TSTP Solution File: GRP163-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Fri Sep 16 22:26:27 EDT 2022
% Result : Unsatisfiable 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 18 unt; 4 typ; 0 def)
% Number of atoms : 32 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 1 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 2 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ( greatest_lower_bound(a,b) = a )
<=> ( greatest_lower_bound(a,b) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_transb_1) ).
tff(3,plain,
greatest_lower_bound(a,b) = a,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( greatest_lower_bound(b,c) = b )
<=> ( greatest_lower_bound(b,c) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
greatest_lower_bound(b,c) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_transb_2) ).
tff(6,plain,
greatest_lower_bound(b,c) = b,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,b),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
| ( greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(greatest_lower_bound(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(greatest_lower_bound(a,b),c),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
greatest_lower_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(a,greatest_lower_bound(b,c)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
a = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[3]) ).
tff(19,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,b),c),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
greatest_lower_bound(a,c) = a,
inference(transitivity,[status(thm)],[19,17,7,3]) ).
tff(21,plain,
( ( greatest_lower_bound(a,c) != a )
<=> ( greatest_lower_bound(a,c) != a ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
greatest_lower_bound(a,c) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_transb) ).
tff(23,plain,
greatest_lower_bound(a,c) != a,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n027.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 : Wed Aug 31 15:30:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.22/0.35 Usage: tptp [options] [-file:]file
% 0.22/0.35 -h, -? prints this message.
% 0.22/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.22/0.35 -m, -model generate model.
% 0.22/0.35 -p, -proof generate proof.
% 0.22/0.35 -c, -core generate unsat core of named formulas.
% 0.22/0.35 -st, -statistics display statistics.
% 0.22/0.35 -t:timeout set timeout (in second).
% 0.22/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.22/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.22/0.35 -<param>:<value> configuration parameter and value.
% 0.22/0.35 -o:<output-file> file to place output in.
% 0.22/0.40 % SZS status Unsatisfiable
% 0.22/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------