TSTP Solution File: ARI739_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI739_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 14 unt; 2 typ; 0 def)
% Number of atoms : 48 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 12 ~; 8 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 175 ( 0 atm; 55 fun; 99 num; 21 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(log_type,type,
log: $real > $real ).
tff(exp_type,type,
exp: $real > $real ).
tff(1,plain,
( ( log(exp(1)) != 1 )
<=> ( log(exp(1)) != 1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
log(exp(1)) != 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',log_e) ).
tff(3,plain,
log(exp(1)) != 1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $real] :
refl(
( ( $sum(log(exp(X)),$product(-1,X)) = 0 )
<=> ( $sum(log(exp(X)),$product(-1,X)) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
<=> ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [X: $real] :
rewrite(
( ( log(exp(X)) = X )
<=> ( $sum(log(exp(X)),$product(-1,X)) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $real] : ( log(exp(X)) = X )
<=> ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $real] : ( log(exp(X)) = X )
<=> ! [X: $real] : ( log(exp(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [X: $real] : ( log(exp(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',log_exp) ).
tff(10,plain,
! [X: $real] : ( log(exp(X)) = X ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 ),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( log(exp(1)) = 1 ) )
<=> ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( log(exp(1)) = 1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( $sum(-1,log(exp(1))) = 0 )
<=> ( log(exp(1)) = 1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
$sum(log(exp(1)),-1) = $sum(-1,log(exp(1))),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
$product(-1,1) = -1,
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
$sum(log(exp(1)),$product(-1,1)) = $sum(log(exp(1)),-1),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
$sum(log(exp(1)),$product(-1,1)) = $sum(-1,log(exp(1))),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
( ( $sum(log(exp(1)),$product(-1,1)) = 0 )
<=> ( $sum(-1,log(exp(1))) = 0 ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( $sum(log(exp(1)),$product(-1,1)) = 0 )
<=> ( log(exp(1)) = 1 ) ),
inference(transitivity,[status(thm)],[20,15]) ).
tff(22,plain,
( ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( $sum(log(exp(1)),$product(-1,1)) = 0 ) )
<=> ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( log(exp(1)) = 1 ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( $sum(log(exp(1)),$product(-1,1)) = 0 ) )
<=> ( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( log(exp(1)) = 1 ) ) ),
inference(transitivity,[status(thm)],[22,14]) ).
tff(24,plain,
( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( $sum(log(exp(1)),$product(-1,1)) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X: $real] : ( $sum(log(exp(X)),$product(-1,X)) = 0 )
| ( log(exp(1)) = 1 ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ARI739_1 : TPTP v8.1.0. Released v7.0.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 02:08:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------