TSTP Solution File: FLD031-5 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD031-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 14:55:45 EDT 2022
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 47
% Syntax : Number of formulae : 95 ( 23 unt; 7 typ; 0 def)
% Number of atoms : 486 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 637 ( 267 ~; 321 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 232 ( 208 !; 0 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
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(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
( ~ sum(additive_identity,a,additive_identity)
<=> ~ sum(additive_identity,a,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
tff(3,plain,
~ sum(additive_identity,a,additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
tff(6,plain,
defined(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10]) ).
tff(12,axiom,
! [X: $i] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
tff(13,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ defined(a)
| sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) )
<=> ( sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| defined(multiplicative_inverse(X)) )
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
defined(multiplicative_inverse(a)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [X: $i] :
refl(
( ( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X: $i] :
rewrite(
( ( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| product(multiplicative_identity,X,X) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X: $i] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
tff(30,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| product(multiplicative_identity,X,X) )
| ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,axiom,
! [X: $i] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
tff(44,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,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(49,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(50,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)],[49,48]) ).
tff(51,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_resolution,[status(thm)],[50,47,6,3]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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(56,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)],[55]) ).
tff(57,axiom,
! [Z: $i,Y: $i,X: $i] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(unit_resolution,[status(thm)],[64,61,51]) ).
tff(66,plain,
( ~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a))
<=> ~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
tff(68,plain,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( product(multiplicative_identity,a,multiplicative_identity)
<=> product(multiplicative_identity,a,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
tff(71,plain,
product(multiplicative_identity,a,multiplicative_identity),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,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(73,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)],[72]) ).
tff(74,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(75,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(76,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)],[75]) ).
tff(77,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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
tff(78,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)],[77,76]) ).
tff(79,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)],[78,74]) ).
tff(80,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)],[79]) ).
tff(81,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)],[80,73]) ).
tff(82,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,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(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,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,a,multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)) )
<=> ( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,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,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,a,multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(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,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,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,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,a,multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(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,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,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,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,a,multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,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,multiplicative_identity,multiplicative_inverse(a))
| ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,81,71,68,65,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD031-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 03:03:34 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------