TSTP Solution File: RNG011-5 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 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 20 03:17:40 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 17 ( 8 unt; 5 typ; 0 def)
% Number of atoms : 18 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 2 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_identity_type,type,
additive_identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ( multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity )
<=> ( multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
tff(3,plain,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity )
<=> ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',middle_associator) ).
tff(8,plain,
! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity )
| ( multiply(multiply(associator(a,a,b),a),associator(a,a,b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 21:27:14 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------