TSTP Solution File: FLD041-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD041-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 14:55:51 EDT 2022
% Result : Unsatisfiable 0.53s 0.63s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 124
% Syntax : Number of formulae : 257 ( 63 unt; 10 typ; 0 def)
% Number of atoms : 1609 ( 0 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 2404 (1122 ~;1145 |; 0 &)
% ( 137 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 80 ( 80 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 991 ( 921 !; 0 ?; 991 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( defined(multiplicative_identity)
<=> defined(multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
tff(3,plain,
defined(multiplicative_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X: $i] :
rewrite(
( ( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
tff(10,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [X: $i] :
rewrite(
( ( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
tff(38,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) )
| ~ defined(multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity),
inference(unit_resolution,[status(thm)],[44,41,3]) ).
tff(46,plain,
( ~ sum(additive_identity,additive_identity,multiplicative_identity)
<=> ~ sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',different_identities) ).
tff(48,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sum(U,Z,W)
| ~ sum(X,Y,U) )
<=> ( sum(U,Z,W)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) ) )),
rewrite(
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
rewrite(
( ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
( ( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
tff(55,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[64,58,48,45,31]) ).
tff(66,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity),
inference(unit_resolution,[status(thm)],[68,27,65]) ).
tff(70,plain,
( defined(c)
<=> defined(c) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
tff(72,plain,
defined(c),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(c)
| sum(additive_identity,c,c) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
sum(additive_identity,c,c),
inference(unit_resolution,[status(thm)],[75,13,72]) ).
tff(77,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
tff(79,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,X) )
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[82,13,79]) ).
tff(84,plain,
( sum(additive_identity,c,additive_identity)
<=> sum(additive_identity,c,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).
tff(86,plain,
sum(additive_identity,c,additive_identity),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sum(X,V,W)
| ~ sum(X,Y,U) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) ) )),
rewrite(
( ( ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) ) )),
rewrite(
( ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
( ( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
tff(93,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(additive_identity,additive_identity,c) )
<=> ( ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(additive_identity,additive_identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(additive_identity,additive_identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(additive_identity,additive_identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c)
| sum(additive_identity,additive_identity,c) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
sum(additive_identity,additive_identity,c),
inference(unit_resolution,[status(thm)],[102,96,86,83,76]) ).
tff(104,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,c)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,c)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,c)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,additive_identity,c)
| ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity)
| sum(additive_inverse(multiplicative_identity),multiplicative_identity,c) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,c),
inference(unit_resolution,[status(thm)],[106,96,45,103,31]) ).
tff(108,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,c)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,c)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,c)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,c)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
sum(multiplicative_identity,additive_inverse(multiplicative_identity),c),
inference(unit_resolution,[status(thm)],[110,27,107]) ).
tff(112,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,c,additive_identity)
| sum(c,additive_identity,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,c,additive_identity)
| sum(c,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,c,additive_identity)
| sum(c,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(additive_identity,c,additive_identity)
| sum(c,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
sum(c,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[114,27,86]) ).
tff(116,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,multiplicative_identity,multiplicative_identity) )
<=> ( ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(c,multiplicative_identity,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
sum(c,multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[121,96,115,17]) ).
tff(123,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(c,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,c,multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(c,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,c,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(c,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,c,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(c,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,c,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
sum(multiplicative_identity,c,multiplicative_identity),
inference(unit_resolution,[status(thm)],[125,27,122]) ).
tff(127,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
tff(129,plain,
defined(b),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
^ [X: $i] :
rewrite(
( ( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(134,plain,
( ! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,axiom,
! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
tff(136,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[138,131]) ).
tff(140,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(b)
| product(multiplicative_identity,b,b) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(b)
| product(multiplicative_identity,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(b)
| product(multiplicative_identity,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(b)
| product(multiplicative_identity,b,b) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
product(multiplicative_identity,b,b),
inference(unit_resolution,[status(thm)],[142,139,129]) ).
tff(144,plain,
( ~ sum(additive_identity,a,additive_identity)
<=> ~ sum(additive_identity,a,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
tff(146,plain,
~ sum(additive_identity,a,additive_identity),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
tff(149,plain,
defined(a),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,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)],[153]) ).
tff(155,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(156,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[156,152]) ).
tff(158,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[158,151]) ).
tff(160,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(162,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_resolution,[status(thm)],[162,159,149,146]) ).
tff(164,plain,
( product(a,b,c)
<=> product(a,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
tff(166,plain,
product(a,b,c),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,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(168,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)],[167]) ).
tff(169,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(170,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(171,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)],[170]) ).
tff(172,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(173,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)],[172,171]) ).
tff(174,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)],[173,169]) ).
tff(175,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)],[174]) ).
tff(176,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)],[175,168]) ).
