%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN008-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.52s 0.71s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 76 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 237 ( 97 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 291 ( 135 ~; 129 |; 0 &)
% ( 27 <=>; 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 : 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 : 141 ( 131 !; 0 ?; 141 :)
% 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,
divide(divide(a,b),c) = divide(zero,c),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
divide(zero,c) = divide(divide(a,b),c),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(( ( divide(zero,X) = zero )
<=> ( divide(zero,X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [X: $i] : ( divide(zero,X) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
tff(21,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,c) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
divide(zero,c) = zero,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
zero = divide(zero,c),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
zero = divide(divide(a,b),c),
inference(transitivity,[status(thm)],[26,16]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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(34,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)],[33,32]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35,31]) ).
tff(37,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(38,plain,
less_equal(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
less_equal(divide(divide(a,c),divide(b,c)),zero),
inference(modus_ponens,[status(thm)],[38,29]) ).
tff(40,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(divide(a,c),divide(b,c))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
divide(zero,divide(divide(a,c),divide(b,c))) = zero,
inference(unit_resolution,[status(thm)],[40,23]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(zero,divide(divide(a,c),divide(b,c))) != zero )
| less_equal(zero,divide(divide(a,c),divide(b,c))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(zero,divide(divide(a,c),divide(b,c))) != zero )
| less_equal(zero,divide(divide(a,c),divide(b,c))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(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(51,plain,
( ~ ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) )
| ( divide(zero,divide(divide(a,c),divide(b,c))) != zero )
| less_equal(zero,divide(divide(a,c),divide(b,c))) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
less_equal(zero,divide(divide(a,c),divide(b,c))),
inference(unit_resolution,[status(thm)],[51,48,41]) ).
tff(53,plain,
( ~ less_equal(divide(a,c),divide(b,c))
<=> ~ less_equal(divide(a,c),divide(b,c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,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(55,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,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(57,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(58,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)],[57,56]) ).
tff(59,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(unit_resolution,[status(thm)],[58,48,55]) ).
tff(60,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(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] :
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(63,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)],[62]) ).
tff(64,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(65,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Y: $i,X: $i] :
( ~ less_equal(X,Y)
| ( X = Y )
| ~ less_equal(Y,X) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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)],[71,69]) ).
tff(73,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(74,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)],[73,72]) ).
tff(75,plain,
~ less_equal(divide(divide(a,c),divide(b,c)),zero),
inference(unit_resolution,[status(thm)],[74,68,59,52]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN008-6 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 17:16:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.52/0.71 % SZS status Unsatisfiable
% 0.52/0.71 % SZS output start Proof
% See solution above
% 0.52/0.72 % E exiting
%------------------------------------------------------------------------------