TSTP Solution File: SYN085-1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN085-1.010 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:53:41 EDT 2022
% Result : Unsatisfiable 0.10s 0.35s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of formulae : 91 ( 12 unt; 11 typ; 0 def)
% Number of atoms : 613 ( 0 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 1021 ( 488 ~; 469 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 13 ( 11 usr; 13 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_10_type,type,
p_10: $o ).
tff(p_9_type,type,
p_9: $o ).
tff(p_8_type,type,
p_8: $o ).
tff(p_7_type,type,
p_7: $o ).
tff(p_6_type,type,
p_6: $o ).
tff(p_5_type,type,
p_5: $o ).
tff(p_4_type,type,
p_4: $o ).
tff(p_3_type,type,
p_3: $o ).
tff(p_2_type,type,
p_2: $o ).
tff(p_1_type,type,
p_1: $o ).
tff(p_0_type,type,
p_0: $o ).
tff(1,plain,
( ( $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
p_10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_11) ).
tff(4,plain,
( p_10
<=> $true ),
inference(iff_true,[status(thm)],[3]) ).
tff(5,plain,
( ~ p_10
<=> ~ $true ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ~ p_10
<=> $false ),
inference(transitivity,[status(thm)],[5,2]) ).
tff(7,axiom,
p_9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_10) ).
tff(8,plain,
( p_9
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ~ p_9
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ p_9
<=> $false ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,axiom,
p_8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_9) ).
tff(12,plain,
( p_8
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ p_8
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ p_8
<=> $false ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,axiom,
p_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_8) ).
tff(16,plain,
( p_7
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ p_7
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ p_7
<=> $false ),
inference(transitivity,[status(thm)],[17,2]) ).
tff(19,axiom,
p_6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_7) ).
tff(20,plain,
( p_6
<=> $true ),
inference(iff_true,[status(thm)],[19]) ).
tff(21,plain,
( ~ p_6
<=> ~ $true ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ~ p_6
<=> $false ),
inference(transitivity,[status(thm)],[21,2]) ).
tff(23,axiom,
p_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_6) ).
tff(24,plain,
( p_5
<=> $true ),
inference(iff_true,[status(thm)],[23]) ).
tff(25,plain,
( ~ p_5
<=> ~ $true ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ p_5
<=> $false ),
inference(transitivity,[status(thm)],[25,2]) ).
tff(27,axiom,
p_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_5) ).
tff(28,plain,
( p_4
<=> $true ),
inference(iff_true,[status(thm)],[27]) ).
tff(29,plain,
( ~ p_4
<=> ~ $true ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ~ p_4
<=> $false ),
inference(transitivity,[status(thm)],[29,2]) ).
tff(31,axiom,
p_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_4) ).
tff(32,plain,
( p_3
<=> $true ),
inference(iff_true,[status(thm)],[31]) ).
tff(33,plain,
( ~ p_3
<=> ~ $true ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ p_3
<=> $false ),
inference(transitivity,[status(thm)],[33,2]) ).
tff(35,axiom,
p_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_3) ).
tff(36,plain,
( p_2
<=> $true ),
inference(iff_true,[status(thm)],[35]) ).
tff(37,plain,
( ~ p_2
<=> ~ $true ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ p_2
<=> $false ),
inference(transitivity,[status(thm)],[37,2]) ).
tff(39,axiom,
p_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_2) ).
tff(40,plain,
( p_1
<=> $true ),
inference(iff_true,[status(thm)],[39]) ).
tff(41,plain,
( ~ p_1
<=> ~ $true ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ~ p_1
<=> $false ),
inference(transitivity,[status(thm)],[41,2]) ).
tff(43,plain,
( ( ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[42,38,34,30,26,22,18,14,10,6]) ).
tff(44,plain,
( ( ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> $false ),
inference(transitivity,[status(thm)],[43,1]) ).
tff(45,plain,
( ( $false
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
~ p_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_goal_1) ).
tff(47,plain,
( p_0
<=> $false ),
inference(iff_false,[status(thm)],[46]) ).
tff(48,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( $false
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(transitivity,[status(thm)],[48,45]) ).
tff(50,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( p_0
| ~ p_1
| ~ p_2 )
<=> ( p_0
| ~ p_1
| ~ p_2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3 ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4 ) ),
inference(transitivity,[status(thm)],[62,57]) ).
tff(64,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5 ) ),
inference(transitivity,[status(thm)],[64,56]) ).
tff(66,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6 ) ),
inference(transitivity,[status(thm)],[66,55]) ).
tff(68,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7 ) ),
inference(transitivity,[status(thm)],[68,54]) ).
tff(70,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8 ) ),
inference(transitivity,[status(thm)],[70,53]) ).
tff(72,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9 ) ),
inference(transitivity,[status(thm)],[72,52]) ).
tff(74,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 )
<=> ( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ) ),
inference(transitivity,[status(thm)],[74,51]) ).
tff(76,axiom,
( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_1) ).
tff(77,plain,
( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( p_0
| ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ),
inference(modus_ponens,[status(thm)],[77,50]) ).
tff(79,plain,
( ~ p_1
| ~ p_2
| ~ p_3
| ~ p_4
| ~ p_5
| ~ p_6
| ~ p_7
| ~ p_8
| ~ p_9
| ~ p_10 ),
inference(modus_ponens,[status(thm)],[78,49]) ).
tff(80,plain,
$false,
inference(modus_ponens,[status(thm)],[79,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SYN085-1.010 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Sep 5 01:41:38 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.10/0.35 % SZS status Unsatisfiable
% 0.10/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------