%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN005-5 : 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 05:08:47 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 72 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 193 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 233 ( 111 ~; 101 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 85 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
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,
^ [X: $i] :
refl(( ( divide(zero,X) = zero )
<=> ( divide(zero,X) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( divide(zero,X) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).
tff(5,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(divide(a,c),divide(b,c))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(zero,divide(divide(a,c),divide(b,c))) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( divide(b,c) = zero )
<=> ( divide(b,c) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
divide(b,c) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_divide_c_is_zero) ).
tff(12,plain,
divide(b,c) = zero,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
zero = divide(b,c),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
divide(divide(a,c),zero) = divide(divide(a,c),divide(b,c)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
divide(zero,zero) = zero,
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
divide(divide(zero,zero),divide(divide(a,c),zero)) = divide(zero,divide(divide(a,c),divide(b,c))),
inference(monotonicity,[status(thm)],[16,14]) ).
tff(18,plain,
divide(divide(a,c),divide(b,c)) = divide(divide(a,c),zero),
inference(symmetry,[status(thm)],[14]) ).
tff(19,plain,
zero = divide(zero,zero),
inference(symmetry,[status(thm)],[16]) ).
tff(20,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,c) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
divide(zero,c) = zero,
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
( ( divide(a,b) = zero )
<=> ( divide(a,b) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
divide(a,b) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_is_zero) ).
tff(24,plain,
divide(a,b) = zero,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
divide(divide(a,b),c) = divide(zero,c),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
divide(divide(a,b),c) = divide(zero,zero),
inference(transitivity,[status(thm)],[25,21,19]) ).
tff(27,plain,
divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) = divide(divide(zero,zero),divide(divide(a,c),zero)),
inference(monotonicity,[status(thm)],[26,18]) ).
tff(28,plain,
divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) = zero,
inference(transitivity,[status(thm)],[27,17,9]) ).
tff(29,plain,
divide(zero,c) = divide(divide(a,b),c),
inference(symmetry,[status(thm)],[25]) ).
tff(30,plain,
zero = divide(zero,c),
inference(symmetry,[status(thm)],[21]) ).
tff(31,plain,
zero = divide(divide(a,b),c),
inference(transitivity,[status(thm)],[30,29]) ).
tff(32,plain,
( ( divide(divide(a,c),zero) = zero )
<=> ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) ) ),
inference(monotonicity,[status(thm)],[14,31]) ).
tff(33,plain,
( ( divide(divide(a,c),zero) != zero )
<=> ( divide(divide(a,c),divide(b,c)) != divide(divide(a,b),c) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(a,c)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
divide(zero,divide(a,c)) = zero,
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
( ( divide(a,c) != zero )
<=> ( divide(a,c) != zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
divide(a,c) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_divide_to_zero) ).
tff(38,plain,
divide(a,c) != zero,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [Y: $i,X: $i] :
refl(( ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) )
<=> ( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',divide_and_equal) ).
tff(45,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ( divide(a,c) = zero )
| ( divide(zero,divide(a,c)) != zero )
| ( divide(divide(a,c),zero) != zero ) )
<=> ( ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(zero,divide(a,c)) != zero )
| ( divide(divide(a,c),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(zero,divide(a,c)) != zero )
| ( divide(divide(a,c),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(zero,divide(a,c)) != zero )
| ( divide(divide(a,c),zero) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,c) = zero )
| ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( divide(divide(a,c),zero) != zero )
| ( divide(zero,divide(a,c)) != zero ) ),
inference(unit_resolution,[status(thm)],[54,48,38]) ).
tff(56,plain,
divide(divide(a,c),zero) != zero,
inference(unit_resolution,[status(thm)],[55,35]) ).
tff(57,plain,
divide(divide(a,c),divide(b,c)) != divide(divide(a,b),c),
inference(modus_ponens,[status(thm)],[56,33]) ).
tff(58,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
<=> ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',quotient_property) ).
tff(62,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero )
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) = zero,
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) )
| ( divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero )
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) )
| ( divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero )
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) != zero ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) )
| ( divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero )
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) != zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) )
| ( divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero )
| ( divide(divide(divide(a,c),divide(b,c)),divide(divide(a,b),c)) != zero ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( divide(divide(a,c),divide(b,c)) = divide(divide(a,b),c) )
| ( divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero ) ),
inference(unit_resolution,[status(thm)],[69,48,66]) ).
tff(71,plain,
divide(divide(divide(a,b),c),divide(divide(a,c),divide(b,c))) != zero,
inference(unit_resolution,[status(thm)],[70,57]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HEN005-5 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 17:14:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54 % SZS output start Proof
% See solution above
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------