TSTP Solution File: SWV132+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV132+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Thu Sep 29 15:10:05 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 4 unt; 10 typ; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 52 ( 8 avg)
% Number of connectives : 189 ( 47 ~; 46 |; 60 &)
% ( 10 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i ).
tff(s_best7_type,type,
s_best7: $i ).
tff(pv1341_type,type,
pv1341: $i ).
tff(tptp_float_0_001_type,type,
tptp_float_0_001: $i ).
tff(s_worst7_type,type,
s_worst7: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(s_sworst7_type,type,
s_sworst7: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $false
| leq(s_best7,n3) )
<=> leq(s_best7,n3) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ ( ( ~ leq(tptp_float_0_001,pv1341)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) )
<=> ~ ( ~ ( ~ leq(tptp_float_0_001,pv1341)
& ( leq(n0,s_best7)
| leq(tptp_float_0_001,pv1341) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) )
| leq(s_best7,n3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ ( ( ~ leq(tptp_float_0_001,pv1341)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gauss_array_0002) ).
tff(5,plain,
~ ( ~ ( ~ leq(tptp_float_0_001,pv1341)
& ( leq(n0,s_best7)
| leq(tptp_float_0_001,pv1341) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) )
| leq(s_best7,n3) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
( ~ leq(tptp_float_0_001,pv1341)
& ( leq(n0,s_best7)
| leq(tptp_float_0_001,pv1341) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) ),
inference(or_elim,[status(thm)],[5]) ).
tff(7,plain,
~ leq(tptp_float_0_001,pv1341),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
( leq(tptp_float_0_001,pv1341)
<=> $false ),
inference(iff_false,[status(thm)],[7]) ).
tff(9,plain,
( ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
<=> ( $false
| leq(s_best7,n3) ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
<=> leq(s_best7,n3) ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
<=> ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) ),
inference(and_elim,[status(thm)],[6]) ).
tff(13,plain,
( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
leq(s_best7,n3),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( leq(s_best7,n3)
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ leq(s_best7,n3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ leq(s_best7,n3)
<=> $false ),
inference(transitivity,[status(thm)],[16,1]) ).
tff(18,plain,
~ leq(s_best7,n3),
inference(or_elim,[status(thm)],[5]) ).
tff(19,plain,
$false,
inference(modus_ponens,[status(thm)],[18,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV132+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.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 : Sun Sep 4 01:37:15 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------