TSTP Solution File: KRS141+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS141+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 : Sat Sep 17 17:44:56 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 46 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 266 ( 108 ~; 75 |; 40 &)
% ( 31 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 7 >; 1 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 83 ( 79 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(rp_type,type,
rp: ( $i * $i ) > $o ).
tff(ii_type,type,
ii: $i ).
tff(cc_type,type,
cc: $i > $o ).
tff(cr_type,type,
cr: $i > $o ).
tff(io_type,type,
io: $i ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(xsd_integer_type,type,
xsd_integer: $i > $o ).
tff(xsd_string_type,type,
xsd_string: $i > $o ).
tff(cowlNothing_type,type,
cowlNothing: $i > $o ).
tff(1,plain,
( cr(ii)
<=> cr(ii) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
cr(ii),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(3,plain,
cr(ii),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [X: $i] :
rewrite(
( ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) ),
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
( ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
rewrite(
( ( rp(X,Y)
=> cc(Y) )
<=> ( cc(Y)
| ~ rp(X,Y) ) ))),
( ! [Y: $i] :
( rp(X,Y)
=> cc(Y) )
<=> ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )),
( ( cr(X)
=> ! [Y: $i] :
( rp(X,Y)
=> cc(Y) ) )
<=> ( cr(X)
=> ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) )),
rewrite(
( ( cr(X)
=> ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
<=> ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) )),
( ( cr(X)
=> ! [Y: $i] :
( rp(X,Y)
=> cc(Y) ) )
<=> ( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( cr(X)
=> ! [Y: $i] :
( rp(X,Y)
=> cc(Y) ) )
<=> ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( cr(X)
=> ! [Y: $i] :
( rp(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(13,plain,
! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
| ~ cr(ii)
| ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) ) )
<=> ( ~ ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
| ~ cr(ii)
| ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
| ~ cr(ii)
| ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ cr(X)
| ! [Y: $i] :
( cc(Y)
| ~ rp(X,Y) ) )
| ~ cr(ii)
| ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( ~ cc(io)
<=> ~ cc(io) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) )
<=> ~ cc(io) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
tff(27,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cc(io)
& cowlThing(io) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
~ cc(io),
inference(modus_ponens,[status(thm)],[28,22]) ).
tff(30,plain,
~ cc(io),
inference(modus_ponens,[status(thm)],[29,21]) ).
tff(31,plain,
( rp(ii,io)
<=> rp(ii,io) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
rp(ii,io),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(33,plain,
rp(ii,io),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ( ~ ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) )
| cc(io)
| ~ rp(ii,io) )
<=> ( ~ ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) )
| cc(io)
| ~ rp(ii,io) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) )
| cc(io)
| ~ rp(ii,io) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [Y: $i] :
( cc(Y)
| ~ rp(ii,Y) )
| cc(io)
| ~ rp(ii,io) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,33,30,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS141+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 09:49:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------