TSTP Solution File: SWC406-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC406-1 : 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 11:57:45 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 37 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 169 ( 81 ~; 74 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ~ memberP(sk2,sk6)
<=> ~ memberP(sk4,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/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(4,plain,
~ memberP(sk2,sk6),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ memberP(sk4,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/sandbox2/benchmark/theBenchmark.p',co1_14) ).
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/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(13,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
^ [A: $i] :
rewrite(
( ( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(20,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ memberP(sk3,sk6) )
<=> ( memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ memberP(sk3,sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ memberP(sk3,sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| memberP(sk4,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk3,sk6) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,23,13,10,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC406-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 00:44:18 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------