%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP174-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:07:21 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 55 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 73 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 8 ~; 4 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 63 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
( ( greatest_lower_bound(identity,a) = a )
<=> ( greatest_lower_bound(identity,a) = a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
greatest_lower_bound(identity,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05b_1) ).
tff(3,plain,
greatest_lower_bound(identity,a) = a,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(8,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(18,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(multiply(inverse(a),a),multiply(identity,a)),
inference(monotonicity,[status(thm)],[23,13]) ).
tff(25,plain,
greatest_lower_bound(multiply(inverse(a),a),multiply(identity,a)) = greatest_lower_bound(identity,a),
inference(symmetry,[status(thm)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
tff(30,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)],[29,28]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,27]) ).
tff(33,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(inverse(a),identity),a) = greatest_lower_bound(multiply(inverse(a),a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
multiply(greatest_lower_bound(inverse(a),identity),a) = greatest_lower_bound(multiply(inverse(a),a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( ( greatest_lower_bound(identity,inverse(a)) = inverse(a) )
<=> ( greatest_lower_bound(identity,inverse(a)) = inverse(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05b_2) ).
tff(37,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(identity,inverse(a)) = greatest_lower_bound(inverse(a),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
greatest_lower_bound(identity,inverse(a)) = greatest_lower_bound(inverse(a),identity),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
greatest_lower_bound(inverse(a),identity) = inverse(a),
inference(transitivity,[status(thm)],[47,37]) ).
tff(49,plain,
multiply(greatest_lower_bound(inverse(a),identity),a) = multiply(inverse(a),a),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
multiply(inverse(a),a) = multiply(greatest_lower_bound(inverse(a),identity),a),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
identity = a,
inference(transitivity,[status(thm)],[23,50,34,25,3]) ).
tff(52,plain,
( ( identity != a )
<=> ( identity != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
identity != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p05b) ).
tff(54,plain,
identity != a,
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 : GRP174-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:45:10 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------