),0) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,2)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,2)),$product(-1,2)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(5),$product(-1,f(6))),0) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,2)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,2)),$product(-1,2)))))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f(5),$product(-1,f(6))),0) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$lesseq($sum(f(5),$product(-1,f(6))),0),
inference(unit_resolution,[status(thm)],[33,17]) ).
tff(35,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $greatereq($sum(f(7),$product(-1,f(6))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $greatereq($sum(f(7),$product(-1,f(6))),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( $lesseq($sum($product(-1,f(7)),f(6)),0)
<=> $greatereq($sum(f(7),$product(-1,f(6))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
$sum(f(6),$product(-1,f(7))) = $sum($product(-1,f(7)),f(6)),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2))))) = $product(-1,f(7)),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))) = f(6),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
$sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))) = $sum(f(6),$product(-1,f(7))),
inference(monotonicity,[status(thm)],[39,38]) ).
tff(41,plain,
$sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))) = $sum($product(-1,f(7)),f(6)),
inference(transitivity,[status(thm)],[40,37]) ).
tff(42,plain,
( $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))),0)
<=> $lesseq($sum($product(-1,f(7)),f(6)),0) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))),0)
<=> $greatereq($sum(f(7),$product(-1,f(6))),0) ),
inference(transitivity,[status(thm)],[42,36]) ).
tff(44,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $greatereq($sum(f(7),$product(-1,f(6))),0) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))),0) )
<=> ( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $greatereq($sum(f(7),$product(-1,f(6))),0) ) ),
inference(transitivity,[status(thm)],[44,35]) ).
tff(46,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $lesseq($sum(f($sum(1,$sum($sum(8,$product(-1,1)),$product(-1,2)))),$product(-1,f($sum(2,$sum($sum(8,$product(-1,1)),$product(-1,2)))))),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [U: $int] : $lesseq($sum(f($sum(1,U)),$product(-1,f($sum(2,U)))),0)
| $greatereq($sum(f(7),$product(-1,f(6))),0) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$greatereq($sum(f(7),$product(-1,f(6))),0),
inference(unit_resolution,[status(thm)],[47,17]) ).
tff(49,plain,
$false,
inference(theory_lemma,[status(thm)],[48,34,27,24,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO524_1 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 13:52:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------