TSTP Solution File: HEN003-5 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 22:39:45 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 69 ( 32 unt; 3 typ; 0 def)
% Number of atoms : 219 ( 213 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 281 ( 133 ~; 125 |; 0 &)
% ( 23 <=>; 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 : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 110 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_property) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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,a),divide(zero,a)),divide(divide(a,zero),a)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(divide(a,a),divide(zero,a)),divide(divide(a,zero),a)) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( divide(divide(X,Y),X) = zero )
<=> ( divide(divide(X,Y),X) = zero ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
<=> ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
<=> ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_smaller_than_numerator) ).
tff(14,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( divide(divide(X,Y),X) = zero )
| ( divide(divide(a,zero),a) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
divide(divide(a,zero),a) = zero,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
zero = divide(divide(a,zero),a),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
refl(
( ( divide(zero,X) = zero )
<=> ( divide(zero,X) = zero ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] : ( divide(zero,X) = zero )
<=> ! [X: $i] : ( divide(zero,X) = zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [X: $i] : ( divide(zero,X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).
tff(24,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] : ( divide(zero,X) = zero ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,a) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
divide(zero,a) = zero,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
divide(divide(a,a),divide(zero,a)) = divide(divide(a,a),zero),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
divide(divide(a,a),zero) = divide(divide(a,a),divide(zero,a)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
divide(divide(divide(a,a),zero),zero) = divide(divide(divide(a,a),divide(zero,a)),divide(divide(a,zero),a)),
inference(monotonicity,[status(thm)],[30,19]) ).
tff(32,plain,
divide(divide(divide(a,a),zero),zero) = zero,
inference(transitivity,[status(thm)],[31,9]) ).
tff(33,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(divide(a,a),zero)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
divide(zero,divide(divide(a,a),zero)) = zero,
inference(unit_resolution,[status(thm)],[33,26]) ).
tff(35,plain,
( ~ ! [X: $i] : ( divide(zero,X) = zero )
| ( divide(zero,divide(a,a)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
divide(zero,divide(a,a)) = zero,
inference(unit_resolution,[status(thm)],[35,26]) ).
tff(37,plain,
( ( divide(a,a) != zero )
<=> ( divide(a,a) != zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
divide(a,a) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
tff(39,plain,
divide(a,a) != zero,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,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(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(quant_intro,[status(thm)],[40]) ).
tff(42,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(43,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(44,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)],[43]) ).
tff(45,axiom,
! [Y: $i,X: $i] :
( ( divide(X,Y) != zero )
| ( divide(Y,X) != zero )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',divide_and_equal) ).
tff(46,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) )
<=> ( ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(zero,divide(a,a)) != zero )
| ( divide(divide(a,a),zero) != zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(a,a) = zero )
| ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ( divide(divide(a,a),zero) != zero )
| ( divide(zero,divide(a,a)) != zero ) ),
inference(unit_resolution,[status(thm)],[55,49,39]) ).
tff(57,plain,
divide(divide(a,a),zero) != zero,
inference(unit_resolution,[status(thm)],[56,36]) ).
tff(58,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ( divide(divide(a,a),zero) = zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero )
| ( divide(divide(divide(a,a),zero),zero) != zero ) )
<=> ( ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero )
| ( divide(divide(divide(a,a),zero),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero )
| ( divide(divide(divide(a,a),zero),zero) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero )
| ( divide(divide(divide(a,a),zero),zero) != zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ( divide(Y,X) != zero )
| ( divide(X,Y) != zero ) )
| ( divide(divide(a,a),zero) = zero )
| ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( divide(divide(divide(a,a),zero),zero) != zero )
| ( divide(zero,divide(divide(a,a),zero)) != zero ) ),
inference(unit_resolution,[status(thm)],[63,49,57]) ).
tff(65,plain,
divide(divide(divide(a,a),zero),zero) != zero,
inference(unit_resolution,[status(thm)],[64,34]) ).
tff(66,plain,
$false,
inference(unit_resolution,[status(thm)],[65,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 21:40:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------