TSTP Solution File: HEN010-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 22:39:54 EDT 2022
% Result : Unsatisfiable 22.43s 14.57s
% Output : Proof 22.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 45
% Syntax : Number of formulae : 106 ( 41 unt; 5 typ; 0 def)
% Number of atoms : 312 ( 124 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 375 ( 171 ~; 167 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 182 ( 169 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_equal_type,type,
less_equal: ( $i * $i ) > $o ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(zero_type,type,
zero: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( divide(X,X) = zero )
<=> ( divide(X,X) = zero ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( divide(X,X) = zero )
<=> ! [X: $i] : ( divide(X,X) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( divide(X,X) = zero )
<=> ! [X: $i] : ( divide(X,X) = zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( divide(X,X) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
tff(5,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( divide(X,X) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( divide(X,X) = zero )
| ( divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
zero = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [X: $i] :
refl(
( ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) )
<=> ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) )
<=> ! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) )
<=> ! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
tff(15,plain,
! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [X: $i] : ( divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) )
| ( divide(identity,divide(identity,divide(identity,a))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))) = divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero)
<=> less_equal(divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) ),
inference(monotonicity,[status(thm)],[21,10]) ).
tff(23,plain,
( less_equal(divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))))
<=> less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,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)],[27,26]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29,25]) ).
tff(31,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(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
less_equal(divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero),
inference(modus_ponens,[status(thm)],[32,23]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( less_equal(divide(X,Y),X)
<=> less_equal(divide(X,Y),X) )),
inference(bind,[status(th)],]) ).
tff(35,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)],[34]) ).
tff(36,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(37,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(38,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : less_equal(divide(X,Y),X),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,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(47,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a))
| ( divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a))
| ( divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a))
| ( divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a))
| ( divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a))
| ( divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero ) ),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)) = zero,
inference(unit_resolution,[status(thm)],[53,42]) ).
tff(55,plain,
zero = divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
<=> less_equal(divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( less_equal(divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
<=> less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
less_equal(divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),divide(identity,a)),divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))),
inference(unit_resolution,[status(thm)],[58,40]) ).
tff(60,plain,
less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))),
inference(modus_ponens,[status(thm)],[59,57]) ).
tff(61,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(62,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(63,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(64,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)],[63]) ).
tff(65,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(66,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero)
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) )
<=> ( ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero)
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero)
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero)
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero )
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ),
inference(unit_resolution,[status(thm)],[75,69,60]) ).
tff(77,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) = zero,
inference(unit_resolution,[status(thm)],[76,33]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,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(82,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero )
| less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero )
| less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero )
| less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero )
| less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ( divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero )
| less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(unit_resolution,[status(thm)],[87,84]) ).
tff(89,plain,
less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(unit_resolution,[status(thm)],[88,77]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : less_equal(divide(X,Y),X)
| less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)),
inference(unit_resolution,[status(thm)],[90,40]) ).
tff(92,plain,
( ( divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) )
<=> ( divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
tff(94,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) )
<=> ( ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) )
| ( divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) )
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,69,94,91,89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 21:52:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 22.43/14.57 % SZS status Unsatisfiable
% 22.43/14.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------