TSTP Solution File: NUM878_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM878_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 13:12:25 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 37 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 48 ~; 5 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number arithmetic : 268 ( 0 atm; 119 fun; 118 num; 31 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 12 !; 17 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(1,plain,
( ( ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
| $false )
<=> ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( 0 = 0 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$sum(0,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
$product(-1,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
$product(0,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
$product(-1,$product(0,0)) = $product(-1,0),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
$product(-1,$product(0,0)) = 0,
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
$sum(0,$product(-1,$product(0,0))) = $sum(0,0),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
$sum(0,$product(-1,$product(0,0))) = 0,
inference(transitivity,[status(thm)],[9,4]) ).
tff(11,plain,
( ( $sum(0,$product(-1,$product(0,0))) = 0 )
<=> ( 0 = 0 ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( $sum(0,$product(-1,$product(0,0))) = 0 )
<=> $true ),
inference(transitivity,[status(thm)],[11,3]) ).
tff(13,plain,
( ( $sum(0,$product(-1,$product(0,0))) != 0 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( $sum(0,$product(-1,$product(0,0))) != 0 )
<=> $false ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,plain,
( ( ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> ( ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
| $false ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ) ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,plain,
( ~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
~ ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $int] :
refl(
( ( $sum(X,$product(-1,$product(X,X))) != 0 )
<=> ( $sum(X,$product(-1,$product(X,X))) != 0 ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 )
<=> ! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 )
<=> ~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ? [X: $int] : ( $sum($product(X,X),$product(-1,X)) = 0 )
<=> ~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ? [X: $int] : ( $product(X,X) = X )
<=> ~ ? [X: $int] : ( $sum($product(X,X),$product(-1,X)) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ? [X: $int] : ( $product(X,X) = X )
<=> ~ ? [X: $int] : ( $product(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
~ ? [X: $int] : ( $product(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotent_element) ).
tff(26,plain,
~ ? [X: $int] : ( $product(X,X) = X ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
~ ? [X: $int] : ( $product(X,X) = X ),
inference(modus_ponens,[status(thm)],[26,24]) ).
tff(28,plain,
~ ? [X: $int] : ( $product(X,X) = X ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
~ ? [X: $int] : ( $product(X,X) = X ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
~ ? [X: $int] : ( $sum($product(X,X),$product(-1,X)) = 0 ),
inference(modus_ponens,[status(thm)],[29,23]) ).
tff(31,plain,
~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 ),
inference(modus_ponens,[status(thm)],[30,22]) ).
tff(32,plain,
~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
~ ? [X: $int] : ( $sum(X,$product(-1,$product(X,X))) = 0 ),
inference(modus_ponens,[status(thm)],[32,21]) ).
tff(34,plain,
^ [X: $int] : refl($oeq($sum(X,$product(-1,$product(X,X))) != 0,$sum(X,$product(-1,$product(X,X))) != 0)),
inference(bind,[status(th)],]) ).
tff(35,plain,
! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ),
inference(nnf-neg,[status(sab)],[33,34]) ).
tff(36,plain,
! [X: $int] : ( $sum(X,$product(-1,$product(X,X))) != 0 ),
inference(modus_ponens,[status(thm)],[35,20]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM878_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:31:55 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------