TSTP Solution File: GRP156-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 22:26:25 EDT 2022
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 40 ( 26 unt; 6 typ; 0 def)
% Number of atoms : 46 ( 43 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(1,plain,
( ( least_upper_bound(a,b) = b )
<=> ( least_upper_bound(a,b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_mono1c_1) ).
tff(3,plain,
least_upper_bound(a,b) = b,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
b = least_upper_bound(a,b),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(a,least_upper_bound(a,b)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
greatest_lower_bound(a,least_upper_bound(a,b)) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
refl(
( ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
tff(11,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(a,least_upper_bound(a,b)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
greatest_lower_bound(a,least_upper_bound(a,b)) = a,
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
a = greatest_lower_bound(a,least_upper_bound(a,b)),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
a = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[16,6]) ).
tff(18,plain,
multiply(a,c) = multiply(greatest_lower_bound(a,b),c),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
multiply(greatest_lower_bound(a,b),c) = multiply(a,c),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(greatest_lower_bound(a,b),c) = greatest_lower_bound(multiply(a,c),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
multiply(greatest_lower_bound(a,b),c) = greatest_lower_bound(multiply(a,c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(greatest_lower_bound(a,b),c),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(a,c),
inference(transitivity,[status(thm)],[29,19]) ).
tff(31,plain,
( ( greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c) )
<=> ( greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_mono1c) ).
tff(33,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 15:26:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------