TSTP Solution File: PUZ013-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 14:10:50 EDT 2022
% Result : Unsatisfiable 0.08s 0.31s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 34
% Syntax : Number of formulae : 83 ( 9 unt; 7 typ; 0 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 352 ( 150 ~; 150 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 9 ( 7 usr; 9 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(some_germans_play_type,type,
some_germans_play: $o ).
tff(some_english_sing_not_type,type,
some_english_sing_not: $o ).
tff(some_monitors_are_awake_type,type,
some_monitors_are_awake: $o ).
tff(some_english_sing_type,type,
some_english_sing: $o ).
tff(some_scotch_dance_not_type,type,
some_scotch_dance_not: $o ).
tff(some_irish_fight_not_type,type,
some_irish_fight_not: $o ).
tff(some_monitors_are_not_awake_type,type,
some_monitors_are_not_awake: $o ).
tff(1,plain,
( ( $false
| ~ some_germans_play )
<=> ~ some_germans_play ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $false
| ~ some_english_sing_not
| $false )
<=> ~ some_english_sing_not ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ some_monitors_are_awake,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_some_monitors_are_awake) ).
tff(4,plain,
( some_monitors_are_awake
<=> $false ),
inference(iff_false,[status(thm)],[3]) ).
tff(5,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
some_english_sing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c18) ).
tff(7,plain,
( some_english_sing
<=> $true ),
inference(iff_true,[status(thm)],[6]) ).
tff(8,plain,
( ~ some_english_sing
<=> ~ $true ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ some_english_sing
<=> $false ),
inference(transitivity,[status(thm)],[8,5]) ).
tff(10,plain,
( ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake )
<=> ( $false
| ~ some_english_sing_not
| $false ) ),
inference(monotonicity,[status(thm)],[9,4]) ).
tff(11,plain,
( ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake )
<=> ~ some_english_sing_not ),
inference(transitivity,[status(thm)],[10,2]) ).
tff(12,plain,
( ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake )
<=> ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake )
<=> ( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
tff(15,plain,
( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ some_english_sing
| ~ some_english_sing_not
| some_monitors_are_awake ),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
~ some_english_sing_not,
inference(modus_ponens,[status(thm)],[16,11]) ).
tff(18,plain,
( some_english_sing_not
<=> $false ),
inference(iff_false,[status(thm)],[17]) ).
tff(19,plain,
( ( some_english_sing_not
| ~ some_germans_play )
<=> ( $false
| ~ some_germans_play ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( some_english_sing_not
| ~ some_germans_play )
<=> ~ some_germans_play ),
inference(transitivity,[status(thm)],[19,1]) ).
tff(21,plain,
( ( $false
| some_english_sing_not
| ~ some_germans_play
| $false )
<=> ( some_english_sing_not
| ~ some_germans_play ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
some_scotch_dance_not,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c19) ).
tff(23,plain,
( some_scotch_dance_not
<=> $true ),
inference(iff_true,[status(thm)],[22]) ).
tff(24,plain,
( ~ some_scotch_dance_not
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ some_scotch_dance_not
<=> $false ),
inference(transitivity,[status(thm)],[24,5]) ).
tff(26,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not )
<=> ( $false
| some_english_sing_not
| ~ some_germans_play
| $false ) ),
inference(monotonicity,[status(thm)],[9,25]) ).
tff(27,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not )
<=> ( some_english_sing_not
| ~ some_germans_play ) ),
inference(transitivity,[status(thm)],[26,21]) ).
tff(28,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not
| ~ some_germans_play )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ some_english_sing
| some_english_sing_not )
<=> ( ~ some_english_sing
| some_english_sing_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not
| ~ some_germans_play )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not
| ~ some_germans_play ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not
| ~ some_germans_play )
<=> ( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not ) ),
inference(transitivity,[status(thm)],[34,29]) ).
tff(36,axiom,
( ~ some_english_sing
| some_english_sing_not
| ~ some_scotch_dance_not
| ~ some_germans_play ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
tff(37,plain,
( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ some_english_sing
| some_english_sing_not
| ~ some_germans_play
| ~ some_scotch_dance_not ),
inference(modus_ponens,[status(thm)],[37,28]) ).
