TSTP Solution File: ALG200+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG200+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 6 16:09:07 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 8 unt; 8 typ; 0 def)
% Number of atoms : 299 ( 259 equ)
% Maximal formula atoms : 42 ( 7 avg)
% Number of connectives : 384 ( 125 ~; 150 |; 80 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(e6_type,type,
e6: $i ).
tff(op_type,type,
op: ( $i * $i ) > $i ).
tff(e5_type,type,
e5: $i ).
tff(e4_type,type,
e4: $i ).
tff(e3_type,type,
e3: $i ).
tff(e2_type,type,
e2: $i ).
tff(e1_type,type,
e1: $i ).
tff(e0_type,type,
e0: $i ).
tff(1,plain,
( ( $false
| $false
| $false
| $false
| $false
| $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ~ ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ~ ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ~ ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(transitivity,[status(thm)],[5,3]) ).
tff(7,axiom,
~ ~ ( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(8,plain,
( ( op(e0,e0) = e0 )
& ( op(e1,e1) = e1 )
& ( op(e2,e2) = e2 )
& ( op(e3,e3) = e3 )
& ( op(e4,e4) = e4 )
& ( op(e5,e5) = e5 )
& ( op(e6,e6) = e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
op(e6,e6) = e6,
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
( ( op(e6,e6) = e6 )
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ( op(e6,e6) != e6 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( op(e6,e6) != e6 )
<=> $false ),
inference(transitivity,[status(thm)],[11,2]) ).
tff(13,plain,
op(e5,e5) = e5,
inference(and_elim,[status(thm)],[8]) ).
tff(14,plain,
( ( op(e5,e5) = e5 )
<=> $true ),
inference(iff_true,[status(thm)],[13]) ).
tff(15,plain,
( ( op(e5,e5) != e5 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( op(e5,e5) != e5 )
<=> $false ),
inference(transitivity,[status(thm)],[15,2]) ).
tff(17,plain,
op(e4,e4) = e4,
inference(and_elim,[status(thm)],[8]) ).
tff(18,plain,
( ( op(e4,e4) = e4 )
<=> $true ),
inference(iff_true,[status(thm)],[17]) ).
tff(19,plain,
( ( op(e4,e4) != e4 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( op(e4,e4) != e4 )
<=> $false ),
inference(transitivity,[status(thm)],[19,2]) ).
tff(21,plain,
op(e3,e3) = e3,
inference(and_elim,[status(thm)],[8]) ).
tff(22,plain,
( ( op(e3,e3) = e3 )
<=> $true ),
inference(iff_true,[status(thm)],[21]) ).
tff(23,plain,
( ( op(e3,e3) != e3 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( op(e3,e3) != e3 )
<=> $false ),
inference(transitivity,[status(thm)],[23,2]) ).
tff(25,plain,
op(e2,e2) = e2,
inference(and_elim,[status(thm)],[8]) ).
tff(26,plain,
( ( op(e2,e2) = e2 )
<=> $true ),
inference(iff_true,[status(thm)],[25]) ).
tff(27,plain,
( ( op(e2,e2) != e2 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( op(e2,e2) != e2 )
<=> $false ),
inference(transitivity,[status(thm)],[27,2]) ).
tff(29,plain,
op(e1,e1) = e1,
inference(and_elim,[status(thm)],[8]) ).
tff(30,plain,
( ( op(e1,e1) = e1 )
<=> $true ),
inference(iff_true,[status(thm)],[29]) ).
tff(31,plain,
( ( op(e1,e1) != e1 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( op(e1,e1) != e1 )
<=> $false ),
inference(transitivity,[status(thm)],[31,2]) ).
tff(33,plain,
op(e0,e0) = e0,
inference(and_elim,[status(thm)],[8]) ).
tff(34,plain,
( ( op(e0,e0) = e0 )
<=> $true ),
inference(iff_true,[status(thm)],[33]) ).
tff(35,plain,
( ( op(e0,e0) != e0 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( op(e0,e0) != e0 )
<=> $false ),
inference(transitivity,[status(thm)],[35,2]) ).
tff(37,plain,
( ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) )
<=> ( $false
| $false
| $false
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[36,32,28,24,20,16,12]) ).
tff(38,plain,
( ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) )
<=> $false ),
inference(transitivity,[status(thm)],[37,1]) ).
tff(39,plain,
( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ),
inference(and_elim,[status(thm)],[8]) ).
tff(40,plain,
$false,
inference(modus_ponens,[status(thm)],[39,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG200+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 13:49:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------