%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN002-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 28 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 33 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_equal_type,type,
less_equal: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
( ( divide(zero,a) != zero )
<=> ( divide(zero,a) != zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
divide(zero,a) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_over_a_is_zero) ).
tff(3,plain,
divide(zero,a) != zero,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(zero,a)
| ( divide(zero,a) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(zero,a)
| ( divide(zero,a) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(zero,a)
| ( divide(zero,a) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(zero,a)
| ( divide(zero,a) = zero ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ less_equal(zero,a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(( less_equal(zero,X)
<=> less_equal(zero,X) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] : less_equal(zero,X)
<=> ! [X: $i] : less_equal(zero,X) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : less_equal(zero,X)
<=> ! [X: $i] : less_equal(zero,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X: $i] : less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
tff(19,plain,
! [X: $i] : less_equal(zero,X),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : less_equal(zero,X),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] : less_equal(zero,X),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X: $i] : less_equal(zero,X)
| less_equal(zero,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : HEN002-3 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 17:11:32 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.41 % SZS status Unsatisfiable
% 0.24/0.41 % SZS output start Proof
% See solution above
% 0.24/0.41 % E exiting
%------------------------------------------------------------------------------