tff(39,plain,
( some_english_sing_not
| ~ some_germans_play ),
inference(modus_ponens,[status(thm)],[38,27]) ).
tff(40,plain,
~ some_germans_play,
inference(modus_ponens,[status(thm)],[39,20]) ).
tff(41,plain,
( some_germans_play
<=> $false ),
inference(iff_false,[status(thm)],[40]) ).
tff(42,plain,
( ( some_germans_play
| $false
| $false )
<=> some_germans_play ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( $false
| $false
| some_irish_fight_not )
<=> some_irish_fight_not ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( $false
| some_monitors_are_not_awake )
<=> some_monitors_are_not_awake ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( some_monitors_are_awake
| some_monitors_are_not_awake )
<=> ( $false
| some_monitors_are_not_awake ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(46,plain,
( ( some_monitors_are_awake
| some_monitors_are_not_awake )
<=> some_monitors_are_not_awake ),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
( ( some_monitors_are_not_awake
| some_monitors_are_awake )
<=> ( some_monitors_are_awake
| some_monitors_are_not_awake ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
( some_monitors_are_not_awake
| some_monitors_are_awake ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13) ).
tff(49,plain,
( some_monitors_are_awake
| some_monitors_are_not_awake ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
some_monitors_are_not_awake,
inference(modus_ponens,[status(thm)],[49,46]) ).
tff(51,plain,
( some_monitors_are_not_awake
<=> $true ),
inference(iff_true,[status(thm)],[50]) ).
tff(52,plain,
( ~ some_monitors_are_not_awake
<=> ~ $true ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ~ some_monitors_are_not_awake
<=> $false ),
inference(transitivity,[status(thm)],[52,5]) ).
tff(54,plain,
( ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not )
<=> ( $false
| $false
| some_irish_fight_not ) ),
inference(monotonicity,[status(thm)],[9,53]) ).
tff(55,plain,
( ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not )
<=> some_irish_fight_not ),
inference(transitivity,[status(thm)],[54,43]) ).
tff(56,plain,
( ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not )
<=> ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not )
<=> ( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
tff(59,plain,
( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ some_english_sing
| ~ some_monitors_are_not_awake
| some_irish_fight_not ),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,plain,
some_irish_fight_not,
inference(modus_ponens,[status(thm)],[60,55]) ).
tff(62,plain,
( some_irish_fight_not
<=> $true ),
inference(iff_true,[status(thm)],[61]) ).
tff(63,plain,
( ~ some_irish_fight_not
<=> ~ $true ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ~ some_irish_fight_not
<=> $false ),
inference(transitivity,[status(thm)],[63,5]) ).
tff(65,plain,
( ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not )
<=> ( some_germans_play
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[25,64]) ).
tff(66,plain,
( ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not )
<=> some_germans_play ),
inference(transitivity,[status(thm)],[65,42]) ).
tff(67,plain,
( ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not )
<=> ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ some_scotch_dance_not
| ~ some_irish_fight_not
| some_germans_play )
<=> ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ some_scotch_dance_not
| ~ some_irish_fight_not )
<=> ( ~ some_scotch_dance_not
| ~ some_irish_fight_not ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ some_scotch_dance_not
| ~ some_irish_fight_not
| some_germans_play )
<=> ( ~ some_scotch_dance_not
| ~ some_irish_fight_not
| some_germans_play ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ some_scotch_dance_not
| ~ some_irish_fight_not
| some_germans_play )
<=> ( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,axiom,
( ~ some_scotch_dance_not
| ~ some_irish_fight_not
| some_germans_play ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
tff(73,plain,
( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( some_germans_play
| ~ some_scotch_dance_not
| ~ some_irish_fight_not ),
inference(modus_ponens,[status(thm)],[73,67]) ).
tff(75,plain,
some_germans_play,
inference(modus_ponens,[status(thm)],[74,66]) ).
tff(76,plain,
$false,
inference(modus_ponens,[status(thm)],[75,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : PUZ013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n027.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Fri Sep 2 18:33:19 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.08/0.31 % SZS status Unsatisfiable
% 0.08/0.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------