%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO018-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:00:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 34 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 7 ~; 3 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_identity_type,type,
additive_identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = additive_identity )
<=> ( multiply(X,inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
tff(5,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(multiplicative_identity,inverse(multiplicative_identity)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(multiplicative_identity,inverse(multiplicative_identity)) = additive_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
tff(14,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(multiplicative_identity,inverse(multiplicative_identity)) = multiply(inverse(multiplicative_identity),multiplicative_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(multiplicative_identity,inverse(multiplicative_identity)) = multiply(inverse(multiplicative_identity),multiplicative_identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(inverse(multiplicative_identity),multiplicative_identity) = multiply(multiplicative_identity,inverse(multiplicative_identity)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(( ( multiply(X,multiplicative_identity) = X )
<=> ( multiply(X,multiplicative_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
tff(24,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(inverse(multiplicative_identity),multiplicative_identity) = inverse(multiplicative_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(inverse(multiplicative_identity),multiplicative_identity) = inverse(multiplicative_identity),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
inverse(multiplicative_identity) = multiply(inverse(multiplicative_identity),multiplicative_identity),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
inverse(multiplicative_identity) = additive_identity,
inference(transitivity,[status(thm)],[29,19,9]) ).
tff(31,plain,
( ( inverse(multiplicative_identity) != additive_identity )
<=> ( inverse(multiplicative_identity) != additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
inverse(multiplicative_identity) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
tff(33,plain,
inverse(multiplicative_identity) != additive_identity,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : BOO018-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 11:33:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.36 % E exiting
%------------------------------------------------------------------------------