TSTP Solution File: SWV065+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV065+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Thu Sep 29 15:09:50 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 37 ( 8 unt; 11 typ; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 86 ( 20 ~; 5 |; 36 &)
% ( 23 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n5_type,type,
n5: $i ).
tff(pv53_type,type,
pv53: $i ).
tff(n135300_type,type,
n135300: $i ).
tff(pv10_type,type,
pv10: $i ).
tff(1,plain,
( ~ leq(n0,n0)
<=> ~ leq(succ(tptp_minus_1),succ(tptp_minus_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ leq(n0,n0)
<=> ~ leq(n0,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
<=> ~ leq(n0,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) )
<=> ~ ( ~ ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0006) ).
tff(6,plain,
~ ( ~ ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
~ leq(n0,n0),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
~ leq(n0,n0),
inference(modus_ponens,[status(thm)],[8,2]) ).
tff(10,plain,
~ leq(succ(tptp_minus_1),succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[9,1]) ).
tff(11,plain,
( gt(n1,n0)
<=> gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( gt(n1,n0)
<=> gt(n1,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
tff(14,plain,
gt(n1,n0),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ~ ( leq(succ(tptp_minus_1),succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) )
| leq(succ(tptp_minus_1),succ(tptp_minus_1))
| ~ gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) ),
inference(tautology,[status(thm)],]) ).
tff(17,plain,
~ ( leq(succ(tptp_minus_1),succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) ),
inference(unit_resolution,[status(thm)],[16,15,10]) ).
tff(18,plain,
^ [X: $i,Y: $i] :
refl(
( ( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ( leq(X,Y)
<=> gt(succ(Y),X) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
tff(22,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
| ( leq(succ(tptp_minus_1),succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV065+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 01:37:57 EDT 2022
% 0.12/0.34 % 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------