TSTP Solution File: SWC050-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC050-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 11:54:54 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 37
% Syntax : Number of formulae : 74 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 403 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 572 ( 284 ~; 233 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 25 ( 21 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(rearsegP_type,type,
rearsegP: ( $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
| rearsegP(sk3,sk5) )
<=> rearsegP(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,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[11,2]) ).
tff(13,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) )
<=> ( $false
| rearsegP(sk3,sk5) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) )
<=> rearsegP(sk3,sk5) ),
inference(transitivity,[status(thm)],[13,1]) ).
tff(15,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( rearsegP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
( rearsegP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(18,plain,
( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
rearsegP(sk3,sk5),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
( ( $false
| rearsegP(sk4,sk5) )
<=> rearsegP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) )
<=> ( $false
| rearsegP(sk4,sk5) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(23,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) )
<=> rearsegP(sk4,sk5) ),
inference(transitivity,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( rearsegP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
( rearsegP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
tff(27,plain,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
rearsegP(sk4,sk5),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
( ( $false
| neq(sk5,nil) )
<=> neq(sk5,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( $false
| neq(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(32,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> neq(sk5,nil) ),
inference(transitivity,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
tff(36,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
neq(sk5,nil),
inference(modus_ponens,[status(thm)],[37,32]) ).
tff(39,plain,
( ( ssList(sk5)
| $false )
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(41,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ssList(sk5) ),
inference(transitivity,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(44,plain,
( ssList(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
^ [A: $i] :
refl(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ( ~ ssList(A)
| $false
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
rewrite(
( ( ~ ssList(A)
| $false
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ~ rearsegP(sk1,A)
<=> ~ rearsegP(sk3,A) )),
rewrite(
( ~ rearsegP(sk2,A)
<=> ~ rearsegP(sk4,A) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A)
| ~ neq(A,nil) ) )),
rewrite(
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(56,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ),
inference(modus_ponens,[status(thm)],[57,51]) ).
tff(59,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ),
inference(modus_ponens,[status(thm)],[58,49]) ).
tff(60,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) ),
inference(modus_ponens,[status(thm)],[60,47]) ).
tff(62,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ rearsegP(sk3,sk5)
| ~ rearsegP(sk4,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ rearsegP(sk3,sk5)
| ~ rearsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ rearsegP(sk3,sk5)
| ~ rearsegP(sk4,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk3,A)
| ~ rearsegP(sk4,A) )
| ~ ssList(sk5)
| ~ neq(sk5,nil)
| ~ rearsegP(sk3,sk5)
| ~ rearsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,61,45,38,29,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC050-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 20:59:18 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------