TSTP Solution File: GRP188-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 22:26:42 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 59 ( 41 unt; 4 typ; 0 def)
% Number of atoms : 77 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 9 ~; 5 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 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 : 93 ( 84 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
| ( least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(b,a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(b,a),b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
least_upper_bound(least_upper_bound(b,a),b) = least_upper_bound(b,least_upper_bound(a,b)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b)) = greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(a,b))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(a,b))) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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(17,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(a,b))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(a,b))) = b,
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
b = greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(a,b))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
b = greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b)),
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
least_upper_bound(b,b) = least_upper_bound(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
least_upper_bound(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b))) = least_upper_bound(b,b),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(30,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
least_upper_bound(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b))) = b,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
b = least_upper_bound(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(b,a),b))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
b = least_upper_bound(b,b),
inference(transitivity,[status(thm)],[35,25]) ).
tff(37,plain,
least_upper_bound(a,b) = least_upper_bound(a,least_upper_bound(b,b)),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(a,b),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
| ( least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(least_upper_bound(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(least_upper_bound(a,b),b),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
least_upper_bound(least_upper_bound(a,b),b) = least_upper_bound(a,least_upper_bound(b,b)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(46,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(a,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(a,b),b),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b),
inference(transitivity,[status(thm)],[50,41,38]) ).
tff(52,plain,
( ( least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b) )
<=> ( least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p38a) ).
tff(54,plain,
least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 15:35:32 EDT 2022
% 0.12/0.34 % 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.
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------