TSTP Solution File: COL055-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL055-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 17:48:14 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 20 ( 4 unt; 3 typ; 0 def)
% Number of atoms : 56 ( 54 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 96 ( 58 ~; 30 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 32 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(response_type,type,
response: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [W: $i,Z: $i] :
refl(
( ( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
<=> ( ( response(a,Z) != W )
| ( response(a,W) != Z ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
<=> ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
<=> ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_happiness) ).
tff(5,plain,
! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ( response(a,b) = b )
<=> ( response(a,b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
response(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fond_bird_exists) ).
tff(10,plain,
response(a,b) = b,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b ) )
<=> ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( ( response(a,b) != b )
| ( response(a,b) != b ) )
<=> ( response(a,b) != b ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b )
| ( response(a,b) != b ) )
<=> ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b ) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b )
| ( response(a,b) != b ) )
<=> ( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b )
| ( response(a,b) != b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
| ( response(a,b) != b ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,10,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COL055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 10:36:00 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------