TSTP Solution File: ARI740_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI740_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 17:02:48 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 75 ( 27 unt; 1 typ; 0 def)
% Number of atoms : 207 ( 126 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 148 ( 36 ~; 64 |; 0 &)
% ( 42 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number arithmetic : 952 ( 63 atm; 258 fun; 548 num; 83 var)
% Number of types : 2 ( 0 usr; 2 ari)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 83 ( 72 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(power_type,type,
power: ( $real * $int ) > $real ).
tff(1,plain,
( ( 4 = power(2,2) )
<=> ( power(2,2) = 4 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( power(2,2) = 4 )
<=> ( 4 = power(2,2) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( power(2,2) != 4 )
<=> ( 4 != power(2,2) ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ( power(2,2) != 4 )
<=> ( power(2,2) != 4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
power(2,2) != 4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_2_2) ).
tff(6,plain,
power(2,2) != 4,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
4 != power(2,2),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
( ( 2 = power(2,1) )
<=> ( power(2,1) = 2 ) ),
inference(commutativity,[status(thm)],]) ).
tff(9,plain,
( ( power(2,1) = 2 )
<=> ( 2 = power(2,1) ) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $real] :
refl(
( ( $sum(X,$product(-1,power(X,1))) = 0 )
<=> ( $sum(X,$product(-1,power(X,1))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
<=> ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $real] :
trans(
monotonicity(rewrite(( $sum(power(X,1),$product(-1,X)) = $sum($product(-1,X),power(X,1)) )),
( ( $sum(power(X,1),$product(-1,X)) = 0 )
<=> ( $sum($product(-1,X),power(X,1)) = 0 ) )),
rewrite(
( ( $sum($product(-1,X),power(X,1)) = 0 )
<=> ( $sum(X,$product(-1,power(X,1))) = 0 ) )),
( ( $sum(power(X,1),$product(-1,X)) = 0 )
<=> ( $sum(X,$product(-1,power(X,1))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $real] : ( $sum(power(X,1),$product(-1,X)) = 0 )
<=> ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $real] :
rewrite(
( ( power(X,1) = X )
<=> ( $sum(power(X,1),$product(-1,X)) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $real] : ( power(X,1) = X )
<=> ! [X: $real] : ( $sum(power(X,1),$product(-1,X)) = 0 ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $real] : ( power(X,1) = X )
<=> ! [X: $real] : ( power(X,1) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [X: $real] : ( power(X,1) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_1) ).
tff(18,plain,
! [X: $real] : ( power(X,1) = X ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: $real] : ( $sum(power(X,1),$product(-1,X)) = 0 ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( power(2,1) = 2 ) )
<=> ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( power(2,1) = 2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( $sum(2,$product(-1,power(2,1))) = 0 )
<=> ( power(2,1) = 2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( $sum(2,$product(-1,power(2,1))) = 0 ) )
<=> ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( power(2,1) = 2 ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( $sum(2,$product(-1,power(2,1))) = 0 ) )
<=> ( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( power(2,1) = 2 ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( $sum(2,$product(-1,power(2,1))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X: $real] : ( $sum(X,$product(-1,power(X,1))) = 0 )
| ( power(2,1) = 2 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
power(2,1) = 2,
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
2 = power(2,1),
inference(modus_ponens,[status(thm)],[29,9]) ).
tff(31,plain,
( ( 2 != power(2,1) )
| $greatereq(power(2,1),2) ),
inference(theory_lemma,[status(thm)],]) ).
tff(32,plain,
$greatereq(power(2,1),2),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ( 0 = $sum(power(2,2),$product(-2,power(2,1))) )
<=> ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ),
inference(commutativity,[status(thm)],]) ).
tff(34,plain,
( ( $sum(power(2,2),$product(-2,power(2,1))) = 0 )
<=> ( 0 = $sum(power(2,2),$product(-2,power(2,1))) ) ),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [X: $real,N: $int] :
refl(
( ( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
<=> ( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
<=> ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [X: $real,N: $int] :
rewrite(
( ( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(power(X,$sum(-1,N)),X))) = 0 ) )
<=> ( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(power(X,$sum(-1,N)),X))) = 0 ) )
<=> ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [X: $real,N: $int] :
rewrite(
( ( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) )
<=> ( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(power(X,$sum(-1,N)),X))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) )
<=> ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(power(X,$sum(-1,N)),X))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) )
<=> ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [X: $real,N: $int] :
trans(
monotonicity(
rewrite(
( $less(0,N)
<=> ~ $lesseq(N,0) )),
rewrite(
( ( power(X,N) = $product(X,power(X,$difference(N,1))) )
<=> ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) )),
( ( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) )
<=> ( ~ $lesseq(N,0)
=> ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ) )),
rewrite(
( ( ~ $lesseq(N,0)
=> ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) )
<=> ( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ) )),
( ( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) )
<=> ( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X: $real,N: $int] :
( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) )
<=> ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X: $real,N: $int] :
( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_s_alt) ).
