TSTP Solution File: SWC328-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC328-1 : 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 11:57:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 47 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 121 ( 60 ~; 41 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(equalelemsP_type,type,
equalelemsP: $i > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( $false
| ~ segmentP(sk4,sk3) )
<=> ~ segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( equalelemsP(nil)
<=> equalelemsP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( equalelemsP(nil)
<=> equalelemsP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause1) ).
tff(6,plain,
equalelemsP(nil),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
equalelemsP(sk3),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
( equalelemsP(sk3)
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ~ equalelemsP(sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ equalelemsP(sk3)
<=> $false ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ equalelemsP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ( $false
| ~ segmentP(sk4,sk3) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( ~ equalelemsP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ~ segmentP(sk4,sk3) ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ equalelemsP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) )
<=> ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(17,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ~ equalelemsP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[18,13]) ).
tff(20,plain,
~ segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(24,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,sk3) )
<=> ( ~ ssList(U)
| segmentP(U,sk3) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| segmentP(U,nil) )
<=> ( ~ ssList(U)
| segmentP(U,sk3) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) )
| ~ ssList(sk4)
| segmentP(sk4,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) )
| ~ ssList(sk4)
| segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) )
| ~ ssList(sk4)
| segmentP(sk4,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk3) )
| ~ ssList(sk4)
| segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35,25,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC328-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % 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 00:01:48 EDT 2022
% 0.13/0.34 % 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
%------------------------------------------------------------------------------