TSTP Solution File: SWC082-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC082-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 11:55:07 EDT 2022
% Result : Unsatisfiable 0.17s 0.41s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 69 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 274 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 392 ( 195 ~; 157 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 18 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( $false
| segmentP(sk3,sk5) )
<=> segmentP(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(6,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk3,sk5) )
<=> ( $false
| segmentP(sk3,sk5) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk3,sk5) )
<=> segmentP(sk3,sk5) ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk3,sk5) )
<=> ( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( segmentP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(16,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
segmentP(sk3,sk5),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
( ( $false
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk4,sk5) )
<=> ( $false
| segmentP(sk4,sk5) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(21,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(transitivity,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ neq(sk4,nil)
| segmentP(sk4,sk5) )
<=> ( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( segmentP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
( segmentP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(25,plain,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
segmentP(sk4,sk5),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
( ( $false
| neq(sk5,nil) )
<=> neq(sk5,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( $false
| neq(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(30,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> neq(sk5,nil) ),
inference(transitivity,[status(thm)],[29,28]) ).
tff(31,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(34,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
neq(sk5,nil),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
( ( ssList(sk5)
| $false )
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(39,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ssList(sk5) ),
inference(transitivity,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(42,plain,
( ssList(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
^ [A: $i] :
refl(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ~ segmentP(sk2,A)
<=> ~ segmentP(sk4,A) )),
rewrite(
( ~ segmentP(sk1,A)
<=> ~ segmentP(sk3,A) )),
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ segmentP(sk3,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ segmentP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(52,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(modus_ponens,[status(thm)],[53,47]) ).
tff(55,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk4,sk5)
| ~ segmentP(sk3,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk4,sk5)
| ~ segmentP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk4,sk5)
| ~ segmentP(sk3,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk4,sk5)
| ~ segmentP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,56,43,36,27,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWC082-1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Sep 3 21:17:20 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.17/0.41 % SZS status Unsatisfiable
% 0.17/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------