TSTP Solution File: GRP138-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 22:26:20 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 80 ( 54 unt; 5 typ; 0 def)
% Number of atoms : 106 ( 100 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 12 ~; 8 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 105 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(5,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(a,b) = greatest_lower_bound(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(15,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(greatest_lower_bound(b,a),c)) = greatest_lower_bound(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(greatest_lower_bound(b,a),c)) = greatest_lower_bound(b,a),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(c,greatest_lower_bound(b,a)) = greatest_lower_bound(greatest_lower_bound(b,a),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
greatest_lower_bound(c,greatest_lower_bound(b,a)) = greatest_lower_bound(greatest_lower_bound(b,a),c),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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(26,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)],[25,24]) ).
tff(27,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)],[26]) ).
tff(28,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)],[27,23]) ).
tff(29,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(c,greatest_lower_bound(b,a)) = greatest_lower_bound(greatest_lower_bound(c,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
greatest_lower_bound(c,greatest_lower_bound(b,a)) = greatest_lower_bound(greatest_lower_bound(c,b),a),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
greatest_lower_bound(greatest_lower_bound(c,b),a) = greatest_lower_bound(c,greatest_lower_bound(b,a)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(36,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,c) = least_upper_bound(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
least_upper_bound(a,c) = least_upper_bound(c,a),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ( least_upper_bound(a,c) = a )
<=> ( least_upper_bound(a,c) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
least_upper_bound(a,c) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_glb1a_1) ).
tff(43,plain,
least_upper_bound(a,c) = a,
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
a = least_upper_bound(a,c),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
a = least_upper_bound(c,a),
inference(transitivity,[status(thm)],[44,40]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
tff(50,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(c,least_upper_bound(c,b)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
greatest_lower_bound(c,least_upper_bound(c,b)) = c,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(b,c) = least_upper_bound(c,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
least_upper_bound(b,c) = least_upper_bound(c,b),
inference(unit_resolution,[status(thm)],[55,38]) ).
tff(57,plain,
( ( least_upper_bound(b,c) = b )
<=> ( least_upper_bound(b,c) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
least_upper_bound(b,c) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_glb1a_2) ).
tff(59,plain,
least_upper_bound(b,c) = b,
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
b = least_upper_bound(b,c),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
b = least_upper_bound(c,b),
inference(transitivity,[status(thm)],[60,56]) ).
tff(62,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,least_upper_bound(c,b)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
greatest_lower_bound(c,b) = c,
inference(transitivity,[status(thm)],[62,54]) ).
tff(64,plain,
greatest_lower_bound(greatest_lower_bound(c,b),a) = greatest_lower_bound(c,least_upper_bound(c,a)),
inference(monotonicity,[status(thm)],[63,45]) ).
tff(65,plain,
greatest_lower_bound(c,least_upper_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(c,b),a),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(c,least_upper_bound(c,a)) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
greatest_lower_bound(c,least_upper_bound(c,a)) = c,
inference(unit_resolution,[status(thm)],[66,52]) ).
tff(68,plain,
c = greatest_lower_bound(c,least_upper_bound(c,a)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
c = greatest_lower_bound(greatest_lower_bound(b,a),c),
inference(transitivity,[status(thm)],[68,65,31,21]) ).
tff(70,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(greatest_lower_bound(b,a),c)),
inference(monotonicity,[status(thm)],[9,69]) ).
tff(71,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[70,19,10]) ).
tff(72,plain,
( ( least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b) )
<=> ( least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_glb1a) ).
tff(74,plain,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 14:56:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------