TSTP Solution File: BOO011-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO011-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 17:18:40 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 17 unt; 4 typ; 0 def)
% Number of atoms : 35 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( add(X,inverse(X)) = multiplicative_identity )
<=> ( add(X,inverse(X)) = multiplicative_identity ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
tff(5,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(additive_identity,inverse(additive_identity)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(additive_identity,inverse(additive_identity)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
tff(14,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,inverse(additive_identity)) = inverse(additive_identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(additive_identity,inverse(additive_identity)) = inverse(additive_identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
inverse(additive_identity) = add(additive_identity,inverse(additive_identity)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
inverse(additive_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( inverse(additive_identity) != multiplicative_identity )
<=> ( inverse(additive_identity) != multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
tff(23,plain,
inverse(additive_identity) != multiplicative_identity,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO011-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 02:53:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------