TSTP Solution File: SYN003-1.006 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN003-1.006 : 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 23:53:07 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 51
% Syntax : Number of formulae : 122 ( 13 unt; 12 typ; 0 def)
% Number of atoms : 332 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 385 ( 163 ~; 150 |; 0 &)
% ( 72 <=>; 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 : 14 ( 12 usr; 14 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(r_1_type,type,
r_1: $o ).
tff(p_2_type,type,
p_2: $o ).
tff(p_1_type,type,
p_1: $o ).
tff(r_type,type,
r: $o ).
tff(r_2_type,type,
r_2: $o ).
tff(p_3_type,type,
p_3: $o ).
tff(r_3_type,type,
r_3: $o ).
tff(p_4_type,type,
p_4: $o ).
tff(r_4_type,type,
r_4: $o ).
tff(p_5_type,type,
p_5: $o ).
tff(r_5_type,type,
r_5: $o ).
tff(p_6_type,type,
p_6: $o ).
tff(1,plain,
( ( $false
| $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( r_1
| $false )
<=> r_1 ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_4) ).
tff(5,plain,
( r
<=> $true ),
inference(iff_true,[status(thm)],[4]) ).
tff(6,plain,
( ~ r
<=> ~ $true ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ~ r
<=> $false ),
inference(transitivity,[status(thm)],[6,2]) ).
tff(8,plain,
( ( r_1
| ~ r )
<=> ( r_1
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( r_1
| ~ r )
<=> r_1 ),
inference(transitivity,[status(thm)],[8,3]) ).
tff(10,plain,
( ( ~ r
| r_1 )
<=> ( r_1
| ~ r ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( ~ r
| r_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_1) ).
tff(12,plain,
( r_1
| ~ r ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
r_1,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
( r_1
<=> $true ),
inference(iff_true,[status(thm)],[13]) ).
tff(15,plain,
( ~ r_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ r_1
<=> $false ),
inference(transitivity,[status(thm)],[15,2]) ).
tff(17,plain,
( ( ~ p_2
| $false
| $false )
<=> ~ p_2 ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( r_2
| $false )
<=> r_2 ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( r_2
| ~ r )
<=> ( r_2
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(20,plain,
( ( r_2
| ~ r )
<=> r_2 ),
inference(transitivity,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ r
| r_2 )
<=> ( r_2
| ~ r ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
( ~ r
| r_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_2) ).
tff(23,plain,
( r_2
| ~ r ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
r_2,
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
( r_2
<=> $true ),
inference(iff_true,[status(thm)],[24]) ).
tff(26,plain,
( ~ r_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ~ r_2
<=> $false ),
inference(transitivity,[status(thm)],[26,2]) ).
tff(28,plain,
( ( ~ p_3
| $false
| $false )
<=> ~ p_3 ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( r_3
| $false )
<=> r_3 ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( r_3
| ~ r )
<=> ( r_3
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(31,plain,
( ( r_3
| ~ r )
<=> r_3 ),
inference(transitivity,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ r
| r_3 )
<=> ( r_3
| ~ r ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
( ~ r
| r_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_3) ).
tff(34,plain,
( r_3
| ~ r ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
r_3,
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
( r_3
<=> $true ),
inference(iff_true,[status(thm)],[35]) ).
tff(37,plain,
( ~ r_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ r_3
<=> $false ),
inference(transitivity,[status(thm)],[37,2]) ).
tff(39,plain,
( ( ~ p_4
| $false
| $false )
<=> ~ p_4 ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( r_4
| $false )
<=> r_4 ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( r_4
| ~ r )
<=> ( r_4
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(42,plain,
( ( r_4
| ~ r )
<=> r_4 ),
inference(transitivity,[status(thm)],[41,40]) ).
tff(43,plain,
( ( ~ r
| r_4 )
<=> ( r_4
| ~ r ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
( ~ r
| r_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_4) ).
tff(45,plain,
( r_4
| ~ r ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
r_4,
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
( r_4
<=> $true ),
inference(iff_true,[status(thm)],[46]) ).
tff(48,plain,
( ~ r_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ r_4
<=> $false ),
inference(transitivity,[status(thm)],[48,2]) ).
tff(50,plain,
( ( ~ p_5
| $false
| $false )
<=> ~ p_5 ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( r_5
| $false )
<=> r_5 ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( r_5
| ~ r )
<=> ( r_5
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(53,plain,
( ( r_5
| ~ r )
<=> r_5 ),
inference(transitivity,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ r
| r_5 )
<=> ( r_5
| ~ r ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
( ~ r
| r_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_5) ).
tff(56,plain,
( r_5
| ~ r ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
r_5,
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
( r_5
<=> $true ),
inference(iff_true,[status(thm)],[57]) ).
tff(59,plain,
( ~ r_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ r_5
<=> $false ),
inference(transitivity,[status(thm)],[59,2]) ).
tff(61,axiom,
~ p_6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_2) ).
tff(62,plain,
( p_6
<=> $false ),
inference(iff_false,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ p_5
| p_6
| ~ r_5 )
<=> ( ~ p_5
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[62,60]) ).
