TSTP Solution File: BOO013-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Tue Sep 6 17:18:43 EDT 2022
% Result : Unsatisfiable 2.81s 2.00s
% Output : Proof 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 53
% Syntax : Number of formulae : 103 ( 34 unt; 8 typ; 0 def)
% Number of atoms : 540 ( 37 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 819 ( 393 ~; 381 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 3 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 381 ( 353 !; 0 ?; 381 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(z_type,type,
z: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(x_type,type,
x: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
<=> ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
tff(5,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(z,y,multiply(z,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(z,y,multiply(z,y)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,y,multiply(z,y))
| product(y,z,multiply(z,y)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,y,multiply(z,y))
| product(y,z,multiply(z,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,y,multiply(z,y))
| product(y,z,multiply(z,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,y,multiply(z,y))
| product(y,z,multiply(z,y)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
product(y,z,multiply(z,y)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [X: $i] :
refl(
( product(X,multiplicative_identity,X)
<=> product(X,multiplicative_identity,X) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : product(X,multiplicative_identity,X)
<=> ! [X: $i] : product(X,multiplicative_identity,X) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : product(X,multiplicative_identity,X)
<=> ! [X: $i] : product(X,multiplicative_identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
tff(25,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : product(X,multiplicative_identity,X),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : product(X,multiplicative_identity,X)
| product(z,multiplicative_identity,z) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
product(z,multiplicative_identity,z),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,multiplicative_identity,z)
| product(multiplicative_identity,z,z) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,multiplicative_identity,z)
| product(multiplicative_identity,z,z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,multiplicative_identity,z)
| product(multiplicative_identity,z,z) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(z,multiplicative_identity,z)
| product(multiplicative_identity,z,z) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
product(multiplicative_identity,z,z),
inference(unit_resolution,[status(thm)],[32,16,29]) ).
tff(34,plain,
( product(x,z,additive_identity)
<=> product(x,z,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
tff(36,plain,
product(x,z,additive_identity),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( sum(x,y,multiplicative_identity)
<=> sum(x,y,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
tff(39,plain,
sum(x,y,multiplicative_identity),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ product(V3,X,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| ~ product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| sum(V1,V2,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
( ( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity3) ).
tff(46,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( sum(additive_identity,multiply(z,y),z)
| ~ sum(x,y,multiplicative_identity)
| ~ product(multiplicative_identity,z,z)
| ~ product(y,z,multiply(z,y))
| ~ product(x,z,additive_identity) )
<=> ( ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),z)
| ~ sum(x,y,multiplicative_identity)
| ~ product(multiplicative_identity,z,z)
| ~ product(y,z,multiply(z,y))
| ~ product(x,z,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),z)
| ~ sum(x,y,multiplicative_identity)
| ~ product(multiplicative_identity,z,z)
| ~ product(y,z,multiply(z,y))
| ~ product(x,z,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),z)
| ~ sum(x,y,multiplicative_identity)
| ~ product(multiplicative_identity,z,z)
| ~ product(y,z,multiply(z,y))
| ~ product(x,z,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,y,multiplicative_identity)
| ~ product(x,z,additive_identity)
| ~ product(multiplicative_identity,z,z)
| sum(additive_identity,multiply(z,y),z)
| ~ product(y,z,multiply(z,y)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
sum(additive_identity,multiply(z,y),z),
inference(unit_resolution,[status(thm)],[55,49,39,36,33,20]) ).
tff(57,plain,
( ~ ! [X: $i] : product(X,multiplicative_identity,X)
| product(y,multiplicative_identity,y) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
product(y,multiplicative_identity,y),
inference(unit_resolution,[status(thm)],[57,27]) ).
tff(59,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(y,multiplicative_identity,y)
| product(multiplicative_identity,y,y) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(y,multiplicative_identity,y)
| product(multiplicative_identity,y,y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(y,multiplicative_identity,y)
| product(multiplicative_identity,y,y) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| product(Y,X,Z) )
| ~ product(y,multiplicative_identity,y)
| product(multiplicative_identity,y,y) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
product(multiplicative_identity,y,y),
inference(unit_resolution,[status(thm)],[61,16,58]) ).
tff(63,plain,
( product(x,y,additive_identity)
<=> product(x,y,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
tff(65,plain,
product(x,y,additive_identity),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( sum(x,z,multiplicative_identity)
<=> sum(x,z,multiplicative_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
tff(68,plain,
sum(x,z,multiplicative_identity),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( sum(additive_identity,multiply(z,y),y)
| ~ sum(x,z,multiplicative_identity)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y))
| ~ product(x,y,additive_identity) )
<=> ( ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),y)
| ~ sum(x,z,multiplicative_identity)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y))
| ~ product(x,y,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),y)
| ~ sum(x,z,multiplicative_identity)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y))
| ~ product(x,y,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| sum(additive_identity,multiply(z,y),y)
| ~ sum(x,z,multiplicative_identity)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y))
| ~ product(x,y,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) )
| ~ sum(x,z,multiplicative_identity)
| ~ product(x,y,additive_identity)
| sum(additive_identity,multiply(z,y),y)
| ~ product(multiplicative_identity,y,y)
| ~ product(z,y,multiply(z,y)) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
sum(additive_identity,multiply(z,y),y),
inference(unit_resolution,[status(thm)],[74,49,68,65,62,9]) ).
tff(76,plain,
( ( y != z )
<=> ( y != z ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
tff(78,plain,
y != z,
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
<=> ( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) )
<=> ( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
tff(85,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ( y = z )
| ~ sum(additive_identity,multiply(z,y),z)
| ~ sum(additive_identity,multiply(z,y),y) )
<=> ( ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),z)
| ~ sum(additive_identity,multiply(z,y),y) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),z)
| ~ sum(additive_identity,multiply(z,y),y) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),z)
| ~ sum(additive_identity,multiply(z,y),y) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) )
| ( y = z )
| ~ sum(additive_identity,multiply(z,y),y)
| ~ sum(additive_identity,multiply(z,y),z) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
$false,
inference(unit_resolution,[status(thm)],[94,88,78,75,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Aug 30 03:18:15 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 2.81/2.00 % SZS status Unsatisfiable
% 2.81/2.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------