TSTP Solution File: SYO889_16 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 May 21 09:16:07 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 34 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 176 ( 60 ~; 49 |; 52 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 50 !; 32 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK0: ( '$ki_world' * $i ) > '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_4,type,
sK3: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
a: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
b: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f53,plain,
$false,
inference(subsumption_resolution,[],[f52,f36]) ).
tff(f36,plain,
'$ki_accessible'(sK1,sK0(sK1,sK2)),
inference(subsumption_resolution,[],[f34,f23]) ).
tff(f23,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f20]) ).
tff(f20,plain,
( ! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ~ b(X2,X1)
| ~ a(X2,X1)
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ! [X3: '$ki_world'] :
( ! [X4] :
( ( b(sK0(X3,X4),X4)
& '$ki_accessible'(X3,sK0(X3,X4)) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) )
& ! [X8: '$ki_world'] :
( a(X8,sK2)
| ~ '$ki_accessible'(sK1,X8) )
& '$ki_exists_in_world_$i'(sK1,sK2)
& '$ki_accessible'('$ki_local_world',sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f19,f18,f17]) ).
tff(f17,plain,
! [X3: '$ki_world',X4] :
( ? [X5: '$ki_world'] :
( b(X5,X4)
& '$ki_accessible'(X3,X5) )
=> ( b(sK0(X3,X4),X4)
& '$ki_accessible'(X3,sK0(X3,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
( ? [X6: '$ki_world'] :
( ? [X7] :
( ! [X8: '$ki_world'] :
( a(X8,X7)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'('$ki_local_world',X6) )
=> ( ? [X7] :
( ! [X8: '$ki_world'] :
( a(X8,X7)
| ~ '$ki_accessible'(sK1,X8) )
& '$ki_exists_in_world_$i'(sK1,X7) )
& '$ki_accessible'('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
( ? [X7] :
( ! [X8: '$ki_world'] :
( a(X8,X7)
| ~ '$ki_accessible'(sK1,X8) )
& '$ki_exists_in_world_$i'(sK1,X7) )
=> ( ! [X8: '$ki_world'] :
( a(X8,sK2)
| ~ '$ki_accessible'(sK1,X8) )
& '$ki_exists_in_world_$i'(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
( ! [X0: '$ki_world'] :
( ! [X1] :
( ! [X2: '$ki_world'] :
( ~ b(X2,X1)
| ~ a(X2,X1)
| ~ '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ! [X3: '$ki_world'] :
( ! [X4] :
( ? [X5: '$ki_world'] :
( b(X5,X4)
& '$ki_accessible'(X3,X5) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) )
& ? [X6: '$ki_world'] :
( ? [X7] :
( ! [X8: '$ki_world'] :
( a(X8,X7)
| ~ '$ki_accessible'(X6,X8) )
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'('$ki_local_world',X6) ) ),
inference(rectify,[],[f11]) ).
tff(f11,plain,
( ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ b(X8,X7)
| ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) )
& ! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2: '$ki_world'] :
( b(X2,X1)
& '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ? [X3: '$ki_world'] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( a(X5,X4)
| ~ '$ki_accessible'(X3,X5) )
& '$ki_exists_in_world_$i'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(flattening,[],[f10]) ).
tff(f10,plain,
( ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ b(X8,X7)
| ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) )
& ! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2: '$ki_world'] :
( b(X2,X1)
& '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ? [X3: '$ki_world'] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( a(X5,X4)
| ~ '$ki_accessible'(X3,X5) )
& '$ki_exists_in_world_$i'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,plain,
~ ( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: '$ki_world'] :
( b(X2,X1)
& '$ki_accessible'(X0,X2) ) ) )
& ? [X3: '$ki_world'] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> a(X5,X4) )
& '$ki_exists_in_world_$i'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) )
=> ? [X6: '$ki_world'] :
( ? [X7] :
( ? [X8: '$ki_world'] :
( b(X8,X7)
& a(X8,X7)
& '$ki_accessible'(X6,X8) )
& '$ki_exists_in_world_$i'(X6,X7) )
& '$ki_accessible'('$ki_local_world',X6) ) ),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4) ) ) )
& ? [X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> a(X4,X3) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( b(X4,X3)
& a(X4,X3)
& '$ki_accessible'(X0,X4) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
( ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4) ) ) )
& ? [X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> a(X4,X3) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( ? [X4: '$ki_world'] :
( b(X4,X3)
& a(X4,X3)
& '$ki_accessible'(X0,X4) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f34,plain,
( '$ki_accessible'(sK1,sK0(sK1,sK2))
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f26,f24]) ).
tff(f24,plain,
'$ki_exists_in_world_$i'(sK1,sK2),
inference(cnf_transformation,[],[f20]) ).
tff(f26,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_exists_in_world_$i'(X3,X4)
| '$ki_accessible'(X3,sK0(X3,X4))
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f20]) ).
tff(f52,plain,
~ '$ki_accessible'(sK1,sK0(sK1,sK2)),
inference(resolution,[],[f51,f44]) ).
tff(f44,plain,
b(sK0(sK1,sK2),sK2),
inference(subsumption_resolution,[],[f42,f23]) ).
tff(f42,plain,
( b(sK0(sK1,sK2),sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f27,f24]) ).
tff(f27,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_exists_in_world_$i'(X3,X4)
| b(sK0(X3,X4),X4)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f20]) ).
tff(f51,plain,
! [X0: '$ki_world'] :
( ~ b(X0,sK2)
| ~ '$ki_accessible'(sK1,X0) ),
inference(subsumption_resolution,[],[f50,f25]) ).
tff(f25,plain,
! [X8: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X8)
| a(X8,sK2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f50,plain,
! [X0: '$ki_world'] :
( ~ a(X0,sK2)
| ~ '$ki_accessible'(sK1,X0)
| ~ b(X0,sK2) ),
inference(subsumption_resolution,[],[f48,f23]) ).
tff(f48,plain,
! [X0: '$ki_world'] :
( ~ a(X0,sK2)
| ~ '$ki_accessible'(sK1,X0)
| ~ b(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f28,f24]) ).
tff(f28,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ a(X2,X1)
| ~ '$ki_accessible'(X0,X2)
| ~ b(X2,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n025.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 10:28:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (1504)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (1506)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (1507)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.37 % (1509)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37 % (1510)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37 % (1505)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 TRYING [1,1]
% 0.13/0.37 % (1509)First to succeed.
% 0.13/0.37 TRYING [2,1]
% 0.13/0.37 TRYING [3,1]
% 0.13/0.37 TRYING [1,1]
% 0.13/0.37 TRYING [2,1]
% 0.13/0.37 % (1509)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1504"
% 0.13/0.37 TRYING [3,1]
% 0.13/0.37 TRYING [4,1]
% 0.13/0.37 % (1507)Also succeeded, but the first one will report.
% 0.13/0.37 TRYING [4,1]
% 0.13/0.37 % (1510)Also succeeded, but the first one will report.
% 0.13/0.37 % (1509)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (1509)------------------------------
% 0.13/0.37 % (1509)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37 % (1509)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (1509)Memory used [KB]: 751
% 0.13/0.37 % (1509)Time elapsed: 0.004 s
% 0.13/0.37 % (1509)Instructions burned: 4 (million)
% 0.13/0.37 % (1504)Success in time 0.009 s
%------------------------------------------------------------------------------