TSTP Solution File: RNG040-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG040-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 03:17:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 38 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 297 ( 146 ~; 134 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 2 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 119 ( 105 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(n_type,type,
n: $i ).
tff(l_type,type,
l: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(d_type,type,
d: $i ).
tff(1,plain,
( ~ sum(l,n,additive_identity)
<=> ~ sum(l,n,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(3,plain,
~ sum(l,n,additive_identity),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( product(c,a,n)
<=> product(c,a,n) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
tff(6,plain,
product(c,a,n),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( product(b,a,l)
<=> product(b,a,l) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
tff(9,plain,
product(b,a,l),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( product(d,a,additive_identity)
<=> product(d,a,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
tff(12,plain,
product(d,a,additive_identity),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( sum(b,c,d)
<=> sum(b,c,d) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
tff(15,plain,
sum(b,c,d),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,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)],[19]) ).
tff(21,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/RNG001-0.ax',distributivity3) ).
tff(22,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)],[21,20]) ).
tff(23,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)],[22,18]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,17]) ).
tff(26,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(l,n,additive_identity)
| ~ sum(b,c,d)
| ~ product(d,a,additive_identity)
| ~ product(c,a,n)
| ~ product(b,a,l) )
<=> ( ~ ! [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(l,n,additive_identity)
| ~ sum(b,c,d)
| ~ product(d,a,additive_identity)
| ~ product(c,a,n)
| ~ product(b,a,l) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,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(l,n,additive_identity)
| ~ sum(b,c,d)
| ~ product(d,a,additive_identity)
| ~ product(c,a,n)
| ~ product(b,a,l) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,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(l,n,additive_identity)
| ~ sum(b,c,d)
| ~ product(d,a,additive_identity)
| ~ product(c,a,n)
| ~ product(b,a,l) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25,15,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG040-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 22:17:24 EDT 2022
% 0.12/0.34 % 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.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------