TSTP Solution File: SWC042-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC042-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 11:54:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 45 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 259 ( 113 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 381 ( 184 ~; 165 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 44 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(1,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(3,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( nil != sk1 )
<=> ( app(sk3,sk5) != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(7,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
app(sk3,sk5) != sk3,
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(12,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( nil = U )
<=> ( app(sk3,sk5) = U ) )),
rewrite(
( ( app(U,V) != nil )
<=> ( app(U,V) != app(sk3,sk5) ) )),
( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( app(sk3,sk5) = U )
| ~ ssList(V)
| ( app(U,V) != app(sk3,sk5) ) ) )),
rewrite(
( ( ~ ssList(U)
| ( app(sk3,sk5) = U )
| ~ ssList(V)
| ( app(U,V) != app(sk3,sk5) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ) )),
( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| $false )
<=> ( ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( app(sk3,sk5) = app(sk3,sk5) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( app(sk3,sk5) != app(sk3,sk5) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( app(sk3,sk5) != app(sk3,sk5) )
<=> $false ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| ( app(sk3,sk5) != app(sk3,sk5) ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| $false ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| ( app(sk3,sk5) != app(sk3,sk5) ) )
<=> ( ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(transitivity,[status(thm)],[33,28]) ).
tff(35,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| ( app(sk3,sk5) != app(sk3,sk5) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| ( app(sk3,sk5) != app(sk3,sk5) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(transitivity,[status(thm)],[35,27]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,sk5) = sk3 )
| ( app(sk3,sk5) != app(sk3,sk5) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(sk3,sk5) = U )
| ( app(U,V) != app(sk3,sk5) ) )
| ( app(sk3,sk5) = sk3 )
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,26,13,8,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC042-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 21:16:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------