TSTP Solution File: SYO891_16 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO891_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 0.12s 0.35s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 33 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 124 ( 36 ~; 26 |; 45 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 42 !; 29 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_3,type,
sK2: ( $i * '$ki_world' ) > $i ).
tff(func_def_4,type,
sK3: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
p: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f61,plain,
$false,
inference(subsumption_resolution,[],[f59,f41]) ).
tff(f41,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
( ! [X0: '$ki_world'] :
( ! [X1] :
( ~ p(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& p(sK1,sK0)
& '$ki_accessible'('$ki_local_world',sK1)
& '$ki_exists_in_world_$i'('$ki_local_world',sK0)
& ! [X4] :
( ! [X5: '$ki_world'] :
( ( qmltpeq(X5,X4,sK2(X4,X5))
& '$ki_exists_in_world_$i'(X5,sK2(X4,X5)) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f34,f33,f32]) ).
tff(f32,plain,
( ? [X2] :
( ? [X3: '$ki_world'] :
( p(X3,X2)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X2) )
=> ( ? [X3: '$ki_world'] :
( p(X3,sK0)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
( ? [X3: '$ki_world'] :
( p(X3,sK0)
& '$ki_accessible'('$ki_local_world',X3) )
=> ( p(sK1,sK0)
& '$ki_accessible'('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f34,plain,
! [X4,X5: '$ki_world'] :
( ? [X6] :
( qmltpeq(X5,X4,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
=> ( qmltpeq(X5,X4,sK2(X4,X5))
& '$ki_exists_in_world_$i'(X5,sK2(X4,X5)) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
( ! [X0: '$ki_world'] :
( ! [X1] :
( ~ p(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) )
& ? [X2] :
( ? [X3: '$ki_world'] :
( p(X3,X2)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X2) )
& ! [X4] :
( ! [X5: '$ki_world'] :
( ? [X6] :
( qmltpeq(X5,X4,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(rectify,[],[f19]) ).
tff(f19,plain,
( ! [X5: '$ki_world'] :
( ! [X6] :
( ~ p(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
& ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
& ! [X0] :
( ! [X1: '$ki_world'] :
( ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
( ! [X5: '$ki_world'] :
( ! [X6] :
( ~ p(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
& ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
& ! [X0] :
( ! [X1: '$ki_world'] :
( ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
~ ( ! [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) ) ) )
=> ( ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X5: '$ki_world'] :
( ? [X6] :
( p(X5,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'('$ki_local_world',X5) ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,negated_conjecture,
~ ( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( qmltpeq(X0,X3,X4)
& '$ki_exists_in_world_$i'(X0,X4) ) ) )
=> ( ? [X3] :
( ? [X0: '$ki_world'] :
( p(X0,X3)
& '$ki_accessible'('$ki_local_world',X0) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( p(X0,X3)
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(negated_conjecture,[],[f9]) ).
tff(f9,conjecture,
( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( qmltpeq(X0,X3,X4)
& '$ki_exists_in_world_$i'(X0,X4) ) ) )
=> ( ? [X3] :
( ? [X0: '$ki_world'] :
( p(X0,X3)
& '$ki_accessible'('$ki_local_world',X0) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( p(X0,X3)
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f59,plain,
~ '$ki_accessible'('$ki_local_world',sK1),
inference(resolution,[],[f57,f53]) ).
tff(f53,plain,
~ '$ki_exists_in_world_$i'(sK1,sK0),
inference(subsumption_resolution,[],[f52,f41]) ).
tff(f52,plain,
( ~ '$ki_exists_in_world_$i'(sK1,sK0)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f43,f42]) ).
tff(f42,plain,
p(sK1,sK0),
inference(cnf_transformation,[],[f35]) ).
tff(f43,plain,
! [X0: '$ki_world',X1: $i] :
( ~ p(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f57,plain,
! [X0: '$ki_world'] :
( '$ki_exists_in_world_$i'(X0,sK0)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f51,f40]) ).
tff(f40,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f35]) ).
tff(f51,plain,
! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| '$ki_exists_in_world_$i'(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: '$ki_world',X1: '$ki_world',X2] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X2) ),
inference(flattening,[],[f29]) ).
