TSTP Solution File: SWC103-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC103-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 11:55:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 47 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 46 ~; 30 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $false
| neq(sk3,nil) )
<=> neq(sk3,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[8]) ).
tff(10,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[10,2]) ).
tff(12,plain,
( ( ~ neq(sk4,nil)
| neq(sk3,nil) )
<=> ( $false
| neq(sk3,nil) ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( ~ neq(sk4,nil)
| neq(sk3,nil) )
<=> neq(sk3,nil) ),
inference(transitivity,[status(thm)],[12,3]) ).
tff(14,plain,
( ( ~ neq(sk4,nil)
| neq(sk3,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(16,plain,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
neq(sk3,nil),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( neq(sk3,nil)
<=> $true ),
inference(iff_true,[status(thm)],[17]) ).
tff(19,plain,
( ~ neq(sk3,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ neq(sk3,nil)
<=> $false ),
inference(transitivity,[status(thm)],[19,2]) ).
tff(21,plain,
( ( $false
| frontsegP(sk4,sk3) )
<=> frontsegP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) )
<=> ( $false
| frontsegP(sk4,sk3) ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(23,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) )
<=> frontsegP(sk4,sk3) ),
inference(transitivity,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(26,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
frontsegP(sk4,sk3),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
( frontsegP(sk4,sk3)
<=> $true ),
inference(iff_true,[status(thm)],[27]) ).
tff(29,plain,
( ~ frontsegP(sk4,sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ~ frontsegP(sk4,sk3)
<=> $false ),
inference(transitivity,[status(thm)],[29,2]) ).
tff(31,plain,
( ( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil) )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil) )
<=> $false ),
inference(transitivity,[status(thm)],[31,1]) ).
tff(33,plain,
( ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) )
<=> ( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) )
<=> ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) )
<=> ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(37,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[38,33]) ).
tff(40,plain,
$false,
inference(modus_ponens,[status(thm)],[39,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC103-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 21:29:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------