TSTP Solution File: KRS012-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS012-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 17:44:22 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 66 ( 14 unt; 7 typ; 0 def)
% Number of atoms : 316 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 450 ( 205 ~; 217 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 6 >; 1 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 102 ( 92 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: $i > $o ).
tff(u1r1_type,type,
u1r1: $i > $i ).
tff(exists_type,type,
exists: $i ).
tff(r_type,type,
r: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i > $o ).
tff(e_type,type,
e: $i > $o ).
tff(c_type,type,
c: $i > $o ).
tff(1,plain,
^ [X1: $i] :
refl(
( ( f(X1)
| r(X1,u1r1(X1)) )
<=> ( f(X1)
| r(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13) ).
tff(5,plain,
! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ f(exists)
<=> ~ f(exists) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ f(exists),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(10,plain,
~ f(exists),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
| f(exists)
| r(exists,u1r1(exists)) )
<=> ( ~ ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
| f(exists)
| r(exists,u1r1(exists)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
| f(exists)
| r(exists,u1r1(exists)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X1: $i] :
( f(X1)
| r(X1,u1r1(X1)) )
| f(exists)
| r(exists,u1r1(exists)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
r(exists,u1r1(exists)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X1: $i] :
refl(
( ( f(X1)
| ~ e(u1r1(X1)) )
<=> ( f(X1)
| ~ e(u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12) ).
tff(19,plain,
! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
| f(exists)
| ~ e(u1r1(exists)) )
<=> ( ~ ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
| f(exists)
| ~ e(u1r1(exists)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
| f(exists)
| ~ e(u1r1(exists)) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X1: $i] :
( f(X1)
| ~ e(u1r1(X1)) )
| f(exists)
| ~ e(u1r1(exists)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ e(u1r1(exists)),
inference(unit_resolution,[status(thm)],[24,10,21]) ).
tff(26,plain,
^ [X3: $i,X1: $i] :
refl(
( ( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
<=> ( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
^ [X3: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( e(X3)
| ~ c(X1)
| ~ r(X1,X3) )
<=> ( ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) )),
( ( e(X3)
| ~ c(X1)
| ~ r(X1,X3)
| ~ d(X3) )
<=> ( ~ r(X1,X3)
| ~ c(X1)
| e(X3)
| ~ d(X3) ) )),
rewrite(
( ( ~ r(X1,X3)
| ~ c(X1)
| e(X3)
| ~ d(X3) )
<=> ( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) )),
( ( e(X3)
| ~ c(X1)
| ~ r(X1,X3)
| ~ d(X3) )
<=> ( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X3: $i,X1: $i] :
( e(X3)
| ~ c(X1)
| ~ r(X1,X3)
| ~ d(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [X3: $i,X1: $i] :
( e(X3)
| ~ c(X1)
| ~ r(X1,X3)
| ~ d(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(32,plain,
! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( c(exists)
<=> c(exists) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
c(exists),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(38,plain,
c(exists),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) )
<=> ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists)
| e(u1r1(exists)) )
<=> ( e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists)
| e(u1r1(exists)) )
<=> ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists)
| e(u1r1(exists)) )
<=> ( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists)
| e(u1r1(exists)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ d(X3)
| ~ r(X1,X3)
| ~ c(X1)
| e(X3) )
| e(u1r1(exists))
| ~ d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ d(u1r1(exists)),
inference(unit_resolution,[status(thm)],[44,38,35,25,14]) ).
tff(46,plain,
^ [X2: $i,X1: $i] :
refl(
( ( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
<=> ( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
<=> ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
<=> ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [X2: $i,X1: $i] :
rewrite(
( ( d(X2)
| ~ c(X1)
| ~ r(X1,X2) )
<=> ( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X2: $i,X1: $i] :
( d(X2)
| ~ c(X1)
| ~ r(X1,X2) )
<=> ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X2: $i,X1: $i] :
( d(X2)
| ~ c(X1)
| ~ r(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(52,plain,
! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
| d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) )
<=> ( ~ ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
| d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
| d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X2: $i,X1: $i] :
( d(X2)
| ~ r(X1,X2)
| ~ c(X1) )
| d(u1r1(exists))
| ~ r(exists,u1r1(exists))
| ~ c(exists) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,38,55,14,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KRS012-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 09:37:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------