TSTP Solution File: SWC367-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC367-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 11:57:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 52 ( 15 unt; 7 typ; 0 def)
% Number of atoms : 147 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 170 ( 76 ~; 69 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ( ( nil = sk4 )
| $false )
<=> ( nil = sk4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ rearsegP(sk2,sk1)
<=> ~ rearsegP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ rearsegP(sk2,sk1)
<=> ~ rearsegP(sk2,sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ rearsegP(sk2,sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(5,plain,
~ rearsegP(sk2,sk1),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
~ rearsegP(sk4,sk3),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
( rearsegP(sk4,sk3)
<=> $false ),
inference(iff_false,[status(thm)],[6]) ).
tff(8,plain,
( ( ( nil = sk4 )
| rearsegP(sk4,sk3) )
<=> ( ( nil = sk4 )
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( ( nil = sk4 )
| rearsegP(sk4,sk3) )
<=> ( nil = sk4 ) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( ( nil = sk4 )
| rearsegP(sk4,sk3) )
<=> ( ( nil = sk4 )
| rearsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( ( nil = sk4 )
| rearsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(12,plain,
( ( nil = sk4 )
| rearsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
nil = sk4,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
sk4 = nil,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ssList(sk4)
<=> ssList(nil) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ssList(nil)
<=> ssList(sk4) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ssList(sk3)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(21,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[22,17]) ).
tff(24,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( rearsegP(nil,sk4)
<=> rearsegP(nil,nil) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(26,plain,
( rearsegP(nil,nil)
<=> rearsegP(nil,sk4) ),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ rearsegP(nil,nil)
<=> ~ rearsegP(nil,sk4) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ rearsegP(sk4,sk3)
<=> ~ rearsegP(nil,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
~ rearsegP(nil,nil),
inference(modus_ponens,[status(thm)],[6,28]) ).
tff(30,plain,
~ rearsegP(nil,sk4),
inference(modus_ponens,[status(thm)],[29,27]) ).
tff(31,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| rearsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) )),
( ( ( nil != U )
| ~ ssList(U)
| rearsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| rearsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| rearsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause81) ).
tff(37,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
| ~ ssList(sk4)
| ( nil != sk4 )
| rearsegP(nil,sk4) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
| ~ ssList(sk4)
| ( nil != sk4 )
| rearsegP(nil,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
| ~ ssList(sk4)
| ( nil != sk4 )
| rearsegP(nil,sk4) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| rearsegP(nil,U) )
| ~ ssList(sk4)
| ( nil != sk4 )
| rearsegP(nil,sk4) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ ssList(sk4)
| rearsegP(nil,sk4) ),
inference(unit_resolution,[status(thm)],[43,40,13]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,30,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SWC367-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 : Sun Sep 4 00:39:24 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
%------------------------------------------------------------------------------