TSTP Solution File: NUM490+3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM490+3 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 13:10:02 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 8 unt; 7 typ; 0 def)
% Number of atoms : 30 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 1 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xr_type,type,
xr: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xn,xm) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) )
<=> ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) )
<=> ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
tff(6,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm) )
<=> ( sdtasdt0(xn,xm) = sdtasdt0(xn,xm) ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm) )
<=> $true ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) )
<=> $false ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) )
<=> ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) )
<=> ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) )
| ( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(16,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm),
inference(or_elim,[status(thm)],[15]) ).
tff(17,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
$false,
inference(modus_ponens,[status(thm)],[18,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM490+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 11:07:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------