%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP175-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 60 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 77 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 4 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 72 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
( ( least_upper_bound(identity,b) = b )
<=> ( least_upper_bound(identity,b) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p06a_1) ).
tff(3,plain,
least_upper_bound(identity,b) = b,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
b = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
multiply(b,a) = multiply(least_upper_bound(identity,b),a),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
multiply(least_upper_bound(identity,b),a) = multiply(b,a),
inference(symmetry,[status(thm)],[5]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10,9]) ).
tff(12,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)],[11]) ).
tff(13,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)],[12,8]) ).
tff(14,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),a) = least_upper_bound(multiply(identity,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
multiply(least_upper_bound(identity,b),a) = least_upper_bound(multiply(identity,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
least_upper_bound(multiply(identity,a),multiply(b,a)) = multiply(least_upper_bound(identity,b),a),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
least_upper_bound(multiply(identity,a),multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[16,6]) ).
tff(18,plain,
least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a))) = least_upper_bound(multiply(identity,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a))) = multiply(b,a),
inference(transitivity,[status(thm)],[18,16,6]) ).
tff(20,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(inverse(a),multiply(b,a)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(inverse(a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(monotonicity,[status(thm)],[17]) ).
tff(32,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a))),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(37,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
multiply(inverse(a),multiply(identity,a)) = multiply(inverse(a),a),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
multiply(inverse(a),a) = multiply(inverse(a),multiply(identity,a)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(48,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
identity = multiply(inverse(a),multiply(identity,a)),
inference(transitivity,[status(thm)],[53,43]) ).
tff(55,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[54,32]) ).
tff(56,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(transitivity,[status(thm)],[55,30,20]) ).
tff(57,plain,
( ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) )
<=> ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p06a) ).
tff(59,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP175-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:44:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------