tff(177,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(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) )
<=> ( ~ ! [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(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ~ product(multiplicative_identity,b,b)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiplicative_inverse(a),c,b) )
<=> ( ~ product(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,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,b,b)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiplicative_inverse(a),c,b) )
<=> ( ~ ! [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(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,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,b,b)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiplicative_inverse(a),c,b) )
<=> ( ~ ! [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(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) ) ),
inference(transitivity,[status(thm)],[179,177]) ).
tff(181,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,b,b)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiplicative_inverse(a),c,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,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(a,b,c)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),c,b) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
product(multiplicative_inverse(a),c,b),
inference(unit_resolution,[status(thm)],[182,176,166,163,143]) ).
tff(184,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(185,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)],[184]) ).
tff(186,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(187,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(188,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)],[187]) ).
tff(189,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(190,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[192,185]) ).
tff(194,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),c,b)
| product(c,multiplicative_inverse(a),b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),c,b)
| product(c,multiplicative_inverse(a),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),c,b)
| product(c,multiplicative_inverse(a),b) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),c,b)
| product(c,multiplicative_inverse(a),b) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
product(c,multiplicative_inverse(a),b),
inference(unit_resolution,[status(thm)],[196,193,183]) ).
tff(198,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(199,plain,
( ( ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,c)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,c,c) )
<=> ( sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,c)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,c,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) ) ),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,c)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,c,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) ) ),
inference(transitivity,[status(thm)],[200,198]) ).
tff(202,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| ~ sum(additive_identity,c,c)
| ~ sum(additive_identity,c,c)
| ~ sum(c,additive_identity,additive_identity)
| sum(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) )
| sum(c,c,c)
| ~ sum(c,additive_identity,additive_identity)
| ~ sum(additive_identity,c,c) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
sum(c,c,c),
inference(unit_resolution,[status(thm)],[203,96,115,76]) ).
tff(205,plain,
^ [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
refl(
( ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
inference(bind,[status(th)],]) ).
tff(206,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(208,plain,
^ [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sum(C,D,B)
| ~ sum(X,Y,A) )
<=> ( ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B) )
<=> ( ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(A,Z,B) ) )),
rewrite(
( ( ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(A,Z,B) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C) )
<=> ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(X,Z,C) ) )),
rewrite(
( ( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(X,Z,C) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(Y,Z,D) ) )),
rewrite(
( ( ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B)
| ~ product(Y,Z,D) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
( ( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) )),
inference(bind,[status(th)],]) ).
tff(209,plain,
( ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) )
<=> ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,axiom,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
tff(211,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[211,207]) ).
tff(213,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(skolemize,[status(sab)],[212]) ).
tff(214,plain,
! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
inference(modus_ponens,[status(thm)],[213,206]) ).
tff(215,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(216,plain,
( ( ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ sum(c,c,c)
| sum(b,b,b) )
<=> ( sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ sum(c,c,c)
| sum(b,b,b) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) ) ),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ sum(c,c,c)
| sum(b,b,b) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) ) ),
inference(transitivity,[status(thm)],[217,215]) ).
tff(219,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ product(c,multiplicative_inverse(a),b)
| ~ sum(c,c,c)
| sum(b,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(b,b,b)
| ~ sum(c,c,c)
| ~ product(c,multiplicative_inverse(a),b) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
sum(b,b,b),
inference(unit_resolution,[status(thm)],[220,214,204,197]) ).
tff(222,plain,
( ~ sum(additive_identity,b,additive_identity)
<=> ~ sum(additive_identity,b,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(223,axiom,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
tff(224,plain,
~ sum(additive_identity,b,additive_identity),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,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(226,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(227,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)],[226,225]) ).
tff(228,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(unit_resolution,[status(thm)],[227,159,129,224]) ).
tff(229,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(230,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(231,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)],[230,229]) ).
tff(232,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(unit_resolution,[status(thm)],[231,193,228]) ).
tff(233,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
( ( ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) )
<=> ( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(235,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) ) ),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) )
<=> ( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) ) ),
inference(transitivity,[status(thm)],[235,233]) ).
tff(237,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
( ~ ! [B: $i,D: $i,Z: $i,Y: $i,A: $i,X: $i,C: $i] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) )
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ sum(b,b,b) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(b,b,b) ),
inference(unit_resolution,[status(thm)],[238,214,232]) ).
tff(240,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(unit_resolution,[status(thm)],[239,221]) ).
tff(241,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(242,plain,
( ( sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity) )
<=> ( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ) ),
inference(transitivity,[status(thm)],[243,241]) ).
tff(245,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(246,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,c,multiplicative_identity)
| sum(multiplicative_identity,additive_inverse(multiplicative_identity),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_inverse(multiplicative_identity),c) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
$false,
inference(unit_resolution,[status(thm)],[246,58,240,126,111,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD041-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 02:57:34 EDT 2022
% 0.13/0.33 % 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.
% 0.53/0.63 % SZS status Unsatisfiable
% 0.53/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------