%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN003-2 : 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 05:08:46 AM UTC 2025
% Result : Unsatisfiable 60.86s 61.01s
% Output : Proof 60.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 57
% Syntax : Number of formulae : 132 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 735 ( 53 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1119 ( 541 ~; 520 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 425 ( 398 !; 0 ?; 425 :)
% Comments :
%------------------------------------------------------------------------------
tff(quotient_type,type,
quotient: ( $i * $i * $i ) > $o ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(zero_type,type,
zero: $i ).
tff(less_equal_type,type,
less_equal: ( $i * $i ) > $o ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( quotient(X,Y,divide(X,Y))
<=> quotient(X,Y,divide(X,Y)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
<=> ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
<=> ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
tff(5,plain,
! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
| quotient(divide(x,x),zero,divide(divide(x,x),zero)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
quotient(divide(x,x),zero,divide(divide(x,x),zero)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
<=> ( ~ quotient(X,Y,Z)
| less_equal(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| less_equal(divide(divide(x,x),zero),divide(x,x)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| less_equal(divide(divide(x,x),zero),divide(x,x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| less_equal(divide(divide(x,x),zero),divide(x,x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| less_equal(divide(divide(x,x),zero),divide(x,x)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
less_equal(divide(divide(x,x),zero),divide(x,x)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
<=> ( ~ less_equal(X,Y)
| quotient(X,Y,zero) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(divide(x,x),zero),divide(x,x))
| quotient(divide(divide(x,x),zero),divide(x,x),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(divide(x,x),zero),divide(x,x))
| quotient(divide(divide(x,x),zero),divide(x,x),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(divide(x,x),zero),divide(x,x))
| quotient(divide(divide(x,x),zero),divide(x,x),zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(divide(x,x),zero),divide(x,x))
| quotient(divide(divide(x,x),zero),divide(x,x),zero) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
quotient(divide(divide(x,x),zero),divide(x,x),zero),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(divide(x,x),zero),divide(x,x),zero)
| less_equal(zero,divide(divide(x,x),zero)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(divide(x,x),zero),divide(x,x),zero)
| less_equal(zero,divide(divide(x,x),zero)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(divide(x,x),zero),divide(x,x),zero)
| less_equal(zero,divide(divide(x,x),zero)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(divide(x,x),zero),divide(x,x),zero)
| less_equal(zero,divide(divide(x,x),zero)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
less_equal(zero,divide(divide(x,x),zero)),
inference(unit_resolution,[status(thm)],[34,16,31]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
| quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x),
inference(unit_resolution,[status(thm)],[40,16,37]) ).
tff(42,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x)
| quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x)
| quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x)
| quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(x,divide(identity,divide(identity,zero)))),x)
| quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero),
inference(unit_resolution,[status(thm)],[44,27,41]) ).
tff(46,plain,
( ~ ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
| quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero)))),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero))))
| less_equal(divide(x,divide(identity,divide(identity,zero))),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero))))
| less_equal(divide(x,divide(identity,divide(identity,zero))),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero))))
| less_equal(divide(x,divide(identity,divide(identity,zero))),x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,divide(identity,divide(identity,zero)),divide(x,divide(identity,divide(identity,zero))))
| less_equal(divide(x,divide(identity,divide(identity,zero))),x) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
less_equal(divide(x,divide(identity,divide(identity,zero))),x),
inference(unit_resolution,[status(thm)],[50,16,47]) ).
tff(52,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(identity,divide(identity,zero))),x)
| quotient(divide(x,divide(identity,divide(identity,zero))),x,zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(identity,divide(identity,zero))),x)
| quotient(divide(x,divide(identity,divide(identity,zero))),x,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(identity,divide(identity,zero))),x)
| quotient(divide(x,divide(identity,divide(identity,zero))),x,zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,divide(identity,divide(identity,zero))),x)
| quotient(divide(x,divide(identity,divide(identity,zero))),x,zero) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
quotient(divide(x,divide(identity,divide(identity,zero))),x,zero),
inference(unit_resolution,[status(thm)],[54,27,51]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : quotient(X,Y,divide(X,Y))
| quotient(x,x,divide(x,x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
quotient(x,x,divide(x,x)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
^ [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(( ( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
<=> ( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3) )
<=> ( ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4) )
<=> ( ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| ~ quotient(V3,V2,V4) ) )),
rewrite(( ( ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| ~ quotient(V3,V2,V4) )
<=> ( ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4) )
<=> ( ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5) )
<=> ( ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| ~ quotient(V1,Z,V5) ) )),
rewrite(( ( ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| ~ quotient(V1,Z,V5) )
<=> ( ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5) )
<=> ( ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) )
<=> ( ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| less_equal(V4,V5) ) )),
rewrite(( ( ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1)
| less_equal(V4,V5) )
<=> ( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
( ( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) )
<=> ( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) )
<=> ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
tff(64,plain,
! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))) )
<=> ( ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,V5: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) )
| ~ quotient(x,x,divide(x,x))
| ~ quotient(divide(x,divide(identity,divide(identity,zero))),x,zero)
| less_equal(divide(divide(x,x),zero),zero)
| ~ quotient(divide(x,x),zero,divide(divide(x,x),zero))
| ~ quotient(x,divide(x,divide(identity,divide(identity,zero))),divide(x,divide(x,divide(identity,divide(identity,zero)))))
| ~ quotient(divide(x,divide(x,divide(identity,divide(identity,zero)))),x,zero) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
less_equal(divide(divide(x,x),zero),zero),
inference(unit_resolution,[status(thm)],[73,67,57,55,9,37,45]) ).
