TSTP Solution File: NUM625+3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM625+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 13:10:59 EDT 2022
% Result : Theorem 0.17s 0.42s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 30 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 35 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 0 |; 5 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(xp_type,type,
xp: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xP_type,type,
xP: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( szmzizndt0(xQ) = szmzizndt0(xQ) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( xp = xx )
<=> ( szmzizndt0(xQ) = sdtlpdtrp0(xe,xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( xp = xx )
<=> ( xp = xx ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5496) ).
tff(6,plain,
xp = xx,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
szmzizndt0(xQ) = sdtlpdtrp0(xe,xm),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
sdtlpdtrp0(xe,xm) = szmzizndt0(xQ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) )
<=> ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) )
<=> $true ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) )
<=> $false ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( xx != szmzizndt0(xQ) )
<=> ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( xx != szmzizndt0(xQ) )
<=> ( xx != szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) )
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(16,plain,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) ) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
xx != szmzizndt0(xQ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
xx != szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
sdtlpdtrp0(xe,xm) != szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[18,13]) ).
tff(20,plain,
$false,
inference(modus_ponens,[status(thm)],[19,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM625+3 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n001.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Sep 2 12:49:53 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.42 % SZS status Theorem
% 0.17/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------