TSTP Solution File: RNG038-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG038-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 03:17:51 EDT 2022
% Result : Unsatisfiable 80.19s 51.84s
% Output : Proof 80.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 56 ( 16 unt; 6 typ; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 296 ( 139 ~; 135 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 152 ( 141 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(h_type,type,
h: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( product(additive_identity,X,additive_identity)
<=> product(additive_identity,X,additive_identity) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(additive_identity,X,additive_identity)
<=> ! [X: $i] : product(additive_identity,X,additive_identity) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(additive_identity,X,additive_identity)
<=> ! [X: $i] : product(additive_identity,X,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
tff(5,plain,
! [X: $i] : product(additive_identity,X,additive_identity),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(additive_identity,X,additive_identity),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(additive_identity,X,additive_identity),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(additive_identity,X,additive_identity)
| product(additive_identity,h(additive_identity,a),additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(additive_identity,h(additive_identity,a),additive_identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( product(a,b,additive_identity)
<=> product(a,b,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
product(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
tff(12,plain,
product(a,b,additive_identity),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
<=> ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,U)
| ~ product(X,Y,V)
| equalish(U,V) )
<=> ( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| equalish(U,V) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| equalish(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
tff(19,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ product(a,b,additive_identity)
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) )
<=> ( ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(a,b,additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
equalish(additive_identity,additive_identity),
inference(unit_resolution,[status(thm)],[28,22,12]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
<=> ( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
<=> ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
<=> ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_property) ).
tff(34,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
| ~ equalish(additive_identity,additive_identity)
| product(additive_identity,h(additive_identity,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
| ~ equalish(additive_identity,additive_identity)
| product(additive_identity,h(additive_identity,a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
| ~ equalish(additive_identity,additive_identity)
| product(additive_identity,h(additive_identity,a),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,additive_identity)
| product(X,h(X,Y),Y) )
| ~ equalish(additive_identity,additive_identity)
| product(additive_identity,h(additive_identity,a),a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
product(additive_identity,h(additive_identity,a),a),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
( ~ equalish(a,additive_identity)
<=> ~ equalish(a,additive_identity) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
tff(43,plain,
~ equalish(a,additive_identity),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a)
| equalish(a,additive_identity) )
<=> ( equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a)
| equalish(a,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a)
| equalish(a,additive_identity) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a)
| equalish(a,additive_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,V)
| ~ product(X,Y,U)
| equalish(U,V) )
| equalish(a,additive_identity)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| ~ product(additive_identity,h(additive_identity,a),a) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,22,43,40,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG038-2 : 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 : n009.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 21:52:35 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.
% 80.19/51.84 % SZS status Unsatisfiable
% 80.19/51.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------