%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN007-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:08:48 AM UTC 2025
% Result : Unsatisfiable 0.44s 0.62s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 57 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 281 ( 132 ~; 127 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 147 ( 138 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_equal_type,type,
less_equal: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(zero_type,type,
zero: $i ).
tff(b_type,type,
b: $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(c,a),divide(c,a)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(c,a),divide(c,a)) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(c,a),divide(c,a)) != zero )
| less_equal(divide(c,a),divide(c,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(c,a),divide(c,a)) != zero )
| less_equal(divide(c,a),divide(c,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(c,a),divide(c,a)) != zero )
| less_equal(divide(c,a),divide(c,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(divide(c,a),divide(c,a)) != zero )
| less_equal(divide(c,a),divide(c,a)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
less_equal(divide(c,a),divide(c,a)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
<=> ( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,a),divide(c,a))
| less_equal(divide(c,divide(c,a)),a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,a),divide(c,a))
| less_equal(divide(c,divide(c,a)),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,a),divide(c,a))
| less_equal(divide(c,divide(c,a)),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,a),divide(c,a))
| less_equal(divide(c,divide(c,a)),a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
less_equal(divide(c,divide(c,a)),a),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
( ~ less_equal(divide(c,b),divide(c,a))
<=> ~ less_equal(divide(c,b),divide(c,a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
tff(34,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,divide(c,a)),b)
| less_equal(divide(c,b),divide(c,a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,divide(c,a)),b)
| less_equal(divide(c,b),divide(c,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,divide(c,a)),b)
| less_equal(divide(c,b),divide(c,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) )
| ~ less_equal(divide(c,divide(c,a)),b)
| less_equal(divide(c,b),divide(c,a)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ less_equal(divide(c,divide(c,a)),b),
inference(unit_resolution,[status(thm)],[37,27,34]) ).
tff(39,plain,
( less_equal(a,b)
<=> less_equal(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
tff(41,plain,
less_equal(a,b),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) )
<=> ( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ less_equal(divide(c,divide(c,a)),a)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(a,b) )
<=> ( ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(divide(c,divide(c,a)),a)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(a,b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(divide(c,divide(c,a)),a)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(a,b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(divide(c,divide(c,a)),a)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(a,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_equal(X,Y)
| less_equal(X,Z)
| ~ less_equal(Y,Z) )
| ~ less_equal(a,b)
| less_equal(divide(c,divide(c,a)),b)
| ~ less_equal(divide(c,divide(c,a)),a) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,50,41,38,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HEN007-4 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 17:13:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.44/0.62 % SZS status Unsatisfiable
% 0.44/0.62 % SZS output start Proof
% See solution above
% 0.44/0.63 % E exiting
%------------------------------------------------------------------------------