TSTP Solution File: SWC019-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC019-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 11:54:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 71 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 349 ( 58 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 515 ( 256 ~; 221 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(4,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| frontsegP(U,U) )
<=> ( ~ ssList(U)
| frontsegP(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause61) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
frontsegP(sk3,sk3),
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
^ [A: $i] :
refl(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ~ frontsegP(sk2,A)
<=> ~ frontsegP(sk3,A) )),
rewrite(
( ~ frontsegP(sk1,A)
<=> ~ frontsegP(sk3,A) )),
( ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ frontsegP(sk3,A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ frontsegP(sk3,A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) )),
( ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk2,A) )
<=> ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk2,A)
| ~ frontsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk2,A)
| ~ frontsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk2,A)
| ~ frontsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk2,A)
| ~ frontsegP(sk1,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(25,plain,
! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] :
( ~ ssList(A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ frontsegP(sk1,A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ),
inference(modus_ponens,[status(thm)],[26,20]) ).
tff(28,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ frontsegP(sk3,sk3) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ frontsegP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ frontsegP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ frontsegP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ frontsegP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ neq(sk3,nil)
| ~ frontsegP(sk3,sk3) ),
inference(unit_resolution,[status(thm)],[32,5,29]) ).
tff(34,plain,
~ neq(sk3,nil),
inference(unit_resolution,[status(thm)],[33,16]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,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(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(47,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,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(49,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(50,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)],[49,48]) ).
tff(51,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[50,47,44,5,34]) ).
tff(52,plain,
nil = sk3,
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ( ( nil != sk3 )
| ( nil != sk3 ) )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( nil != sk2 )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ( nil != sk1 )
| ( nil != sk2 ) )
<=> ( ( nil != sk3 )
| ( nil != sk3 ) ) ),
inference(monotonicity,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ( nil != sk1 )
| ( nil != sk2 ) )
<=> ( nil != sk3 ) ),
inference(transitivity,[status(thm)],[56,53]) ).
tff(58,plain,
( ( ( nil != sk1 )
| ( nil != sk2 ) )
<=> ( ( nil != sk1 )
| ( nil != sk2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ( nil != sk2 )
| ( nil != sk1 ) )
<=> ( ( nil != sk1 )
| ( nil != sk2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(61,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[62,57]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC019-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.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 : Sat Sep 3 20:44:24 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.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------