TSTP Solution File: FLD049-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD049-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.41s 0.52s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 88
% Syntax : Number of formulae : 172 ( 45 unt; 11 typ; 0 def)
% Number of atoms : 868 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1209 ( 538 ~; 595 |; 0 &)
% ( 76 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 426 ( 398 !; 0 ?; 426 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $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(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_5) ).
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),multiply(c,multiplicative_inverse(d)))
<=> product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
tff(37,plain,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
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),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))) ) ),
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),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))) ),
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),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))),
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,multiply(c,multiplicative_inverse(d)))
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)))
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)))
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)))
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| product(b,multiply(c,multiplicative_inverse(d)),a) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
product(b,multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)),a)
| product(multiply(c,multiplicative_inverse(d)),b,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,multiply(c,multiplicative_inverse(d)),a)
| product(multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)),a)
| product(multiply(c,multiplicative_inverse(d)),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,multiply(c,multiplicative_inverse(d)),a)
| product(multiply(c,multiplicative_inverse(d)),b,a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
product(multiply(c,multiplicative_inverse(d)),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_6) ).
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] :
refl(
( ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [X: $i] :
rewrite(
( ( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) )
<=> ( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
tff(89,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ defined(d)
| sum(additive_identity,d,additive_identity)
| defined(multiplicative_inverse(d)) )
<=> ( sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| defined(multiplicative_inverse(d)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| defined(multiplicative_inverse(d)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(d)
| sum(additive_identity,d,additive_identity)
| defined(multiplicative_inverse(d)) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,d,additive_identity)
| ~ defined(d)
| defined(multiplicative_inverse(d)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
defined(multiplicative_inverse(d)),
inference(unit_resolution,[status(thm)],[98,92,82,79]) ).
tff(100,plain,
( defined(c)
<=> defined(c) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
tff(102,plain,
defined(c),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
<=> ( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( product(X,Y,multiply(X,Y))
| ~ defined(X) )
<=> ( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) )),
( ( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| product(X,Y,multiply(X,Y))
| ~ defined(Y) ) )),
rewrite(
( ( ~ defined(X)
| product(X,Y,multiply(X,Y))
| ~ defined(Y) )
<=> ( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) )),
( ( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [Y: $i,X: $i] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,axiom,
! [Y: $i,X: $i] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
tff(109,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[111,104]) ).
tff(113,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(c)
| ~ defined(multiplicative_inverse(d))
| product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(c)
| ~ defined(multiplicative_inverse(d))
| product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(c)
| ~ defined(multiplicative_inverse(d))
| product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d))) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(c)
| ~ defined(multiplicative_inverse(d))
| product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d))) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d))),
inference(unit_resolution,[status(thm)],[115,112,102,99]) ).
tff(117,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d))) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(c,multiplicative_inverse(d),multiply(c,multiplicative_inverse(d)))
| product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d))) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d))),
inference(unit_resolution,[status(thm)],[119,30,116]) ).
tff(121,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(122,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(123,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)],[122,121]) ).
tff(124,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(unit_resolution,[status(thm)],[123,16,82,79]) ).
tff(125,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(126,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(127,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)],[126,125]) ).
tff(128,plain,
product(d,multiplicative_inverse(d),multiplicative_identity),
inference(unit_resolution,[status(thm)],[127,30,124]) ).
tff(129,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(130,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(c)
| product(multiplicative_identity,c,c) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
product(multiplicative_identity,c,c),
inference(unit_resolution,[status(thm)],[131,54,102]) ).
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(multiplicative_identity,c,c)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),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(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ product(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,multiply(c,multiplicative_inverse(d)),c) )
<=> ( ~ product(multiplicative_identity,c,c)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),c) ) ),
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(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,multiply(c,multiplicative_inverse(d)),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(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),c) ) ),
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(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,multiply(c,multiplicative_inverse(d)),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(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),c) ) ),
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(multiplicative_identity,c,c)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| product(d,multiply(c,multiplicative_inverse(d)),c) ),
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(multiplicative_identity,c,c)
| ~ product(d,multiplicative_inverse(d),multiplicative_identity)
| ~ product(multiplicative_inverse(d),c,multiply(c,multiplicative_inverse(d)))
| product(d,multiply(c,multiplicative_inverse(d)),c) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
product(d,multiply(c,multiplicative_inverse(d)),c),
inference(unit_resolution,[status(thm)],[138,68,132,128,120]) ).
tff(140,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(b)
| ~ defined(c)
| product(b,c,multiply(b,c)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(b)
| ~ defined(c)
| product(b,c,multiply(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(b)
| ~ defined(c)
| product(b,c,multiply(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| product(X,Y,multiply(X,Y)) )
| ~ defined(b)
| ~ defined(c)
| product(b,c,multiply(b,c)) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
product(b,c,multiply(b,c)),
inference(unit_resolution,[status(thm)],[142,112,6,102]) ).
tff(144,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,c,multiply(b,c))
| product(c,b,multiply(b,c)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,c,multiply(b,c))
| product(c,b,multiply(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,c,multiply(b,c))
| product(c,b,multiply(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(b,c,multiply(b,c))
| product(c,b,multiply(b,c)) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
product(c,b,multiply(b,c)),
inference(unit_resolution,[status(thm)],[146,30,143]) ).
tff(148,plain,
( ~ product(a,d,multiply(b,c))
<=> ~ product(a,d,multiply(b,c)) ),
inference(rewrite,[status(thm)],]) ).
tff(149,axiom,
~ product(a,d,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
tff(150,plain,
~ product(a,d,multiply(b,c)),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(d,a,multiply(b,c))
| product(a,d,multiply(b,c)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(d,a,multiply(b,c))
| product(a,d,multiply(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(d,a,multiply(b,c))
| product(a,d,multiply(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(d,a,multiply(b,c))
| product(a,d,multiply(b,c)) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
~ product(d,a,multiply(b,c)),
inference(unit_resolution,[status(thm)],[153,30,150]) ).
tff(155,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(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),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(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ product(c,b,multiply(b,c))
| ~ product(multiply(c,multiplicative_inverse(d)),b,a)
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| product(d,a,multiply(b,c)) )
<=> ( product(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,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,multiply(b,c))
| ~ product(multiply(c,multiplicative_inverse(d)),b,a)
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| product(d,a,multiply(b,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(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),b,a) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,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,multiply(b,c))
| ~ product(multiply(c,multiplicative_inverse(d)),b,a)
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| product(d,a,multiply(b,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(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),b,a) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,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,multiply(b,c))
| ~ product(multiply(c,multiplicative_inverse(d)),b,a)
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| product(d,a,multiply(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,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(d,a,multiply(b,c))
| ~ product(c,b,multiply(b,c))
| ~ product(d,multiply(c,multiplicative_inverse(d)),c)
| ~ product(multiply(c,multiplicative_inverse(d)),b,a) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
$false,
inference(unit_resolution,[status(thm)],[160,68,154,147,139,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD049-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 03:02:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.41/0.52 % SZS status Unsatisfiable
% 0.41/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------