TSTP Solution File: SWV135+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 15:10:06 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 60 ( 15 unt; 11 typ; 0 def)
% Number of atoms : 229 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 266 ( 102 ~; 79 |; 51 &)
% ( 26 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 94 ( 84 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(n2_type,type,
n2: $i ).
tff(pv1325_type,type,
pv1325: $i ).
tff(n3_type,type,
n3: $i ).
tff(s_worst7_type,type,
s_worst7: $i ).
tff(s_sworst7_type,type,
s_sworst7: $i ).
tff(s_best7_type,type,
s_best7: $i ).
tff(1,plain,
( gt(n2,n0)
<=> gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( gt(n2,n0)
<=> gt(n2,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
gt(n2,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
tff(4,plain,
gt(n2,n0),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ gt(Y,X)
| leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( gt(Y,X)
=> leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
tff(12,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(succ(tptp_minus_1))),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))),
inference(unit_resolution,[status(thm)],[18,15,5]) ).
tff(20,plain,
( ~ leq(n0,pv1325)
<=> ~ leq(succ(tptp_minus_1),pv1325) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ leq(n0,pv1325)
<=> ~ leq(n0,pv1325) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
=> leq(n0,pv1325) )
<=> ~ ( ~ ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
| leq(n0,pv1325) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
~ ( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
=> leq(n0,pv1325) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gauss_array_0005) ).
tff(24,plain,
~ ( ~ ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
| leq(n0,pv1325) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ leq(n0,pv1325),
inference(or_elim,[status(thm)],[24]) ).
tff(26,plain,
~ leq(n0,pv1325),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
~ leq(succ(tptp_minus_1),pv1325),
inference(modus_ponens,[status(thm)],[26,20]) ).
tff(28,plain,
( leq(n2,pv1325)
<=> leq(succ(succ(succ(tptp_minus_1))),pv1325) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( leq(n2,pv1325)
<=> leq(n2,pv1325) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) ),
inference(or_elim,[status(thm)],[24]) ).
tff(31,plain,
leq(n2,pv1325),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
leq(n2,pv1325),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
leq(succ(succ(succ(tptp_minus_1))),pv1325),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
rewrite(
( ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) ) )),
rewrite(
( ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
tff(41,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[44,34]) ).
tff(46,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),pv1325)
| ~ leq(succ(succ(succ(tptp_minus_1))),pv1325)
| ~ leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),pv1325)
| ~ leq(succ(succ(succ(tptp_minus_1))),pv1325)
| ~ leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),pv1325)
| ~ leq(succ(succ(succ(tptp_minus_1))),pv1325)
| ~ leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),pv1325)
| ~ leq(succ(succ(succ(tptp_minus_1))),pv1325)
| ~ leq(succ(tptp_minus_1),succ(succ(succ(tptp_minus_1)))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45,33,27,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 01:37:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------