%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP193-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:07:26 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 42
% Syntax : Number of formulae : 133 ( 102 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 169 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 55 ( 18 ~; 14 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 148 ( 135 !; 0 ?; 148 :)
% 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/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,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(identity,c),multiply(b,c))) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
greatest_lower_bound(c,least_upper_bound(multiply(identity,c),multiply(b,c))) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
( ( least_upper_bound(identity,b) = b )
<=> ( least_upper_bound(identity,b) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9a_2) ).
tff(15,plain,
least_upper_bound(identity,b) = b,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
b = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
multiply(b,c) = multiply(least_upper_bound(identity,b),c),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
multiply(least_upper_bound(identity,b),c) = multiply(b,c),
inference(symmetry,[status(thm)],[17]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
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)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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)],[23]) ).
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)],[24,20]) ).
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)) )
| ( multiply(least_upper_bound(identity,b),c) = least_upper_bound(multiply(identity,c),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
multiply(least_upper_bound(identity,b),c) = least_upper_bound(multiply(identity,c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
least_upper_bound(multiply(identity,c),multiply(b,c)) = multiply(least_upper_bound(identity,b),c),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
least_upper_bound(multiply(identity,c),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[28,18]) ).
tff(30,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(34,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
multiply(identity,c) = c,
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
c = multiply(identity,c),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
greatest_lower_bound(c,least_upper_bound(multiply(identity,c),multiply(b,c))) = greatest_lower_bound(multiply(identity,c),multiply(b,c)),
inference(monotonicity,[status(thm)],[39,29]) ).
tff(41,plain,
greatest_lower_bound(multiply(identity,c),multiply(b,c)) = greatest_lower_bound(c,least_upper_bound(multiply(identity,c),multiply(b,c))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c))) = least_upper_bound(multiply(identity,c),multiply(b,c)),
inference(monotonicity,[status(thm)],[29]) ).
tff(43,plain,
least_upper_bound(multiply(identity,c),multiply(b,c)) = least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
multiply(b,c) = least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c))),
inference(transitivity,[status(thm)],[17,27,43]) ).
tff(45,plain,
greatest_lower_bound(multiply(identity,c),multiply(b,c)) = greatest_lower_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c)))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
greatest_lower_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c)))) = greatest_lower_bound(multiply(identity,c),multiply(b,c)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,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(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(quant_intro,[status(thm)],[47]) ).
tff(49,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(50,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(51,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c)))) = multiply(identity,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
greatest_lower_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c)))) = multiply(identity,c),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
multiply(identity,c) = greatest_lower_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),least_upper_bound(multiply(identity,c),multiply(b,c)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
c = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),
inference(transitivity,[status(thm)],[39,56,46,41,12]) ).
tff(58,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),a),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),a) = greatest_lower_bound(c,a),
inference(symmetry,[status(thm)],[58]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,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(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) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,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)],[64]) ).
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)],[65,61]) ).
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) )
| ( greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),c),a),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ( greatest_lower_bound(a,b) = identity )
<=> ( greatest_lower_bound(a,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9a_4) ).
tff(71,plain,
greatest_lower_bound(a,b) = identity,
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(identity,greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
multiply(identity,greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(unit_resolution,[status(thm)],[74,36]) ).
tff(76,plain,
greatest_lower_bound(a,c) = multiply(identity,greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
greatest_lower_bound(c,a) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[10,76,73]) ).
tff(78,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(c,a)) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(c,a)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[72,75]) ).
tff(81,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,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(identity,c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a),c),
inference(unit_resolution,[status(thm)],[83,66]) ).
tff(85,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a),c) = greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a) = greatest_lower_bound(multiply(b,c),a),
inference(monotonicity,[status(thm)],[29]) ).
tff(87,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a),c) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),a),c) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(multiply(identity,c),multiply(b,c)),a),c),
inference(symmetry,[status(thm)],[87]) ).
tff(89,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(90,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)],[89,66]) ).
tff(91,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(92,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/sandbox/benchmark/theBenchmark.p',p8_9a_5) ).
tff(93,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)],[92,91]) ).
tff(94,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)],[93]) ).
tff(95,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)],[76,73,94]) ).
tff(96,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(97,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(unit_resolution,[status(thm)],[96,7]) ).
tff(98,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(a,multiply(b,c)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,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)],[98,95]) ).
tff(100,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)],[99]) ).
tff(101,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(102,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)],[101,53]) ).
tff(103,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)],[102]) ).
tff(104,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)],[98,103,100,90]) ).
tff(105,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)],[104]) ).
tff(106,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)],[105]) ).
tff(107,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(108,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)],[107,66]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(c,least_upper_bound(c,identity)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
greatest_lower_bound(c,least_upper_bound(c,identity)) = c,
inference(unit_resolution,[status(thm)],[109,53]) ).
tff(111,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(112,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)],[111]) ).
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(rewrite,[status(thm)],[]) ).
tff(114,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(115,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(identity,c) = least_upper_bound(c,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
least_upper_bound(identity,c) = least_upper_bound(c,identity),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
( ( least_upper_bound(identity,c) = c )
<=> ( least_upper_bound(identity,c) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9a_3) ).
tff(122,plain,
least_upper_bound(identity,c) = c,
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
c = least_upper_bound(identity,c),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
c = least_upper_bound(c,identity),
inference(transitivity,[status(thm)],[123,119]) ).
tff(125,plain,
greatest_lower_bound(c,c) = greatest_lower_bound(c,least_upper_bound(c,identity)),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
greatest_lower_bound(c,c) = c,
inference(transitivity,[status(thm)],[125,110]) ).
tff(127,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)],[126]) ).
tff(128,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)],[127]) ).
tff(129,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[103,100,90,128,108,106,88,85,82,79,68,59,10]) ).
tff(130,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(131,axiom,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p8_9a) ).
tff(132,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP193-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.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 : Thu Jun 19 15:47:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------