TSTP Solution File: GRP193-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:26:43 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 51
% Syntax : Number of formulae : 143 ( 102 unt; 7 typ; 0 def)
% Number of atoms : 184 ( 176 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 60 ( 19 ~; 15 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 154 ( 140 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $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/sandbox2/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,c) = greatest_lower_bound(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(c,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(c,least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
greatest_lower_bound(c,least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
( ( least_upper_bound(identity,b) = b )
<=> ( least_upper_bound(greatest_lower_bound(a,b),b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( least_upper_bound(identity,b) = b )
<=> ( least_upper_bound(identity,b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9a_2) ).
tff(16,plain,
least_upper_bound(identity,b) = b,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
least_upper_bound(greatest_lower_bound(a,b),b) = b,
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
b = least_upper_bound(greatest_lower_bound(a,b),b),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
multiply(b,c) = multiply(least_upper_bound(greatest_lower_bound(a,b),b),c),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
multiply(least_upper_bound(greatest_lower_bound(a,b),b),c) = multiply(b,c),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(least_upper_bound(greatest_lower_bound(a,b),b),c) = least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
multiply(least_upper_bound(greatest_lower_bound(a,b),b),c) = least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)) = multiply(least_upper_bound(greatest_lower_bound(a,b),b),c),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))) = least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)) = least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [X: $i] :
refl(
( ( multiply(greatest_lower_bound(a,b),X) = X )
<=> ( multiply(greatest_lower_bound(a,b),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X )
<=> ! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [X: $i] :
rewrite(
( ( multiply(identity,X) = X )
<=> ( multiply(greatest_lower_bound(a,b),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(40,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ~ ! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X )
| ( multiply(greatest_lower_bound(a,b),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
multiply(greatest_lower_bound(a,b),c) = c,
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
c = multiply(greatest_lower_bound(a,b),c),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
greatest_lower_bound(c,least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)))),
inference(monotonicity,[status(thm)],[46,33]) ).
tff(48,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)))) = greatest_lower_bound(c,least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)))) = multiply(greatest_lower_bound(a,b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)))) = multiply(greatest_lower_bound(a,b),c),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
multiply(greatest_lower_bound(a,b),c) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
c = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),
inference(transitivity,[status(thm)],[46,58,48,12]) ).
tff(60,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),a),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),a) = greatest_lower_bound(c,a),
inference(symmetry,[status(thm)],[60]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
tff(66,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)],[65,64]) ).
tff(67,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)],[66]) ).
tff(68,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)],[67,63]) ).
tff(69,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(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),c),a),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ ! [X: $i] : ( multiply(greatest_lower_bound(a,b),X) = X )
| ( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(unit_resolution,[status(thm)],[71,43]) ).
tff(73,plain,
greatest_lower_bound(a,c) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
greatest_lower_bound(c,a) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[10,73]) ).
tff(75,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(c,a)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[72]) ).
tff(78,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,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(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a),c),
inference(unit_resolution,[status(thm)],[79,68]) ).
tff(81,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a),c) = greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a) = greatest_lower_bound(multiply(b,c),a),
inference(monotonicity,[status(thm)],[31]) ).
tff(83,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a),c) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,c)),a),c),
inference(symmetry,[status(thm)],[83]) ).
tff(85,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(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),
inference(unit_resolution,[status(thm)],[85,68]) ).
tff(87,plain,
( ( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) )
<=> ( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9a_5) ).
tff(89,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
greatest_lower_bound(a,c) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[73,90]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(a,multiply(b,c)),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(monotonicity,[status(thm)],[94,91]) ).
tff(96,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(unit_resolution,[status(thm)],[97,55]) ).
tff(99,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),
inference(transitivity,[status(thm)],[94,99,96,86]) ).
tff(101,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),c),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),c) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c),
inference(symmetry,[status(thm)],[101]) ).
tff(103,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(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),greatest_lower_bound(c,c)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),greatest_lower_bound(c,c)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),c),
inference(unit_resolution,[status(thm)],[103,68]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(c,least_upper_bound(c,greatest_lower_bound(b,a))) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
greatest_lower_bound(c,least_upper_bound(c,greatest_lower_bound(b,a))) = c,
inference(unit_resolution,[status(thm)],[105,55]) ).
tff(107,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(108,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(unit_resolution,[status(thm)],[107,7]) ).
tff(109,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
least_upper_bound(c,greatest_lower_bound(b,a)) = least_upper_bound(c,greatest_lower_bound(a,b)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) = least_upper_bound(c,greatest_lower_bound(b,a)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,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(113,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)],[112]) ).
tff(114,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(115,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(116,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(greatest_lower_bound(a,b),c) = least_upper_bound(c,greatest_lower_bound(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = least_upper_bound(c,greatest_lower_bound(a,b)),
inference(unit_resolution,[status(thm)],[119,118]) ).
tff(121,plain,
( ( least_upper_bound(identity,c) = c )
<=> ( least_upper_bound(greatest_lower_bound(a,b),c) = c ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( least_upper_bound(identity,c) = c )
<=> ( least_upper_bound(identity,c) = c ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9a_3) ).
tff(124,plain,
least_upper_bound(identity,c) = c,
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = c,
inference(modus_ponens,[status(thm)],[124,121]) ).
tff(126,plain,
c = least_upper_bound(greatest_lower_bound(a,b),c),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
c = least_upper_bound(c,greatest_lower_bound(b,a)),
inference(transitivity,[status(thm)],[126,120,111]) ).
tff(128,plain,
greatest_lower_bound(c,c) = greatest_lower_bound(c,least_upper_bound(c,greatest_lower_bound(b,a))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
greatest_lower_bound(c,c) = c,
inference(transitivity,[status(thm)],[128,106]) ).
tff(130,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),greatest_lower_bound(c,c)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),c) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),a),greatest_lower_bound(c,c)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[99,96,86,131,104,102,84,81,78,76,70,61,10]) ).
tff(133,plain,
( ( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) )
<=> ( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p8_9a) ).
tff(135,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[135,132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:37:27 EDT 2022
% 0.13/0.34 % 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.
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------