TSTP Solution File: FLD049-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD049-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 14:55:55 EDT 2022
% Result : Unsatisfiable 0.17s 0.56s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 81
% Syntax : Number of formulae : 151 ( 44 unt; 12 typ; 0 def)
% Number of atoms : 724 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 999 ( 454 ~; 478 |; 0 &)
% ( 67 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 417 ( 383 !; 0 ?; 417 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(s_type,type,
s: $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(k_type,type,
k: $i ).
tff(1,plain,
( ~ sum(additive_identity,b,additive_identity)
<=> ~ sum(additive_identity,b,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
tff(3,plain,
~ sum(additive_identity,b,additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
tff(6,plain,
defined(b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity) )
<=> ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity)
| ~ defined(X) ) )),
rewrite(
( ( sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
( ( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
tff(13,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(b)
| sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(b)
| sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(b)
| sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(b)
| sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ( ~ product(X,Y,Z)
| product(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( product(Y,X,Z)
| ~ product(X,Y,Z) )
<=> ( ~ product(X,Y,Z)
| product(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] :
( product(Y,X,Z)
| ~ product(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [Z: $i,Y: $i,X: $i] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(b,multiplicative_inverse(b),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(b,multiplicative_inverse(b),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(b,multiplicative_inverse(b),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(b,multiplicative_inverse(b),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( product(a,multiplicative_inverse(b),s)
<=> product(a,multiplicative_inverse(b),s) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
tff(37,plain,
product(a,multiplicative_inverse(b),s),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,multiplicative_inverse(b),s)
| product(multiplicative_inverse(b),a,s) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,multiplicative_inverse(b),s)
| product(multiplicative_inverse(b),a,s) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,multiplicative_inverse(b),s)
| product(multiplicative_inverse(b),a,s) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,multiplicative_inverse(b),s)
| product(multiplicative_inverse(b),a,s) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
product(multiplicative_inverse(b),a,s),
inference(unit_resolution,[status(thm)],[40,30,37]) ).
tff(42,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
tff(44,plain,
defined(a),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [X: $i] :
rewrite(
( ( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
tff(51,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(a)
| product(multiplicative_identity,a,a) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(a)
| product(multiplicative_identity,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(a)
| product(multiplicative_identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(a)
| product(multiplicative_identity,a,a) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
product(multiplicative_identity,a,a),
inference(unit_resolution,[status(thm)],[57,54,44]) ).
tff(59,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( product(X,V,W)
| ~ product(X,Y,U) )
<=> ( ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( ~ product(X,Y,U)
| product(X,V,W)
| ~ product(Y,Z,V) ) )),
rewrite(
( ( ~ product(X,Y,U)
| product(X,V,W)
| ~ product(Y,Z,V) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W)
| ~ product(U,Z,W) ) )),
rewrite(
( ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W)
| ~ product(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
( ( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
tff(65,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(b),a,s)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,s,a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(b),a,s)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,s,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(b),a,s)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,s,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(b),a,s)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,s,a) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
product(b,s,a),
inference(unit_resolution,[status(thm)],[71,68,58,41,34]) ).
tff(73,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,s,a)
| product(s,b,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,s,a)
| product(s,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,s,a)
| product(s,b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,s,a)
| product(s,b,a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
product(s,b,a),
inference(unit_resolution,[status(thm)],[75,30,72]) ).
tff(77,plain,
( ~ sum(additive_identity,d,additive_identity)
<=> ~ sum(additive_identity,d,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
tff(79,plain,
~ sum(additive_identity,d,additive_identity),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( defined(d)
<=> defined(d) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
tff(82,plain,
defined(d),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(unit_resolution,[status(thm)],[85,16,82,79]) ).
tff(87,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(d),d,multiplicative_identity)
| product(d,multiplicative_inverse(d),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(d),d,multiplicative_identity)
| product(d,multiplicative_inverse(d),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(d),d,multiplicative_identity)
| product(d,multiplicative_inverse(d),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(d),d,multiplicative_identity)
| product(d,multiplicative_inverse(d),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
product(d,multiplicative_inverse(d),multiplicative_identity),
inference(unit_resolution,[status(thm)],[89,30,86]) ).
tff(91,plain,
( product(c,multiplicative_inverse(d),s)
<=> product(c,multiplicative_inverse(d),s) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
tff(93,plain,
product(c,multiplicative_inverse(d),s),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),s)
| product(multiplicative_inverse(d),c,s) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),s)
| product(multiplicative_inverse(d),c,s) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),s)
| product(multiplicative_inverse(d),c,s) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),s)
| product(multiplicative_inverse(d),c,s) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
product(multiplicative_inverse(d),c,s),
inference(unit_resolution,[status(thm)],[96,30,93]) ).
tff(98,plain,
( defined(c)
<=> defined(c) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
tff(100,plain,
defined(c),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
product(multiplicative_identity,c,c),
inference(unit_resolution,[status(thm)],[103,54,100]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,s)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,s,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,s)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,s,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,s)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,s,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
| ~ product(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,s)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,s,c) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
product(d,s,c),
inference(unit_resolution,[status(thm)],[107,68,104,97,90]) ).
tff(109,plain,
( ~ product(b,c,k)
<=> ~ product(b,c,k) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
~ product(b,c,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
tff(111,plain,
~ product(b,c,k),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,b,k)
| product(b,c,k) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,b,k)
| product(b,c,k) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,b,k)
| product(b,c,k) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,b,k)
| product(b,c,k) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
~ product(c,b,k),
inference(unit_resolution,[status(thm)],[114,30,111]) ).
tff(116,plain,
( product(a,d,k)
<=> product(a,d,k) ),
inference(rewrite,[status(thm)],]) ).
tff(117,axiom,
product(a,d,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
tff(118,plain,
product(a,d,k),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,d,k)
| product(d,a,k) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,d,k)
| product(d,a,k) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,d,k)
| product(d,a,k) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,d,k)
| product(d,a,k) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
product(d,a,k),
inference(unit_resolution,[status(thm)],[121,30,118]) ).
tff(123,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( product(U,Z,W)
| ~ product(X,Y,U) )
<=> ( product(U,Z,W)
| ~ product(X,Y,U) ) )),
( ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) ) )),
rewrite(
( ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
rewrite(
( ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(127,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
tff(129,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( product(c,b,k)
| ~ product(s,b,a)
| ~ product(d,s,c)
| ~ product(d,a,k) )
<=> ( product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(s,b,a)
| ~ product(d,s,c)
| ~ product(d,a,k) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(s,b,a)
| ~ product(d,s,c)
| ~ product(d,a,k) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(s,b,a)
| ~ product(d,s,c)
| ~ product(d,a,k) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,b,k)
| ~ product(d,a,k)
| ~ product(d,s,c)
| ~ product(s,b,a) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
$false,
inference(unit_resolution,[status(thm)],[138,132,122,115,108,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : FLD049-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 02:57:35 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.17/0.56 % SZS status Unsatisfiable
% 0.17/0.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------