TSTP Solution File: KRS169+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 17:45:03 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 32 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 123 ( 37 ~; 3 |; 50 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 40 ( 38 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(rhasHead_type,type,
rhasHead: ( $i * $i ) > $o ).
tff(iY_type,type,
iY: $i ).
tff(iX_type,type,
iX: $i ).
tff(rhasLeader_type,type,
rhasLeader: ( $i * $i ) > $o ).
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,
( ~ rhasHead(iX,iY)
<=> ~ rhasHead(iX,iY) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) )
<=> ~ rhasHead(iX,iY) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
tff(7,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
~ rhasHead(iX,iY),
inference(modus_ponens,[status(thm)],[8,2]) ).
tff(10,plain,
~ rhasHead(iX,iY),
inference(modus_ponens,[status(thm)],[9,1]) ).
tff(11,plain,
( rhasLeader(iX,iY)
<=> rhasLeader(iX,iY) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
rhasLeader(iX,iY),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(13,plain,
rhasLeader(iX,iY),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ ( rhasLeader(iX,iY)
<=> rhasHead(iX,iY) )
| ~ rhasLeader(iX,iY)
| rhasHead(iX,iY) ),
inference(tautology,[status(thm)],]) ).
tff(15,plain,
~ ( rhasLeader(iX,iY)
<=> rhasHead(iX,iY) ),
inference(unit_resolution,[status(thm)],[14,13,10]) ).
tff(16,plain,
^ [X: $i,Y: $i] :
refl(
( ( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
<=> ( rhasLeader(X,Y)
<=> rhasHead(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
<=> ! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
<=> ! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(20,plain,
! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
| ( rhasLeader(iX,iY)
<=> rhasHead(iX,iY) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,22,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:43:35 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------