%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN001-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:45 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 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; 3 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ( divide(a,identity) != zero )
<=> ( divide(a,identity) != zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
divide(a,identity) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_everything_divide_id_is_zero) ).
tff(3,plain,
divide(a,identity) != zero,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( divide(X,identity) = zero )
<=> ( divide(X,identity) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] : ( divide(X,identity) = zero )
<=> ! [X: $i] : ( divide(X,identity) = zero ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] : ( divide(X,identity) = zero )
<=> ! [X: $i] : ( divide(X,identity) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] : ( divide(X,identity) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',identity_is_largest) ).
tff(8,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [X: $i] : ( divide(X,identity) = zero )
| ( divide(a,identity) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HEN001-5 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 17:12:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------