TSTP Solution File: ARI741_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI741_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Tue Sep 6 17:02:49 EDT 2022
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 38 ( 9 unt; 2 typ; 0 def)
% Number of atoms : 129 ( 67 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 97 ( 15 ~; 51 |; 0 &)
% ( 25 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number arithmetic : 442 ( 50 atm; 101 fun; 258 num; 33 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 28 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(pow_type,type,
pow: ( $real * $real ) > $real ).
tff(sqr_type,type,
sqr: $real > $real ).
tff(1,plain,
( ( pow(2,2) != 4 )
<=> ( pow(2,2) != 4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
pow(2,2) != 4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_2_21) ).
tff(3,plain,
pow(2,2) != 4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $real] :
refl(
( ( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
<=> ( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [X: $real] :
rewrite(
( ( $lesseq(X,0)
| ( $sum(sqr(X),$product(-1,pow(X,2))) = 0 ) )
<=> ( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $real] :
( $lesseq(X,0)
| ( $sum(sqr(X),$product(-1,pow(X,2))) = 0 ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $real] :
rewrite(
( ( $lesseq(X,0)
| ( $sum(pow(X,2),$product(-1,sqr(X))) = 0 ) )
<=> ( $lesseq(X,0)
| ( $sum(sqr(X),$product(-1,pow(X,2))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $real] :
( $lesseq(X,0)
| ( $sum(pow(X,2),$product(-1,sqr(X))) = 0 ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( $sum(sqr(X),$product(-1,pow(X,2))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $real] :
rewrite(
( ( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) )
<=> ( $lesseq(X,0)
| ( $sum(pow(X,2),$product(-1,sqr(X))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( $sum(pow(X,2),$product(-1,sqr(X))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $real] :
trans(
monotonicity(
rewrite(
( $less(0,X)
<=> ~ $lesseq(X,0) )),
( ( $less(0,X)
=> ( pow(X,2) = sqr(X) ) )
<=> ( ~ $lesseq(X,0)
=> ( pow(X,2) = sqr(X) ) ) )),
rewrite(
( ( ~ $lesseq(X,0)
=> ( pow(X,2) = sqr(X) ) )
<=> ( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ) )),
( ( $less(0,X)
=> ( pow(X,2) = sqr(X) ) )
<=> ( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $real] :
( $less(0,X)
=> ( pow(X,2) = sqr(X) ) )
<=> ! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $real] :
( $less(0,X)
=> ( pow(X,2) = sqr(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_x_two) ).
tff(16,plain,
! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $real] :
( $lesseq(X,0)
| ( pow(X,2) = sqr(X) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $real] :
( $lesseq(X,0)
| ( $sum(pow(X,2),$product(-1,sqr(X))) = 0 ) ),
inference(modus_ponens,[status(thm)],[17,11]) ).
tff(19,plain,
! [X: $real] :
( $lesseq(X,0)
| ( $sum(sqr(X),$product(-1,pow(X,2))) = 0 ) ),
inference(modus_ponens,[status(thm)],[18,9]) ).
tff(20,plain,
! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ),
inference(modus_ponens,[status(thm)],[19,7]) ).
tff(21,plain,
! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) ),
inference(modus_ponens,[status(thm)],[21,5]) ).
tff(23,plain,
( ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| ( pow(2,2) = 4 ) )
<=> ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| ( pow(2,2) = 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( $false
| ( pow(2,2) = 4 ) )
<=> ( pow(2,2) = 4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( $sum(4,$product(-1,pow(2,2))) = 0 )
<=> ( pow(2,2) = 4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
$sum($product(2,2),$product(-1,pow(2,2))) = $sum(4,$product(-1,pow(2,2))),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 )
<=> ( $sum(4,$product(-1,pow(2,2))) = 0 ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 )
<=> ( pow(2,2) = 4 ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( $lesseq(2,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( $lesseq(2,0)
| ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 ) )
<=> ( $false
| ( pow(2,2) = 4 ) ) ),
inference(monotonicity,[status(thm)],[29,28]) ).
tff(31,plain,
( ( $lesseq(2,0)
| ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 ) )
<=> ( pow(2,2) = 4 ) ),
inference(transitivity,[status(thm)],[30,24]) ).
tff(32,plain,
( ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| $lesseq(2,0)
| ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 ) )
<=> ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| ( pow(2,2) = 4 ) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| $lesseq(2,0)
| ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 ) )
<=> ( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| ( pow(2,2) = 4 ) ) ),
inference(transitivity,[status(thm)],[32,23]) ).
tff(34,plain,
( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| $lesseq(2,0)
| ( $sum($product(2,2),$product(-1,pow(2,2))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $real] :
( $lesseq(X,0)
| ( $sum($product(X,X),$product(-1,pow(X,2))) = 0 ) )
| ( pow(2,2) = 4 ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,22,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ARI741_1 : TPTP v8.1.0. Released v7.0.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 30 01:52:15 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------