%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO011-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:00:07 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 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 : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( add(X,inverse(X)) = multiplicative_identity )
<=> ( add(X,inverse(X)) = multiplicative_identity ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
tff(5,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(additive_identity,inverse(additive_identity)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(additive_identity,inverse(additive_identity)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
tff(14,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,inverse(additive_identity)) = inverse(additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(additive_identity,inverse(additive_identity)) = inverse(additive_identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
inverse(additive_identity) = add(additive_identity,inverse(additive_identity)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
inverse(additive_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( inverse(additive_identity) != multiplicative_identity )
<=> ( inverse(additive_identity) != multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
tff(23,plain,
inverse(additive_identity) != multiplicative_identity,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO011-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.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 11:38:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------