tff(64,plain,
( ( ~ p_5
| p_6
| ~ r_5 )
<=> ~ p_5 ),
inference(transitivity,[status(thm)],[63,50]) ).
tff(65,plain,
( ( ~ p_5
| p_6
| ~ r_5 )
<=> ( ~ p_5
| p_6
| ~ r_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ p_5
| ~ r_5
| p_6 )
<=> ( ~ p_5
| p_6
| ~ r_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
( ~ p_5
| ~ r_5
| p_6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_5) ).
tff(68,plain,
( ~ p_5
| p_6
| ~ r_5 ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ p_5
| p_6
| ~ r_5 ),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
~ p_5,
inference(modus_ponens,[status(thm)],[69,64]) ).
tff(71,plain,
( p_5
<=> $false ),
inference(iff_false,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ p_4
| p_5
| ~ r_4 )
<=> ( ~ p_4
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[71,49]) ).
tff(73,plain,
( ( ~ p_4
| p_5
| ~ r_4 )
<=> ~ p_4 ),
inference(transitivity,[status(thm)],[72,39]) ).
tff(74,plain,
( ( ~ p_4
| p_5
| ~ r_4 )
<=> ( ~ p_4
| p_5
| ~ r_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ p_4
| ~ r_4
| p_5 )
<=> ( ~ p_4
| p_5
| ~ r_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
( ~ p_4
| ~ r_4
| p_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_4) ).
tff(77,plain,
( ~ p_4
| p_5
| ~ r_4 ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ p_4
| p_5
| ~ r_4 ),
inference(modus_ponens,[status(thm)],[77,74]) ).
tff(79,plain,
~ p_4,
inference(modus_ponens,[status(thm)],[78,73]) ).
tff(80,plain,
( p_4
<=> $false ),
inference(iff_false,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ p_3
| p_4
| ~ r_3 )
<=> ( ~ p_3
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[80,38]) ).
tff(82,plain,
( ( ~ p_3
| p_4
| ~ r_3 )
<=> ~ p_3 ),
inference(transitivity,[status(thm)],[81,28]) ).
tff(83,plain,
( ( ~ p_3
| p_4
| ~ r_3 )
<=> ( ~ p_3
| p_4
| ~ r_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ p_3
| ~ r_3
| p_4 )
<=> ( ~ p_3
| p_4
| ~ r_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
( ~ p_3
| ~ r_3
| p_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_3) ).
tff(86,plain,
( ~ p_3
| p_4
| ~ r_3 ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ p_3
| p_4
| ~ r_3 ),
inference(modus_ponens,[status(thm)],[86,83]) ).
tff(88,plain,
~ p_3,
inference(modus_ponens,[status(thm)],[87,82]) ).
tff(89,plain,
( p_3
<=> $false ),
inference(iff_false,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ p_2
| p_3
| ~ r_2 )
<=> ( ~ p_2
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[89,27]) ).
tff(91,plain,
( ( ~ p_2
| p_3
| ~ r_2 )
<=> ~ p_2 ),
inference(transitivity,[status(thm)],[90,17]) ).
tff(92,plain,
( ( ~ p_2
| p_3
| ~ r_2 )
<=> ( ~ p_2
| p_3
| ~ r_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ p_2
| ~ r_2
| p_3 )
<=> ( ~ p_2
| p_3
| ~ r_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( ~ p_2
| ~ r_2
| p_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_2) ).
tff(95,plain,
( ~ p_2
| p_3
| ~ r_2 ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ p_2
| p_3
| ~ r_2 ),
inference(modus_ponens,[status(thm)],[95,92]) ).
tff(97,plain,
~ p_2,
inference(modus_ponens,[status(thm)],[96,91]) ).
tff(98,plain,
( p_2
<=> $false ),
inference(iff_false,[status(thm)],[97]) ).
tff(99,axiom,
p_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_1) ).
tff(100,plain,
( p_1
<=> $true ),
inference(iff_true,[status(thm)],[99]) ).
tff(101,plain,
( ~ p_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ p_1
<=> $false ),
inference(transitivity,[status(thm)],[101,2]) ).
tff(103,plain,
( ( ~ p_1
| p_2
| ~ r_1 )
<=> ( $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[102,98,16]) ).
tff(104,plain,
( ( ~ p_1
| p_2
| ~ r_1 )
<=> $false ),
inference(transitivity,[status(thm)],[103,1]) ).
tff(105,plain,
( ( ~ p_1
| p_2
| ~ r_1 )
<=> ( ~ p_1
| p_2
| ~ r_1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ p_1
| ~ r_1
| p_2 )
<=> ( ~ p_1
| p_2
| ~ r_1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
( ~ p_1
| ~ r_1
| p_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_1) ).
tff(108,plain,
( ~ p_1
| p_2
| ~ r_1 ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ p_1
| p_2
| ~ r_1 ),
inference(modus_ponens,[status(thm)],[108,105]) ).
tff(110,plain,
$false,
inference(modus_ponens,[status(thm)],[109,104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN003-1.006 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 00:58:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------