TSTP Solution File: SET054-7 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET054-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20 05:05:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 4 unt; 2 typ; 0 def)
% Number of atoms : 71 ( 26 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 86 ( 39 ~; 33 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 34 ( 32 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(1,plain,
( ~ subclass(x,x)
<=> ~ subclass(x,x) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ subclass(x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_is_reflexive_1) ).
tff(3,plain,
~ subclass(x,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( X != Y )
| subclass(Y,X) )
<=> ( ( X != Y )
| subclass(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
<=> ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
<=> ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| subclass(x,x) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| subclass(x,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( $false
| subclass(x,x) )
<=> subclass(x,x) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( x = x )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( x != x )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( x != x )
<=> $false ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
( ( ( x != x )
| subclass(x,x) )
<=> ( $false
| subclass(x,x) ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( ( x != x )
| subclass(x,x) )
<=> subclass(x,x) ),
inference(transitivity,[status(thm)],[17,12]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| ( x != x )
| subclass(x,x) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| subclass(x,x) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| ( x != x )
| subclass(x,x) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| subclass(x,x) ) ),
inference(transitivity,[status(thm)],[19,11]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| ( x != x )
| subclass(x,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(Y,X) )
| subclass(x,x) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET054-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 02:11:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------