TSTP Solution File: RNG125+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 20 03:18:33 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 40 ( 3 unt; 7 typ; 0 def)
% Number of atoms : 187 ( 42 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 173 ( 19 ~; 68 |; 65 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 !; 42 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(xb_type,type,
xb: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xu_type,type,
xu: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(xa_type,type,
xa: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $true
& $true )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $true
| aDivisorOf0(xu,xb)
| $true )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ~ ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb) )
<=> ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ~ ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
tff(6,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
& doDivides0(xu,xb) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
doDivides0(xu,xb),
inference(and_elim,[status(thm)],[6]) ).
tff(10,plain,
( doDivides0(xu,xb)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) )
<=> ( $true
| aDivisorOf0(xu,xb)
| $true ) ),
inference(monotonicity,[status(thm)],[10,8]) ).
tff(12,plain,
( ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[11,3]) ).
tff(13,plain,
( ( $true
| $true
| aDivisorOf0(xu,xa) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ~ ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa) )
<=> ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ ~ ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).
tff(16,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
& doDivides0(xu,xa) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
<=> $true ),
inference(iff_true,[status(thm)],[17]) ).
tff(19,plain,
doDivides0(xu,xa),
inference(and_elim,[status(thm)],[16]) ).
tff(20,plain,
( doDivides0(xu,xa)
<=> $true ),
inference(iff_true,[status(thm)],[19]) ).
tff(21,plain,
( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
<=> ( $true
| $true
| aDivisorOf0(xu,xa) ) ),
inference(monotonicity,[status(thm)],[20,18]) ).
tff(22,plain,
( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
<=> $true ),
inference(transitivity,[status(thm)],[21,13]) ).
tff(23,plain,
( ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> ( $true
& $true ) ),
inference(monotonicity,[status(thm)],[22,12]) ).
tff(24,plain,
( ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[23,2]) ).
tff(25,plain,
( ~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[25,1]) ).
tff(27,plain,
( ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) )
<=> ~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ ( ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| doDivides0(xu,xa)
| aDivisorOf0(xu,xa) )
& ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
| doDivides0(xu,xb)
| aDivisorOf0(xu,xb) ) )
<=> ~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
~ ( ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| doDivides0(xu,xa)
| aDivisorOf0(xu,xa) )
& ( ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) )
| doDivides0(xu,xb)
| aDivisorOf0(xu,xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).
tff(31,plain,
~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ( doDivides0(xu,xa)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xa ) )
| aDivisorOf0(xu,xa) )
& ( doDivides0(xu,xb)
| aDivisorOf0(xu,xb)
| ? [W0: $i] :
( aElement0(W0)
& ( sdtasdt0(xu,W0) = xb ) ) ) ),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
$false,
inference(modus_ponens,[status(thm)],[32,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n003.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Sep 2 22:48:40 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.33 Usage: tptp [options] [-file:]file
% 0.14/0.33 -h, -? prints this message.
% 0.14/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.33 -m, -model generate model.
% 0.14/0.33 -p, -proof generate proof.
% 0.14/0.33 -c, -core generate unsat core of named formulas.
% 0.14/0.33 -st, -statistics display statistics.
% 0.14/0.33 -t:timeout set timeout (in second).
% 0.14/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.33 -<param>:<value> configuration parameter and value.
% 0.14/0.33 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------