TSTP Solution File: SWC213-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC213-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 11:56:11 EDT 2022
% Result : Unsatisfiable 0.16s 0.42s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 76 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 339 ( 94 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 502 ( 245 ~; 222 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 68 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(1,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(4,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(9,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(23,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[26,23,20,10,5]) ).
tff(28,plain,
nil = sk3,
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ( app(app(sk5,sk3),sk6) = nil )
<=> ( nil = app(app(sk5,sk3),sk6) ) ),
inference(commutativity,[status(thm)],]) ).
tff(30,plain,
( ( app(app(sk5,sk3),sk6) != nil )
<=> ( nil != app(app(sk5,sk3),sk6) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( neq(sk2,nil)
<=> neq(app(app(sk5,sk3),sk6),nil) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(34,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
neq(app(app(sk5,sk3),sk6),nil),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
( ssList(sk2)
<=> ssList(app(app(sk5,sk3),sk6)) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(39,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
ssList(app(app(sk5,sk3),sk6)),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ssList(app(app(sk5,sk3),sk6))
| ~ ssList(nil)
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) )
<=> ( ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(app(app(sk5,sk3),sk6))
| ~ ssList(nil)
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(app(app(sk5,sk3),sk6))
| ~ ssList(nil)
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(app(app(sk5,sk3),sk6))
| ~ ssList(nil)
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk3),sk6))
| ( app(app(sk5,sk3),sk6) != nil )
| ~ neq(app(app(sk5,sk3),sk6),nil) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
app(app(sk5,sk3),sk6) != nil,
inference(unit_resolution,[status(thm)],[56,23,50,40,35]) ).
tff(58,plain,
nil != app(app(sk5,sk3),sk6),
inference(modus_ponens,[status(thm)],[57,30]) ).
tff(59,plain,
( ( ( nil != sk3 )
| ( nil = sk4 ) )
<=> ( ( nil != sk3 )
| ( nil = app(app(sk5,sk3),sk6) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ( nil != sk3 )
| ( nil = sk4 ) )
<=> ( ( nil != sk3 )
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ( nil = sk4 )
| ( nil != sk3 ) )
<=> ( ( nil != sk3 )
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
( ( nil = sk4 )
| ( nil != sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(63,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
( ( nil != sk3 )
| ( nil = app(app(sk5,sk3),sk6) ) ),
inference(modus_ponens,[status(thm)],[64,59]) ).
tff(66,plain,
$false,
inference(unit_resolution,[status(thm)],[65,58,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWC213-1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Sep 3 22:51:25 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.16/0.42 % SZS status Unsatisfiable
% 0.16/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------