TSTP Solution File: SYN028-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN028-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 23:53:12 EDT 2022
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 25
% Syntax : Number of formulae : 67 ( 6 unt; 5 typ; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 82 ~; 76 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 7 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(s_type,type,
s: $o ).
tff(r_type,type,
r: $o ).
tff(q_type,type,
q: $o ).
tff(p_type,type,
p: $o ).
tff(t_type,type,
t: $o ).
tff(1,plain,
( ( $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $false
| s )
<=> s ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( $false
| r )
<=> r ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( q
| $false )
<=> q ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_something) ).
tff(7,plain,
( p
<=> $false ),
inference(iff_false,[status(thm)],[6]) ).
tff(8,plain,
( ( q
| p )
<=> ( q
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( q
| p )
<=> q ),
inference(transitivity,[status(thm)],[8,5]) ).
tff(10,plain,
( ( q
| p )
<=> ( q
| p ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( q
| p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(12,plain,
( q
| p ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( q
| p ),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
q,
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( q
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ q
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ q
<=> $false ),
inference(transitivity,[status(thm)],[16,2]) ).
tff(18,plain,
( ( ~ q
| r )
<=> ( $false
| r ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( ~ q
| r )
<=> r ),
inference(transitivity,[status(thm)],[18,4]) ).
tff(20,plain,
( ( ~ q
| r )
<=> ( ~ q
| r ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
( ~ q
| r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
tff(22,plain,
( ~ q
| r ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ q
| r ),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ q
| r ),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
r,
inference(modus_ponens,[status(thm)],[24,19]) ).
tff(26,plain,
( r
<=> $true ),
inference(iff_true,[status(thm)],[25]) ).
tff(27,plain,
( ~ r
<=> ~ $true ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ r
<=> $false ),
inference(transitivity,[status(thm)],[27,2]) ).
tff(29,plain,
( ( ~ r
| s )
<=> ( $false
| s ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ r
| s )
<=> s ),
inference(transitivity,[status(thm)],[29,3]) ).
tff(31,plain,
( ( ~ r
| s )
<=> ( ~ r
| s ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
( ~ r
| s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(33,plain,
( ~ r
| s ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ r
| s ),
inference(modus_ponens,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ r
| s ),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
s,
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
( s
<=> $true ),
inference(iff_true,[status(thm)],[36]) ).
tff(38,plain,
( ~ s
<=> ~ $true ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ~ s
<=> $false ),
inference(transitivity,[status(thm)],[38,2]) ).
tff(40,plain,
( ( ~ r
| ~ s )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[28,39]) ).
tff(41,plain,
( ( ~ r
| ~ s )
<=> $false ),
inference(transitivity,[status(thm)],[40,1]) ).
tff(42,plain,
( ( ~ r
| ~ s
| $false )
<=> ( ~ r
| ~ s ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( $false
| ~ t )
<=> ~ t ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( p
| ~ t )
<=> ( $false
| ~ t ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(45,plain,
( ( p
| ~ t )
<=> ~ t ),
inference(transitivity,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ t
| p )
<=> ( p
| ~ t ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( ~ t
| p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
tff(48,plain,
( p
| ~ t ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ t,
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
( t
<=> $false ),
inference(iff_false,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ r
| ~ s
| t )
<=> ( ~ r
| ~ s
| $false ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ r
| ~ s
| t )
<=> ( ~ r
| ~ s ) ),
inference(transitivity,[status(thm)],[51,42]) ).
tff(53,plain,
( ( ~ r
| ~ s
| t )
<=> ( ~ r
| ~ s
| t ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ r
| ~ s
| t )
<=> ( ~ r
| ~ s
| t ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ s
| ~ r )
<=> ( ~ r
| ~ s ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ s
| ~ r
| t )
<=> ( ~ r
| ~ s
| t ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ s
| ~ r
| t )
<=> ( ~ r
| ~ s
| t ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,axiom,
( ~ s
| ~ r
| t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(59,plain,
( ~ r
| ~ s
| t ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ r
| ~ s
| t ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
( ~ r
| ~ s ),
inference(modus_ponens,[status(thm)],[60,52]) ).
tff(62,plain,
$false,
inference(modus_ponens,[status(thm)],[61,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN028-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n008.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 : Mon Sep 5 01:08:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Unsatisfiable
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------