TSTP Solution File: RNG001-5 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG001-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20 03:17:34 EDT 2022
% Result : Unsatisfiable 204.35s 130.95s
% Output : Proof 204.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 53
% Syntax : Number of formulae : 114 ( 38 unt; 6 typ; 0 def)
% Number of atoms : 755 ( 0 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 1173 ( 567 ~; 543 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 557 ( 509 !; 0 ?; 557 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( sum(X,additive_identity,X)
<=> sum(X,additive_identity,X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : sum(X,additive_identity,X)
<=> ! [X: $i] : sum(X,additive_identity,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : sum(X,additive_identity,X)
<=> ! [X: $i] : sum(X,additive_identity,X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
tff(5,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : sum(X,additive_identity,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : sum(X,additive_identity,X)
| sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [X: $i] :
refl(
( sum(additive_identity,X,X)
<=> sum(additive_identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
tff(25,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : sum(additive_identity,X,X)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
refl(
( product(X,Y,multiply(X,Y))
<=> product(X,Y,multiply(X,Y)) )),
inference(bind,[status(th)],]) ).
tff(31,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)],[30]) ).
tff(32,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(33,axiom,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
tff(34,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] : product(X,Y,multiply(X,Y)),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] : product(X,Y,multiply(X,Y))
| product(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) ) )),
rewrite(
( ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
tff(45,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[54,48,38,29]) ).
tff(56,plain,
( ~ product(a,additive_identity,additive_identity)
<=> ~ product(a,additive_identity,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
tff(58,plain,
~ product(a,additive_identity,additive_identity),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
tff(65,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) )
<=> ( product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[74,68,58,38,29]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) )
<=> ( ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,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)
| 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,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| 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(80,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| 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)],[79]) ).
tff(81,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
tff(82,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)],[81,80]) ).
tff(83,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)],[82,78]) ).
tff(84,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)],[83]) ).
tff(85,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)],[84,77]) ).
tff(86,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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity) )
<=> ( sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
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) )
| sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(monotonicity,[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) )
| sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,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(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
~ sum(additive_identity,multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[91,85,75,55,20]) ).
tff(93,plain,
^ [X: $i] :
refl(
( sum(additive_inverse(X),X,additive_identity)
<=> sum(additive_inverse(X),X,additive_identity) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [X: $i] : sum(additive_inverse(X),X,additive_identity)
<=> ! [X: $i] : sum(additive_inverse(X),X,additive_identity) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X: $i] : sum(additive_inverse(X),X,additive_identity)
<=> ! [X: $i] : sum(additive_inverse(X),X,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
tff(97,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
( ~ ! [X: $i] : sum(additive_inverse(X),X,additive_identity)
| sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[100,99]) ).
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_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_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_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) )
<=> ( ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
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,multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_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_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[103]) ).
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,multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_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_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
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,multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,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_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,85,101,55,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG001-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 21:10:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 204.35/130.95 % SZS status Unsatisfiable
% 204.35/130.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------