tff(45,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( power(X,N) = $product(power(X,$sum(-1,N)),X) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(power(X,$sum(-1,N)),X))) = 0 ) ),
inference(modus_ponens,[status(thm)],[46,40]) ).
tff(48,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ),
inference(modus_ponens,[status(thm)],[47,38]) ).
tff(49,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) ),
inference(modus_ponens,[status(thm)],[49,36]) ).
tff(51,plain,
( ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) )
<=> ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( $false
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) )
<=> ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 )
<=> ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( $lesseq(2,0)
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( $lesseq(2,0)
| ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 ) )
<=> ( $false
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[54,53]) ).
tff(56,plain,
( ( $lesseq(2,0)
| ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 ) )
<=> ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ),
inference(transitivity,[status(thm)],[55,52]) ).
tff(57,plain,
( ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| $lesseq(2,0)
| ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 ) )
<=> ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| $lesseq(2,0)
| ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 ) )
<=> ( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ) ),
inference(transitivity,[status(thm)],[57,51]) ).
tff(59,plain,
( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| $lesseq(2,0)
| ( $sum(power(2,2),$product(-1,$product(2,power(2,$sum(-1,2))))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X: $real,N: $int] :
( $lesseq(N,0)
| ( $sum(power(X,N),$product(-1,$product(X,power(X,$sum(-1,N))))) = 0 ) )
| ( $sum(power(2,2),$product(-2,power(2,1))) = 0 ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$sum(power(2,2),$product(-2,power(2,1))) = 0,
inference(unit_resolution,[status(thm)],[60,50]) ).
tff(62,plain,
0 = $sum(power(2,2),$product(-2,power(2,1))),
inference(modus_ponens,[status(thm)],[61,34]) ).
tff(63,plain,
( ( 0 != $sum(power(2,2),$product(-2,power(2,1))) )
| $greatereq($sum(power(2,2),$product(-2,power(2,1))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(64,plain,
$greatereq($sum(power(2,2),$product(-2,power(2,1))),0),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ $greatereq(power(2,1),2)
| ~ $greatereq($sum(power(2,2),$product(-2,power(2,1))),0)
| $greatereq(power(2,2),4) ),
inference(theory_lemma,[status(thm)],]) ).
tff(66,plain,
$greatereq(power(2,2),4),
inference(unit_resolution,[status(thm)],[65,64,32]) ).
tff(67,plain,
( ( 2 != power(2,1) )
| $lesseq(power(2,1),2) ),
inference(theory_lemma,[status(thm)],]) ).
tff(68,plain,
$lesseq(power(2,1),2),
inference(unit_resolution,[status(thm)],[67,30]) ).
tff(69,plain,
( ( 0 != $sum(power(2,2),$product(-2,power(2,1))) )
| $lesseq($sum(power(2,2),$product(-2,power(2,1))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(70,plain,
$lesseq($sum(power(2,2),$product(-2,power(2,1))),0),
inference(unit_resolution,[status(thm)],[69,62]) ).
tff(71,plain,
( ~ $lesseq(power(2,1),2)
| ~ $lesseq($sum(power(2,2),$product(-2,power(2,1))),0)
| $lesseq(power(2,2),4) ),
inference(theory_lemma,[status(thm)],]) ).
tff(72,plain,
$lesseq(power(2,2),4),
inference(unit_resolution,[status(thm)],[71,70,68]) ).
tff(73,plain,
( ( 4 = power(2,2) )
| ~ $lesseq(power(2,2),4)
| ~ $greatereq(power(2,2),4) ),
inference(theory_lemma,[status(thm)],]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,72,66,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ARI740_1 : TPTP v8.1.0. Released v7.0.0.
% 0.16/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Aug 30 02:07:33 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.22/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.22/0.37 Usage: tptp [options] [-file:]file
% 0.22/0.37 -h, -? prints this message.
% 0.22/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.22/0.37 -m, -model generate model.
% 0.22/0.37 -p, -proof generate proof.
% 0.22/0.37 -c, -core generate unsat core of named formulas.
% 0.22/0.37 -st, -statistics display statistics.
% 0.22/0.37 -t:timeout set timeout (in second).
% 0.22/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.22/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.22/0.37 -<param>:<value> configuration parameter and value.
% 0.22/0.37 -o:<output-file> file to place output in.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------