%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN009-5 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:08:49 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.97s
% Output : Proof 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 49
% Syntax : Number of formulae : 127 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 427 ( 419 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 552 ( 259 ~; 254 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 270 ( 254 !; 0 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( divide(X,identity) = zero )
<=> ( divide(X,identity) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( divide(X,identity) = zero )
<=> ! [X: $i] : ( divide(X,identity) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( divide(X,identity) = zero )
<=> ! [X: $i] : ( divide(X,identity) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( divide(X,identity) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',identity_is_largest) ).
tff(5,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( divide(X,identity) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( divide(X,identity) = zero )
| ( divide(divide(identity,divide(identity,a)),identity) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(identity,divide(identity,a)),identity) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
<=> ( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),identity) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),identity) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),identity) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),identity) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( divide(divide(identity,divide(identity,a)),identity) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ) ),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero,
inference(unit_resolution,[status(thm)],[20,9]) ).
tff(22,plain,
zero = divide(divide(identity,divide(identity,a)),identity),
inference(symmetry,[status(thm)],[9]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,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)],[26,25]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28,24]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))) = zero,
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))) = divide(divide(identity,divide(identity,a)),identity),
inference(transitivity,[status(thm)],[31,22]) ).
tff(33,plain,
divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = divide(divide(divide(identity,divide(identity,a)),identity),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
zero = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))),
inference(symmetry,[status(thm)],[31]) ).
tff(35,plain,
divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(divide(identity,identity),divide(identity,a))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero,
inference(transitivity,[status(thm)],[35,33,21]) ).
tff(37,plain,
^ [Y: $i,X: $i] :
refl(( ( divide(divide(X,Y),X) = zero )
<=> ( divide(divide(X,Y),X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(38,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)],[37]) ).
tff(39,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(40,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(41,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) = zero,
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
<=> ( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,divide(identity,a)),zero),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero,
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,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(63,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ) )
<=> ( ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero )
| ( divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero )
| ( divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero,
inference(unit_resolution,[status(thm)],[72,66,56,36]) ).
tff(74,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ) ),
inference(unit_resolution,[status(thm)],[76,52]) ).
tff(78,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero,
inference(unit_resolution,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)) = zero,
inference(unit_resolution,[status(thm)],[79,29]) ).
tff(81,plain,
zero = divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
divide(zero,divide(divide(identity,a),divide(identity,a))) = divide(divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),divide(divide(identity,a),divide(identity,a))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( divide(zero,divide(divide(identity,a),divide(identity,a))) = zero )
<=> ( divide(divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),divide(divide(identity,a),divide(identity,a))) = zero ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( divide(divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),divide(divide(identity,a),divide(identity,a))) = zero )
<=> ( divide(zero,divide(divide(identity,a),divide(identity,a))) = zero ) ),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [X: $i] : ( divide(X,identity) = zero )
| ( divide(divide(identity,a),identity) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
divide(divide(identity,a),identity) = zero,
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,a),identity) != zero )
| ( divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,a),identity) != zero )
| ( divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,a),identity) != zero )
| ( divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,a),identity) != zero )
| ( divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ( divide(divide(identity,a),identity) != zero )
| ( divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero ) ),
inference(unit_resolution,[status(thm)],[89,16]) ).
tff(91,plain,
divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))) = zero,
inference(unit_resolution,[status(thm)],[90,86]) ).
tff(92,plain,
zero = divide(divide(identity,a),identity),
inference(symmetry,[status(thm)],[86]) ).
tff(93,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)) = divide(divide(identity,a),identity),
inference(transitivity,[status(thm)],[80,92]) ).
tff(94,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),divide(divide(identity,a),divide(identity,a))) = divide(divide(divide(identity,a),identity),divide(divide(identity,a),divide(identity,a))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,identity),a)),divide(divide(identity,a),divide(identity,a))) = zero,
inference(transitivity,[status(thm)],[94,91]) ).
tff(96,plain,
divide(zero,divide(divide(identity,a),divide(identity,a))) = zero,
inference(modus_ponens,[status(thm)],[95,84]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(divide(identity,a),zero),divide(identity,a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
divide(divide(divide(identity,a),zero),divide(identity,a)) = zero,
inference(unit_resolution,[status(thm)],[97,43]) ).
tff(99,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,a),zero),divide(identity,a)) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,a),zero),divide(identity,a)) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,a),zero),divide(identity,a)) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(divide(identity,a),zero),divide(identity,a)) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) = zero ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
divide(divide(divide(identity,a),divide(identity,a)),zero) = zero,
inference(unit_resolution,[status(thm)],[101,52,98]) ).
tff(103,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ) )
<=> ( ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(identity,a),divide(identity,a)) = zero )
| ( divide(divide(divide(identity,a),divide(identity,a)),zero) != zero )
| ( divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
divide(divide(identity,a),divide(identity,a)) = zero,
inference(unit_resolution,[status(thm)],[108,66,102,96]) ).
tff(110,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,a),divide(identity,a)) != zero )
| ( divide(divide(identity,divide(identity,a)),a) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,a),divide(identity,a)) != zero )
| ( divide(divide(identity,divide(identity,a)),a) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,a),divide(identity,a)) != zero )
| ( divide(divide(identity,divide(identity,a)),a) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(divide(X,Y),Z) != zero )
| ( divide(divide(X,Z),Y) = zero ) )
| ( divide(divide(identity,a),divide(identity,a)) != zero )
| ( divide(divide(identity,divide(identity,a)),a) = zero ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ( divide(divide(identity,a),divide(identity,a)) != zero )
| ( divide(divide(identity,divide(identity,a)),a) = zero ) ),
inference(unit_resolution,[status(thm)],[112,52]) ).
tff(114,plain,
divide(divide(identity,divide(identity,a)),a) = zero,
inference(unit_resolution,[status(thm)],[113,109]) ).
tff(115,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),a) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),a) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),a) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(divide(Z,Y),divide(Z,X)) = zero ) )
| ( divide(divide(identity,divide(identity,a)),a) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ( divide(divide(identity,divide(identity,a)),a) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ) ),
inference(unit_resolution,[status(thm)],[117,16]) ).
tff(119,plain,
divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero,
inference(unit_resolution,[status(thm)],[118,114]) ).
tff(120,plain,
( ( divide(identity,a) != divide(identity,divide(identity,divide(identity,a))) )
<=> ( divide(identity,a) != divide(identity,divide(identity,divide(identity,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(122,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(identity,a) = divide(identity,divide(identity,divide(identity,a))) )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(identity,a) = divide(identity,divide(identity,divide(identity,a))) )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(identity,a) = divide(identity,divide(identity,divide(identity,a))) )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(identity,a) = divide(identity,divide(identity,divide(identity,a))) )
| ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero )
| ( divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ) ),
inference(unit_resolution,[status(thm)],[125,66,122]) ).
tff(127,plain,
$false,
inference(unit_resolution,[status(thm)],[126,119,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-5 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:15:10 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.97 % SZS status Unsatisfiable
% 0.77/0.97 % SZS output start Proof
% See solution above
% 0.82/0.99 % E exiting
%------------------------------------------------------------------------------