TSTP Solution File: HEN008-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Fri Sep 16 22:39:51 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 43
% Syntax : Number of formulae : 105 ( 38 unt; 6 typ; 0 def)
% Number of atoms : 303 ( 104 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 369 ( 170 ~; 164 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 159 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_equal_type,type,
less_equal: ( $i * $i ) > $o ).
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( less_equal(a,b)
<=> less_equal(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
tff(3,plain,
less_equal(a,b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
<=> ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(a,b)
| ( divide(a,b) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(a,b)
| ( divide(a,b) = zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(a,b)
| ( divide(a,b) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(a,b)
| ( divide(a,b) = zero ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
divide(a,b) = zero,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
zero = divide(a,b),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
divide(zero,c) = divide(divide(a,b),c),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
divide(divide(a,b),c) = divide(zero,c),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( less_equal(divide(divide(a,b),c),zero)
<=> less_equal(divide(zero,c),zero) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( less_equal(divide(zero,c),zero)
<=> less_equal(divide(divide(a,b),c),zero) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( less_equal(divide(X,Y),X)
<=> less_equal(divide(X,Y),X) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
<=> ! [Y: $i,X: $i] : less_equal(divide(X,Y),X) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
<=> ! [Y: $i,X: $i] : less_equal(divide(X,Y),X) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
tff(24,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(zero,c),zero) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
less_equal(divide(zero,c),zero),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
less_equal(divide(divide(a,b),c),zero),
inference(modus_ponens,[status(thm)],[28,19]) ).
tff(30,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(divide(a,b),c),zero) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(divide(a,b),c),zero) = zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(divide(a,b),c),zero) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(divide(a,b),c),zero) = zero ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(divide(a,b),c),zero) = zero ) ),
inference(unit_resolution,[status(thm)],[32,10]) ).
tff(34,plain,
divide(divide(divide(a,b),c),zero) = zero,
inference(unit_resolution,[status(thm)],[33,29]) ).
tff(35,plain,
zero = divide(divide(divide(a,b),c),zero),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( less_equal(zero,divide(divide(a,b),c))
<=> less_equal(divide(divide(divide(a,b),c),zero),divide(divide(a,b),c)) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( less_equal(divide(divide(divide(a,b),c),zero),divide(divide(a,b),c))
<=> less_equal(zero,divide(divide(a,b),c)) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(divide(divide(a,b),c),zero),divide(divide(a,b),c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
less_equal(divide(divide(divide(a,b),c),zero),divide(divide(a,b),c)),
inference(unit_resolution,[status(thm)],[38,26]) ).
tff(40,plain,
less_equal(zero,divide(divide(a,b),c)),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,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(42,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(43,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(44,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)],[43]) ).
tff(45,axiom,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
tff(46,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(a,b),c) = zero )
| ~ less_equal(zero,divide(divide(a,b),c)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(a,b),c) = zero )
| ~ less_equal(zero,divide(divide(a,b),c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(a,b),c) = zero )
| ~ less_equal(zero,divide(divide(a,b),c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,b),c),zero)
| ( divide(divide(a,b),c) = zero )
| ~ less_equal(zero,divide(divide(a,b),c)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( divide(divide(a,b),c) = zero )
| ~ less_equal(zero,divide(divide(a,b),c)) ),
inference(unit_resolution,[status(thm)],[52,49,29]) ).
tff(54,plain,
divide(divide(a,b),c) = zero,
inference(unit_resolution,[status(thm)],[53,40]) ).
tff(55,plain,
zero = divide(divide(a,b),c),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( less_equal(divide(divide(a,c),divide(b,c)),zero)
<=> less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c))
<=> less_equal(divide(divide(a,c),divide(b,c)),zero) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))
<=> less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))
<=> ! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))
<=> ! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
tff(62,plain,
! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))
| less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
less_equal(divide(divide(a,c),divide(b,c)),zero),
inference(modus_ponens,[status(thm)],[66,57]) ).
tff(68,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c))
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c))
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c))
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c))
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero,
inference(unit_resolution,[status(thm)],[70,10,66]) ).
tff(72,plain,
zero = divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( less_equal(zero,divide(divide(a,c),divide(b,c)))
<=> less_equal(divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),divide(divide(a,c),divide(b,c))) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( less_equal(divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),divide(divide(a,c),divide(b,c)))
<=> less_equal(zero,divide(divide(a,c),divide(b,c))) ),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),divide(divide(a,c),divide(b,c))) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
less_equal(divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),divide(divide(a,c),divide(b,c))),
inference(unit_resolution,[status(thm)],[75,26]) ).
tff(77,plain,
less_equal(zero,divide(divide(a,c),divide(b,c))),
inference(modus_ponens,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ less_equal(divide(a,c),divide(b,c))
<=> ~ less_equal(divide(a,c),divide(b,c)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
tff(80,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( divide(X,Y) != zero )
| less_equal(X,Y) )
<=> ( ( divide(X,Y) != zero )
| less_equal(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
tff(85,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(a,c),divide(b,c)) != zero )
| less_equal(divide(a,c),divide(b,c)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(a,c),divide(b,c)) != zero )
| less_equal(divide(a,c),divide(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(a,c),divide(b,c)) != zero )
| less_equal(divide(a,c),divide(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(a,c),divide(b,c)) != zero )
| less_equal(divide(a,c),divide(b,c)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(unit_resolution,[status(thm)],[90,87,80]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c))) )
<=> ( ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c))) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(a,c),divide(b,c)) = zero )
| ~ less_equal(zero,divide(divide(a,c),divide(b,c)))
| ~ less_equal(divide(divide(a,c),divide(b,c)),zero) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
~ less_equal(divide(divide(a,c),divide(b,c)),zero),
inference(unit_resolution,[status(thm)],[97,49,91,77]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 21:55:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------