TSTP Solution File: ARI535_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI535_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 17:01:57 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 30 ( 3 unt; 1 typ; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 137 ( 80 ~; 40 |; 0 &)
% ( 15 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number arithmetic : 318 ( 0 atm; 72 fun; 194 num; 52 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 24 !; 24 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $int * $int * $int ) > $o ).
tff(1,plain,
( ( ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
| $false )
<=> ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( ~ p(2,2,4)
| p(2,2,4) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( p(2,2,$product(2,2))
<=> p(2,2,4) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ~ p(2,2,$sum(2,2))
<=> ~ p(2,2,4) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) )
<=> ( ~ p(2,2,4)
| p(2,2,4) ) ),
inference(monotonicity,[status(thm)],[5,4]) ).
tff(7,plain,
( ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) )
<=> $true ),
inference(transitivity,[status(thm)],[6,3]) ).
tff(8,plain,
( ~ ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) )
<=> $false ),
inference(transitivity,[status(thm)],[8,2]) ).
tff(10,plain,
( ( ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
| ~ ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) ) )
<=> ( ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
| $false ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
| ~ ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) ) )
<=> ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) ),
inference(transitivity,[status(thm)],[10,1]) ).
tff(12,plain,
( ~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
| ~ ( ~ p(2,2,$sum(2,2))
| p(2,2,$product(2,2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
~ ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [X: $int,Y: $int] :
refl(
( ~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
<=> ~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
<=> ! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) )
<=> ~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ? [X: $int,Y: $int] :
( p(2,Y,$sum(2,Y))
=> p(X,2,$product(X,2)) )
<=> ~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
~ ? [X: $int,Y: $int] :
( p(2,Y,$sum(2,Y))
=> p(X,2,$product(X,2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(19,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[21,16]) ).
tff(23,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[22,16]) ).
tff(24,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
~ ? [X: $int,Y: $int] :
( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[24,16]) ).
tff(26,plain,
^ [X: $int,Y: $int] :
refl(
$oeq(
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ))),
inference(bind,[status(th)],]) ).
tff(27,plain,
! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(nnf-neg,[status(sab)],[25,26]) ).
tff(28,plain,
! [X: $int,Y: $int] :
~ ( ~ p(2,Y,$sum(2,Y))
| p(X,2,$product(2,X)) ),
inference(modus_ponens,[status(thm)],[27,15]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI535_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.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 : Tue Aug 30 00:12:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------