TSTP Solution File: KRS152+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS152+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 17:44:59 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 71 ( 13 unt; 12 typ; 0 def)
% Number of atoms : 267 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 353 ( 149 ~; 50 |; 82 &)
% ( 72 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 48 ( 44 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
tff(cC12_type,type,
cC12: $i > $o ).
tff(iV21080_type,type,
iV21080: $i ).
tff(cC8_type,type,
cC8: $i > $o ).
tff(cTEST_type,type,
cTEST: $i > $o ).
tff(cC10_type,type,
cC10: $i > $o ).
tff(iV21081_type,type,
iV21081: $i ).
tff(cC4_type,type,
cC4: $i > $o ).
tff(cC2_type,type,
cC2: $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,
^ [X: $i] :
refl(
( ( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) )
<=> ( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) )
<=> ( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) )
<=> ! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(7,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] :
( cTEST(X)
<=> ( cC12(X)
& ~ cC8(X) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] :
( cTEST(X)
<=> ~ ( cC8(X)
| ~ cC12(X) ) )
| ( cTEST(iV21080)
<=> ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( cTEST(iV21080)
<=> ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( cTEST(iV21080)
<=> cTEST(iV21080) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
cTEST(iV21080),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(15,plain,
cTEST(iV21080),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( cTEST(iV21080)
<=> ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) )
| ~ cTEST(iV21080)
| ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) ),
inference(tautology,[status(thm)],]) ).
tff(17,plain,
( ~ ( cTEST(iV21080)
<=> ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) )
| ~ ( cC8(iV21080)
| ~ cC12(iV21080) ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
~ ( cC8(iV21080)
| ~ cC12(iV21080) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
^ [X: $i] :
refl(
( ( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) )
<=> ( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $i] :
rewrite(
( ( cC10(X)
<=> ( cC2(X)
& cC4(X) ) )
<=> ( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) )
<=> ! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(25,plain,
! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( cC10(X)
<=> ( cC2(X)
& cC4(X) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ~ ! [X: $i] :
( cC10(X)
<=> ~ ( ~ cC2(X)
| ~ cC4(X) ) )
| ( cC10(iV21081)
<=> ~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( cC10(iV21081)
<=> ~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) ) ),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( cC4(iV21081)
<=> cC4(iV21081) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
cC4(iV21081),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
tff(33,plain,
cC4(iV21081),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( cC2(iV21081)
<=> cC2(iV21081) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
cC2(iV21081),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
tff(36,plain,
cC2(iV21081),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) )
| ~ cC2(iV21081)
| ~ cC4(iV21081) ),
inference(tautology,[status(thm)],]) ).
tff(38,plain,
~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) ),
inference(unit_resolution,[status(thm)],[37,36,33]) ).
tff(39,plain,
( ~ ( cC10(iV21081)
<=> ~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) ) )
| cC10(iV21081)
| ~ cC2(iV21081)
| ~ cC4(iV21081) ),
inference(tautology,[status(thm)],]) ).
tff(40,plain,
( ~ ( cC10(iV21081)
<=> ~ ( ~ cC2(iV21081)
| ~ cC4(iV21081) ) )
| cC10(iV21081) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
cC10(iV21081),
inference(unit_resolution,[status(thm)],[40,30]) ).
tff(42,plain,
( ~ ~ ( ~ cC12(iV21080)
| ~ cC10(iV21081) )
<=> ( ~ cC12(iV21080)
| ~ cC10(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( cC12(iV21080)
& cC10(iV21081) )
<=> ~ ( ~ cC12(iV21080)
| ~ cC10(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ( cC12(iV21080)
& cC10(iV21081) )
<=> ~ ~ ( ~ cC12(iV21080)
| ~ cC10(iV21081) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ ( cC12(iV21080)
& cC10(iV21081) )
<=> ( ~ cC12(iV21080)
| ~ cC10(iV21081) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ( cC12(iV21080)
& cC10(iV21081) )
<=> ~ ( cC12(iV21080)
& cC10(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) )
<=> ~ ( cC12(iV21080)
& cC10(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) )
<=> ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) )
<=> ~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
tff(52,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ ( ! [X: $i] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X: $i] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& cowlThing(iV21080)
& cC12(iV21080)
& cC10(iV21081)
& cowlThing(iV21081) ),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
~ ( cC12(iV21080)
& cC10(iV21081) ),
inference(modus_ponens,[status(thm)],[53,47]) ).
tff(55,plain,
~ ( cC12(iV21080)
& cC10(iV21081) ),
inference(modus_ponens,[status(thm)],[54,46]) ).
tff(56,plain,
( ~ cC12(iV21080)
| ~ cC10(iV21081) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
~ cC12(iV21080),
inference(unit_resolution,[status(thm)],[56,41]) ).
tff(58,plain,
( cC8(iV21080)
| ~ cC12(iV21080)
| cC12(iV21080) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,57,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS152+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n005.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 : Thu Sep 1 09:38:03 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 Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------