TSTP Solution File: SWC385-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC385-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 11:57:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 42 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 34 ~; 19 |; 0 &)
% ( 22 <=>; 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 : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 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(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $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,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(5,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
( segmentP(sk4,sk3)
<=> $true ),
inference(iff_true,[status(thm)],[5]) ).
tff(7,plain,
( ~ segmentP(sk4,sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ segmentP(sk4,sk3)
<=> $false ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( ( singletonP(sk3)
| $false )
<=> singletonP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(13,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[16,2]) ).
tff(18,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( singletonP(sk3)
| $false ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> singletonP(sk3) ),
inference(transitivity,[status(thm)],[18,9]) ).
tff(20,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( singletonP(sk3)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(22,plain,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
singletonP(sk3),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
( singletonP(sk3)
<=> $true ),
inference(iff_true,[status(thm)],[23]) ).
tff(25,plain,
( ~ singletonP(sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ singletonP(sk3)
<=> $false ),
inference(transitivity,[status(thm)],[25,2]) ).
tff(27,plain,
( ( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[26,8]) ).
tff(28,plain,
( ( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) )
<=> $false ),
inference(transitivity,[status(thm)],[27,1]) ).
tff(29,plain,
( ( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(32,plain,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
$false,
inference(modus_ponens,[status(thm)],[33,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC385-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 00:42:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------