%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN004-5 : TPTP v9.0.0. Released v1.0.0.
% 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 05:08:46 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 84 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 259 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 331 ( 155 ~; 149 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 6 ( 6 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 : 139 ( 128 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( divide(divide(X,Y),X) = zero )
<=> ( divide(divide(X,Y),X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(a,zero),a) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(a,zero),a) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( divide(a,zero) != a )
<=> ( divide(a,zero) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
divide(a,zero) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
tff(12,plain,
divide(a,zero) != a,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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(17,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)],[16]) ).
tff(18,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(19,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ( divide(a,zero) = a )
| ( divide(a,divide(a,zero)) != zero )
| ( divide(divide(a,zero),a) != zero ) )
<=> ( ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(a,divide(a,zero)) != zero )
| ( divide(divide(a,zero),a) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(a,divide(a,zero)) != zero )
| ( divide(divide(a,zero),a) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(a,divide(a,zero)) != zero )
| ( divide(divide(a,zero),a) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,zero) = a )
| ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( divide(divide(a,zero),a) != zero )
| ( divide(a,divide(a,zero)) != zero ) ),
inference(unit_resolution,[status(thm)],[28,22,12]) ).
tff(30,plain,
divide(a,divide(a,zero)) != zero,
inference(unit_resolution,[status(thm)],[29,9]) ).
tff(31,plain,
^ [X: $i] :
refl(( ( divide(zero,X) = zero )
<=> ( divide(zero,X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
! [X: $i] : ( divide(zero,X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).
tff(35,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(a,divide(a,zero))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
divide(zero,divide(a,divide(a,zero))) = zero,
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
divide(zero,divide(divide(a,divide(a,zero)),zero)) = zero,
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,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)],[46]) ).
tff(48,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)],[47,43]) ).
tff(49,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,divide(a,zero)),divide(zero,divide(a,zero))),divide(divide(a,zero),divide(a,zero))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
divide(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),divide(divide(a,zero),divide(a,zero))) = zero,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
^ [X: $i] :
refl(( ( divide(X,X) = zero )
<=> ( divide(X,X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] : ( divide(X,X) = zero )
<=> ! [X: $i] : ( divide(X,X) = zero ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] : ( divide(X,X) = zero )
<=> ! [X: $i] : ( divide(X,X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
! [X: $i] : ( divide(X,X) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
tff(55,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [X: $i] : ( divide(X,X) = zero )
| ( divide(divide(a,zero),divide(a,zero)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
divide(divide(a,zero),divide(a,zero)) = zero,
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
zero = divide(divide(a,zero),divide(a,zero)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [X: $i] : ( divide(X,X) = zero )
| ( divide(zero,zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
divide(zero,zero) = zero,
inference(unit_resolution,[status(thm)],[61,57]) ).
tff(63,plain,
divide(zero,zero) = divide(divide(a,zero),divide(a,zero)),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(a,zero)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
divide(zero,divide(a,zero)) = zero,
inference(unit_resolution,[status(thm)],[64,37]) ).
tff(66,plain,
divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))) = divide(divide(a,divide(a,zero)),zero),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
divide(divide(a,divide(a,zero)),zero) = divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(divide(divide(a,divide(a,zero)),zero),divide(zero,zero)) = divide(divide(divide(a,divide(a,zero)),divide(zero,divide(a,zero))),divide(divide(a,zero),divide(a,zero))),
inference(monotonicity,[status(thm)],[67,63]) ).
tff(69,plain,
zero = divide(zero,zero),
inference(symmetry,[status(thm)],[62]) ).
tff(70,plain,
divide(divide(divide(a,divide(a,zero)),zero),zero) = divide(divide(divide(a,divide(a,zero)),zero),divide(zero,zero)),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(divide(a,divide(a,zero)),zero),zero) = zero,
inference(transitivity,[status(thm)],[70,68,50]) ).
tff(72,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero ) )
<=> ( ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(divide(divide(a,divide(a,zero)),zero),zero) != zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( divide(divide(a,divide(a,zero)),zero) = zero )
| ( divide(zero,divide(divide(a,divide(a,zero)),zero)) != zero ) ),
inference(unit_resolution,[status(thm)],[77,22,71]) ).
tff(79,plain,
divide(divide(a,divide(a,zero)),zero) = zero,
inference(unit_resolution,[status(thm)],[78,41]) ).
tff(80,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,divide(a,zero)) = zero )
| ( divide(zero,divide(a,divide(a,zero))) != zero )
| ( divide(divide(a,divide(a,zero)),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,divide(a,zero)) = zero )
| ( divide(zero,divide(a,divide(a,zero))) != zero )
| ( divide(divide(a,divide(a,zero)),zero) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,divide(a,zero)) = zero )
| ( divide(zero,divide(a,divide(a,zero))) != zero )
| ( divide(divide(a,divide(a,zero)),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,divide(a,zero)) = zero )
| ( divide(zero,divide(a,divide(a,zero))) != zero )
| ( divide(divide(a,divide(a,zero)),zero) != zero ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( divide(a,divide(a,zero)) = zero )
| ( divide(zero,divide(a,divide(a,zero))) != zero )
| ( divide(divide(a,divide(a,zero)),zero) != zero ) ),
inference(unit_resolution,[status(thm)],[82,22]) ).
tff(84,plain,
$false,
inference(unit_resolution,[status(thm)],[83,79,39,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN004-5 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 17:11:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------