tff(f29,plain,
! [X0: '$ki_world',X1: '$ki_world',X2] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_accessible'(X0,X1)
| ~ '$ki_exists_in_world_$i'(X0,X2) ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
! [X0: '$ki_world',X1: '$ki_world',X2] :
( ( '$ki_accessible'(X0,X1)
& '$ki_exists_in_world_$i'(X0,X2) )
=> '$ki_exists_in_world_$i'(X1,X2) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: '$ki_world',X1: '$ki_world',X3] :
( ( '$ki_accessible'(X0,X1)
& '$ki_exists_in_world_$i'(X0,X3) )
=> '$ki_exists_in_world_$i'(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 11:04:38 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % (10479)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (10481)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.34 % (10480)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.34 Detected minimum model sizes of [1,1]
% 0.12/0.34 % (10483)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.34 Detected maximum model sizes of [2,max]
% 0.12/0.34 TRYING [1,1]
% 0.12/0.34 TRYING [2,1]
% 0.12/0.34 Cannot enumerate next child to try in an incomplete setup
% 0.12/0.34 Detected minimum model sizes of [1,1]
% 0.12/0.34 Detected maximum model sizes of [2,max]
% 0.12/0.34 % (10481)Refutation not found, incomplete strategy% (10481)------------------------------
% 0.12/0.34 % (10481)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.34 TRYING [1,1]
% 0.12/0.34 % (10481)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.34
% 0.12/0.34 % (10481)Memory used [KB]: 806
% 0.12/0.34 % (10481)Time elapsed: 0.003 s
% 0.12/0.34 % (10481)Instructions burned: 5 (million)
% 0.12/0.34 TRYING [2,1]
% 0.12/0.34 Cannot enumerate next child to try in an incomplete setup
% 0.12/0.34 % (10480)Refutation not found, incomplete strategy% (10480)------------------------------
% 0.12/0.34 % (10480)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.34 % (10480)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.34
% 0.12/0.34 % (10480)Memory used [KB]: 801
% 0.12/0.34 % (10480)Time elapsed: 0.002 s
% 0.12/0.34 % (10480)Instructions burned: 4 (million)
% 0.12/0.34 % (10481)------------------------------
% 0.12/0.34 % (10481)------------------------------
% 0.12/0.34 % (10480)------------------------------
% 0.12/0.34 % (10480)------------------------------
% 0.12/0.34 Detected minimum model sizes of [1,1]
% 0.12/0.34 Detected maximum model sizes of [2,max]
% 0.12/0.34 TRYING [1,1]
% 0.12/0.34 TRYING [2,1]
% 0.12/0.34 Cannot enumerate next child to try in an incomplete setup
% 0.12/0.34 % (10483)Refutation not found, incomplete strategy% (10483)------------------------------
% 0.12/0.34 % (10483)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.34 % (10483)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.34
% 0.12/0.34 % (10483)Memory used [KB]: 807
% 0.12/0.34 % (10483)Time elapsed: 0.002 s
% 0.12/0.34 % (10483)Instructions burned: 5 (million)
% 0.12/0.34 % (10483)------------------------------
% 0.12/0.34 % (10483)------------------------------
% 0.12/0.34 % (10484)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.34 % (10486)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.34 % (10485)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35 % (10485)First to succeed.
% 0.12/0.35 Detected minimum model sizes of [1,1]
% 0.12/0.35 Detected maximum model sizes of [2,max]
% 0.12/0.35 TRYING [1,1]
% 0.12/0.35 TRYING [2,1]
% 0.12/0.35 Cannot enumerate next child to try in an incomplete setup
% 0.12/0.35 % (10486)Refutation not found, incomplete strategy% (10486)------------------------------
% 0.12/0.35 % (10486)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35 % (10486)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.35
% 0.12/0.35 % (10486)Memory used [KB]: 818
% 0.12/0.35 % (10486)Time elapsed: 0.003 s
% 0.12/0.35 % (10486)Instructions burned: 5 (million)
% 0.12/0.35 % (10485)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10479"
% 0.12/0.35 % (10486)------------------------------
% 0.12/0.35 % (10486)------------------------------
% 0.12/0.35 % (10484)Also succeeded, but the first one will report.
% 0.12/0.35 % (10485)Refutation found. Thanks to Tanya!
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.35 % (10485)------------------------------
% 0.12/0.35 % (10485)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35 % (10485)Termination reason: Refutation
% 0.12/0.35
% 0.12/0.35 % (10485)Memory used [KB]: 752
% 0.12/0.35 % (10485)Time elapsed: 0.004 s
% 0.12/0.35 % (10485)Instructions burned: 4 (million)
% 0.12/0.35 % (10479)Success in time 0.007 s
%------------------------------------------------------------------------------