TSTP Solution File: MSC019+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC019+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:34:08 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 32 ( 9 unt; 4 typ; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 208 ( 93 ~; 77 |; 16 &)
% ( 19 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 72 ( 66 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(s_contains_type,type,
s_contains: ( $i * $i ) > $o ).
tff(s_MX_type,type,
s_MX: $i ).
tff(s_g019_type,type,
s_g019: $i ).
tff(s_g013_type,type,
s_g013: $i ).
tff(1,plain,
( ~ s_contains(s_g019,s_MX)
<=> ~ s_contains(s_g019,s_MX) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ s_contains(s_g019,s_MX),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexico_in_america_1) ).
tff(3,plain,
~ s_contains(s_g019,s_MX),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( s_contains(X,Y)
& s_contains(Y,Z) )
<=> ~ ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
<=> ~ ~ ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
rewrite(
( ~ ~ ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
<=> ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
<=> ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
( ( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) )
<=> ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y)
| s_contains(X,Z) ) )),
rewrite(
( ( ~ s_contains(Y,Z)
| ~ s_contains(X,Y)
| s_contains(X,Z) )
<=> ( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
( ( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) )
<=> ( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( s_contains(X,Y)
& s_contains(Y,Z) )
=> s_contains(X,Z) )
<=> ( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( s_contains(X,Y)
& s_contains(Y,Z) )
=> s_contains(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( s_contains(X,Y)
& s_contains(Y,Z) )
=> s_contains(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
tff(11,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( s_contains(X,Y)
& s_contains(Y,Z) )
| s_contains(X,Z) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) ),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
( s_contains(s_g013,s_MX)
<=> s_contains(s_g013,s_MX) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
s_contains(s_g013,s_MX),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kb74) ).
tff(18,plain,
s_contains(s_g013,s_MX),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( s_contains(s_g019,s_g013)
<=> s_contains(s_g019,s_g013) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
s_contains(s_g019,s_g013),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kb18) ).
tff(21,plain,
s_contains(s_g019,s_g013),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( s_contains(s_g019,s_MX)
| ~ s_contains(s_g013,s_MX)
| ~ s_contains(s_g019,s_g013) )
<=> ( s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g013,s_MX)
| ~ s_contains(s_g019,s_g013) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g013,s_MX)
| ~ s_contains(s_g019,s_g013) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g013,s_MX)
| ~ s_contains(s_g019,s_g013) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( s_contains(X,Z)
| ~ s_contains(Y,Z)
| ~ s_contains(X,Y) )
| s_contains(s_g019,s_MX)
| ~ s_contains(s_g019,s_g013)
| ~ s_contains(s_g013,s_MX) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,21,18,15,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MSC019+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 03:18:44 EDT 2022
% 0.12/0.34 % 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.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------