TSTP Solution File: HWV027-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV027-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Sep 17 02:10:44 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 56 ( 22 unt; 8 typ; 0 def)
% Number of atoms : 205 ( 69 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 174 ( 26 ~; 125 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 6 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 29 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
tff(level_type,type,
level: $i > $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(t_139_type,type,
t_139: $i ).
tff(int_level_type,type,
int_level: $i > $i ).
tff(p_Reset_type,type,
p_Reset: $i > $o ).
tff(p_Rd_type,type,
p_Rd: $i > $o ).
tff(p_Wr_type,type,
p_Wr: $i > $o ).
tff(1,plain,
( ( int_level(plus(t_139,n1)) = level(plus(t_139,n1)) )
<=> ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ~ p_Reset(t_139)
<=> ~ p_Reset(t_139) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ p_Reset(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(4,plain,
~ p_Reset(t_139),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ p_Rd(t_139)
<=> ~ p_Rd(t_139) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ p_Rd(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(7,plain,
~ p_Rd(t_139),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ~ p_Wr(t_139)
<=> ~ p_Wr(t_139) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ p_Wr(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(10,plain,
~ p_Wr(t_139),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [X_t_42: $i] :
refl(
( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [X_t_42: $i] :
trans(
monotonicity(
rewrite(
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| p_Rd(X_t_42) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| p_Rd(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
rewrite(
( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| p_Rd(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Wr(X_t_42)
| p_Rd(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Wr(X_t_42)
| p_Rd(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_82) ).
tff(17,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( p_Reset(t_139)
| p_Rd(t_139)
| p_Wr(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| p_Wr(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| p_Wr(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| p_Wr(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Wr(t_139)
| p_Rd(t_139)
| p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
int_level(plus(t_139,n1)) = int_level(t_139),
inference(unit_resolution,[status(thm)],[26,20,10,7,4]) ).
tff(28,plain,
int_level(t_139) = int_level(plus(t_139,n1)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [X_t_32: $i] :
refl(
( ( level(X_t_32) = int_level(X_t_32) )
<=> ( level(X_t_32) = int_level(X_t_32) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_21) ).
tff(33,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(t_139) = int_level(t_139) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
level(t_139) = int_level(t_139),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
level(t_139) = int_level(plus(t_139,n1)),
inference(transitivity,[status(thm)],[37,28]) ).
tff(39,plain,
( ( level(t_139) = level(plus(t_139,n1)) )
<=> ( int_level(plus(t_139,n1)) = level(plus(t_139,n1)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( level(t_139) = level(plus(t_139,n1)) )
<=> ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
inference(transitivity,[status(thm)],[39,1]) ).
tff(41,plain,
( ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) )
<=> ( level(t_139) = level(plus(t_139,n1)) ) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
inference(unit_resolution,[status(thm)],[42,35]) ).
tff(44,plain,
level(t_139) = level(plus(t_139,n1)),
inference(modus_ponens,[status(thm)],[43,41]) ).
tff(45,plain,
( ( level(t_139) != level(plus(t_139,n1)) )
<=> ( level(t_139) != level(plus(t_139,n1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
level(t_139) != level(plus(t_139,n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
tff(47,plain,
level(t_139) != level(plus(t_139,n1)),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV027-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 22:07:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------