TSTP Solution File: SWC130-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC130-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 11:55:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 45 ( 18 unt; 6 typ; 0 def)
% Number of atoms : 155 ( 29 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 184 ( 76 ~; 89 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ~ neq(sk4,nil)
<=> ~ neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ neq(sk4,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(3,plain,
~ neq(sk4,nil),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(7,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(15,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(21,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
sk4 = nil,
inference(unit_resolution,[status(thm)],[24,21,18,8,3]) ).
tff(26,plain,
nil = sk4,
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( cyclefreeP(nil)
<=> cyclefreeP(sk4) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( cyclefreeP(sk4)
<=> cyclefreeP(nil) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ cyclefreeP(sk4)
<=> ~ cyclefreeP(nil) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ~ cyclefreeP(sk2)
<=> ~ cyclefreeP(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ cyclefreeP(sk2)
<=> ~ cyclefreeP(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
~ cyclefreeP(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(33,plain,
~ cyclefreeP(sk2),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ cyclefreeP(sk4),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
~ cyclefreeP(nil),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
( cyclefreeP(nil)
<=> cyclefreeP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause7) ).
tff(38,plain,
cyclefreeP(nil),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC130-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.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 : Sat Sep 3 21:47:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------