TSTP Solution File: LAT035-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 18:31:49 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 28
% Syntax : Number of formulae : 62 ( 19 unt; 8 typ; 0 def)
% Number of atoms : 111 ( 100 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 65 ~; 29 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(f_type,type,
f: $i > $i ).
tff(k_type,type,
k: $i > $i ).
tff(bb_type,type,
bb: $i ).
tff(aa_type,type,
aa: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ( f(meet(U,V)) = join(f(U),f(V)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_meet) ).
tff(5,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
| ( f(meet(k(aa),k(bb))) = join(f(k(aa)),f(k(bb))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
f(meet(k(aa),k(bb))) = join(f(k(aa)),f(k(bb))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V: $i,U: $i] :
refl(
( ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ( k(join(U,V)) = meet(k(U),k(V)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_join) ).
tff(14,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
| ( k(join(aa,bb)) = meet(k(aa),k(bb)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
k(join(aa,bb)) = meet(k(aa),k(bb)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
f(k(join(aa,bb))) = f(meet(k(aa),k(bb))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| $false )
<=> ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( k(n1) = k(n1) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( f(n1) = n0 )
<=> ( f(n1) = k(n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( f(n1) = n0 )
<=> ( f(n1) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
f(n1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_top) ).
tff(27,plain,
f(n1) = n0,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
f(n1) = k(n1),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( ( f(n1) = k(n1) )
<=> ( k(n1) = k(n1) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( f(n1) = k(n1) )
<=> $true ),
inference(transitivity,[status(thm)],[29,23]) ).
tff(31,plain,
( ( f(n1) != k(n1) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( f(n1) != k(n1) )
<=> $false ),
inference(transitivity,[status(thm)],[31,22]) ).
tff(33,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| $false ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) )
<=> ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ) ),
inference(transitivity,[status(thm)],[33,21]) ).
tff(35,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( f(k(k(n1))) != k(n1) )
<=> ( f(n1) != k(n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( f(k(n0)) != n0 )
<=> ( f(k(k(n1))) != k(n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comp_join_hemimorphism) ).
tff(45,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[45,43]) ).
tff(47,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) ),
inference(modus_ponens,[status(thm)],[48,42]) ).
tff(50,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(k(n1))) != k(n1) ) ),
inference(modus_ponens,[status(thm)],[49,39]) ).
tff(51,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) ),
inference(modus_ponens,[status(thm)],[50,38]) ).
tff(52,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(n1) != k(n1) ) ),
inference(modus_ponens,[status(thm)],[51,35]) ).
tff(53,plain,
f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))),
inference(modus_ponens,[status(thm)],[52,34]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 : Thu Sep 1 11:00:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------