%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN003-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:08:46 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 63 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 158 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 183 ( 87 ~; 77 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 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 : 105 ( 95 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( divide(zero,X) = zero )
<=> ( divide(zero,X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( divide(zero,X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).
tff(5,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(divide(a,a),divide(divide(a,a),a))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(zero,divide(divide(a,a),divide(divide(a,a),a))) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( divide(divide(X,Y),X) = zero )
<=> ( divide(divide(X,Y),X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
<=> ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
<=> ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_smaller_than_numerator) ).
tff(14,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(a,divide(a,a)),a) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
divide(divide(a,divide(a,a)),a) = zero,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) = divide(zero,divide(divide(a,a),divide(divide(a,a),a))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) = zero,
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
zero = divide(divide(a,divide(a,a)),a),
inference(symmetry,[status(thm)],[18]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(a,a),a) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
divide(divide(a,a),a) = zero,
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
zero = divide(divide(a,a),a),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
divide(divide(a,a),zero) = divide(divide(a,a),divide(divide(a,a),a)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( divide(divide(a,a),zero) = zero )
<=> ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) ) ),
inference(monotonicity,[status(thm)],[25,21]) ).
tff(27,plain,
( ( divide(divide(a,a),zero) != zero )
<=> ( divide(divide(a,a),divide(divide(a,a),a)) != divide(divide(a,divide(a,a)),a) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(a,a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
divide(zero,divide(a,a)) = zero,
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
( ( divide(a,a) != zero )
<=> ( divide(a,a) != zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
divide(a,a) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
tff(32,plain,
divide(a,a) != zero,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [Y: $i,X: $i] :
refl(( ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) )
<=> ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',divide_and_equal) ).
tff(39,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) ),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,plain,
divide(divide(a,a),zero) != zero,
inference(unit_resolution,[status(thm)],[46,29]) ).
tff(48,plain,
divide(divide(a,a),divide(divide(a,a),a)) != divide(divide(a,divide(a,a)),a),
inference(modus_ponens,[status(thm)],[47,27]) ).
tff(49,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_property) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
| ( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) = zero,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) )
| ( divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero )
| ( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) )
| ( divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero )
| ( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) )
| ( divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero )
| ( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) )
| ( divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero )
| ( divide(divide(divide(a,a),divide(divide(a,a),a)),divide(divide(a,divide(a,a)),a)) != zero ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( divide(divide(a,a),divide(divide(a,a),a)) = divide(divide(a,divide(a,a)),a) )
| ( divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero ) ),
inference(unit_resolution,[status(thm)],[60,42,57]) ).
tff(62,plain,
divide(divide(divide(a,divide(a,a)),a),divide(divide(a,a),divide(divide(a,a),a))) != zero,
inference(unit_resolution,[status(thm)],[61,48]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : HEN003-5 : TPTP v9.0.0. Released v1.0.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.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 17:11:18 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.22/0.51 % SZS status Unsatisfiable
% 0.22/0.51 % SZS output start Proof
% See solution above
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------