TSTP Solution File: SWC398-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC398-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Sep 20 11:57:41 EDT 2022
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 47 ( 16 unt; 9 typ; 0 def)
% Number of atoms : 272 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 423 ( 209 ~; 188 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ~ memberP(sk2,sk6)
<=> ~ memberP(app(sk3,sk5),sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ memberP(sk2,sk6)
<=> ~ memberP(sk2,sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ memberP(sk2,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(4,plain,
~ memberP(sk2,sk6),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ memberP(app(sk3,sk5),sk6),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( memberP(sk1,sk6)
<=> memberP(sk3,sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( memberP(sk1,sk6)
<=> memberP(sk1,sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
memberP(sk1,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(9,plain,
memberP(sk1,sk6),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
memberP(sk3,sk6),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(13,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(16,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(20,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
tff(28,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) )
<=> ( memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(sk3,sk5),sk6)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,31,21,16,13,10,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC398-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Sun Sep 4 01:02:03 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------