tff(75,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) )
<=> ( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
tff(80,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( ~ less_equal(zero,divide(divide(x,x),zero))
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(divide(divide(x,x),zero),zero) )
<=> ( ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(divide(x,x),zero))
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(divide(divide(x,x),zero),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(divide(x,x),zero))
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(divide(divide(x,x),zero),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(divide(x,x),zero))
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(divide(divide(x,x),zero),zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(x,x),zero),zero)
| ( zero = divide(divide(x,x),zero) )
| ~ less_equal(zero,divide(divide(x,x),zero)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
zero = divide(divide(x,x),zero),
inference(unit_resolution,[status(thm)],[89,83,74,35]) ).
tff(91,plain,
divide(divide(x,x),zero) = zero,
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( quotient(divide(x,x),zero,divide(divide(x,x),zero))
<=> quotient(divide(x,x),zero,zero) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
quotient(divide(x,x),zero,zero),
inference(modus_ponens,[status(thm)],[9,92]) ).
tff(94,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
<=> ( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
tff(98,plain,
! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
| ~ quotient(divide(x,x),zero,zero)
| less_equal(divide(x,x),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
| ~ quotient(divide(x,x),zero,zero)
| less_equal(divide(x,x),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
| ~ quotient(divide(x,x),zero,zero)
| less_equal(divide(x,x),zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) )
| ~ quotient(divide(x,x),zero,zero)
| less_equal(divide(x,x),zero) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
less_equal(divide(x,x),zero),
inference(unit_resolution,[status(thm)],[103,100,93]) ).
tff(105,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,x,divide(x,x))
| less_equal(divide(x,x),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,x,divide(x,x))
| less_equal(divide(x,x),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,x,divide(x,x))
| less_equal(divide(x,x),x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(x,x,divide(x,x))
| less_equal(divide(x,x),x) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
less_equal(divide(x,x),x),
inference(unit_resolution,[status(thm)],[107,16,57]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,x),x)
| quotient(divide(x,x),x,zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,x),x)
| quotient(divide(x,x),x,zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,x),x)
| quotient(divide(x,x),x,zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) )
| ~ less_equal(divide(x,x),x)
| quotient(divide(x,x),x,zero) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
quotient(divide(x,x),x,zero),
inference(unit_resolution,[status(thm)],[111,27,108]) ).
tff(113,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),x,zero)
| less_equal(zero,divide(x,x)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),x,zero)
| less_equal(zero,divide(x,x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),x,zero)
| less_equal(zero,divide(x,x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) )
| ~ quotient(divide(x,x),x,zero)
| less_equal(zero,divide(x,x)) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
less_equal(zero,divide(x,x)),
inference(unit_resolution,[status(thm)],[115,16,112]) ).
tff(117,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ( ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero )
| ~ less_equal(zero,divide(x,x)) )
<=> ( ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero )
| ~ less_equal(zero,divide(x,x)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero )
| ~ less_equal(zero,divide(x,x)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero )
| ~ less_equal(zero,divide(x,x)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(zero,divide(x,x))
| ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ~ less_equal(divide(x,x),zero)
| ( divide(x,x) = zero ) ),
inference(unit_resolution,[status(thm)],[122,83,116]) ).
tff(124,plain,
divide(x,x) = zero,
inference(unit_resolution,[status(thm)],[123,104]) ).
tff(125,plain,
( quotient(x,x,divide(x,x))
<=> quotient(x,x,zero) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( quotient(x,x,zero)
<=> quotient(x,x,divide(x,x)) ),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ quotient(x,x,zero)
<=> ~ quotient(x,x,divide(x,x)) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ~ quotient(x,x,zero)
<=> ~ quotient(x,x,zero) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
tff(130,plain,
~ quotient(x,x,zero),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
~ quotient(x,x,divide(x,x)),
inference(modus_ponens,[status(thm)],[130,127]) ).
tff(132,plain,
$false,
inference(unit_resolution,[status(thm)],[57,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : HEN003-2 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 17:13:01 EDT 2025
% 0.14/0.36 % CPUTime :
% 60.86/61.01 % SZS status Unsatisfiable
% 60.86/61.01 % SZS output start Proof
% See solution above
% 60.92/61.10 % E exiting
%------------------------------------------------------------------------------