TSTP Solution File: RNG001-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 03:17:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 44
% Syntax : Number of formulae : 93 ( 31 unt; 6 typ; 0 def)
% Number of atoms : 666 ( 0 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 1051 ( 511 ~; 487 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 39 ( 39 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 : 485 ( 441 !; 0 ?; 485 :)
% 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,
^ [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/RNG001-0.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(a,additive_identity,multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( sum(additive_identity,X,X)
<=> sum(additive_identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : sum(additive_identity,X,X)
<=> ! [X: $i] : sum(additive_identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
tff(14,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : sum(additive_identity,X,X),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : sum(additive_identity,X,X)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,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)],[22]) ).
tff(24,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/Axioms/RNG001-0.ax',distributivity1) ).
tff(25,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)],[24,23]) ).
tff(26,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)],[25,21]) ).
tff(27,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)],[26]) ).
tff(28,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)],[27,20]) ).
tff(29,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(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,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) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,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)) )
<=> ( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,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) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,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) )
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,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(34,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(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
( ~ ! [X: $i] : sum(additive_identity,X,X)
| sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)),
inference(unit_resolution,[status(thm)],[36,16]) ).
tff(38,plain,
( ~ product(a,additive_identity,additive_identity)
<=> ~ product(a,additive_identity,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_0_is_0) ).
tff(40,plain,
~ product(a,additive_identity,additive_identity),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,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)],[44]) ).
tff(46,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/Axioms/RNG001-0.ax',distributivity2) ).
tff(47,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)],[46,45]) ).
tff(48,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)],[47,43]) ).
tff(49,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)],[48]) ).
tff(50,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)],[49,42]) ).
tff(51,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))
| ~ 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)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,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)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,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)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,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)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,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(56,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))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[56,50,40,18,9]) ).
tff(58,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(59,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) )
<=> ! [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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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/Axioms/RNG001-0.ax',associativity_of_addition2) ).
tff(64,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| ~ sum(X,V,W) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,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)],[64,60]) ).
tff(66,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)],[65]) ).
tff(67,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)],[66,59]) ).
tff(68,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),multiply(a,additive_identity))
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,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(70,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(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ sum(additive_identity,multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[70,67,57,37,35]) ).
tff(72,plain,
^ [X: $i] :
refl(
( sum(additive_inverse(X),X,additive_identity)
<=> sum(additive_inverse(X),X,additive_identity) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] : sum(additive_inverse(X),X,additive_identity)
<=> ! [X: $i] : sum(additive_inverse(X),X,additive_identity) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i] : sum(additive_inverse(X),X,additive_identity)
<=> ! [X: $i] : sum(additive_inverse(X),X,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
tff(76,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i] : sum(additive_inverse(X),X,additive_identity),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,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(80,plain,
sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,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),multiply(a,additive_identity))
| sum(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(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,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(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
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) )
| 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(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[82]) ).
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) )
| 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(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
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) )
| 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(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),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,67,80,35,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 21:11:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------