TSTP Solution File: LCL962_16 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL962_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 : n028.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 00:37:05 EDT 2024
% Result : Theorem 0.10s 0.34s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 43 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 104 ( 44 ~; 33 |; 9 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 38 ( 33 !; 5 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(type_def_6,type,
'$ki_index': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
'#idx(a)': '$ki_index' ).
tff(func_def_2,type,
'#idx(b)': '$ki_index' ).
tff(func_def_3,type,
sK0: '$ki_world' ).
tff(func_def_4,type,
sK1: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_index' * '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f54,plain,
$false,
inference(subsumption_resolution,[],[f53,f25]) ).
tff(f25,plain,
'$ki_accessible'('#idx(a)','$ki_local_world',sK0),
inference(cnf_transformation,[],[f21]) ).
tff(f21,plain,
( p(sK0)
& '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f20]) ).
tff(f20,plain,
( ? [X0: '$ki_world'] :
( p(X0)
& '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
=> ( p(sK0)
& '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f12,plain,
? [X0: '$ki_world'] :
( p(X0)
& '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ p(X0) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ p(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f53,plain,
~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0),
inference(subsumption_resolution,[],[f52,f26]) ).
tff(f26,plain,
p(sK0),
inference(cnf_transformation,[],[f21]) ).
tff(f52,plain,
( ~ p(sK0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
inference(subsumption_resolution,[],[f51,f43]) ).
tff(f43,plain,
~ p(sK1(sK0)),
inference(subsumption_resolution,[],[f42,f27]) ).
tff(f27,plain,
~ p('$ki_local_world'),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
~ p('$ki_local_world'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).
tff(f42,plain,
( p('$ki_local_world')
| ~ p(sK1(sK0)) ),
inference(resolution,[],[f40,f31]) ).
tff(f31,plain,
! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)') ).
tff(f40,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| ~ p(sK1(sK0)) ),
inference(resolution,[],[f29,f25]) ).
tff(f29,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(sK1(X0))
| p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
( ! [X0: '$ki_world'] :
( ( ~ p(sK1(X0))
& '$ki_accessible'('#idx(b)',X0,sK1(X0)) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).
tff(f23,plain,
! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ~ p(X1)
& '$ki_accessible'('#idx(b)',X0,X1) )
=> ( ~ p(sK1(X0))
& '$ki_accessible'('#idx(b)',X0,sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
( ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ~ p(X1)
& '$ki_accessible'('#idx(b)',X0,X1) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
inference(rectify,[],[f13]) ).
tff(f13,plain,
( ! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'('#idx(b)',X1,X2) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) )
| ! [X0: '$ki_world'] :
( p(X0)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
=> p(X0) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ ! [X2: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,X2)
=> p(X2) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
( ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
=> p(X0) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ~ ! [X3: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,X3)
=> p(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_2) ).
tff(f51,plain,
( p(sK1(sK0))
| ~ p(sK0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
inference(resolution,[],[f49,f32]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)',X0,X1)
| p(X1)
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(flattening,[],[f14]) ).
tff(f14,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ( p(X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,X1)
=> p(X1) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
=> ( p(X0)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X0,X3)
=> p(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_1) ).
tff(f49,plain,
'$ki_accessible'('#idx(b)',sK0,sK1(sK0)),
inference(subsumption_resolution,[],[f48,f27]) ).
tff(f48,plain,
( p('$ki_local_world')
| '$ki_accessible'('#idx(b)',sK0,sK1(sK0)) ),
inference(resolution,[],[f46,f31]) ).
tff(f46,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0)
| '$ki_accessible'('#idx(b)',sK0,sK1(sK0)) ),
inference(resolution,[],[f28,f25]) ).
tff(f28,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| '$ki_accessible'('#idx(b)',X0,sK1(X0))
| p(X2)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : LCL962_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon May 20 01:32:22 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (2163)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (2165)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.33 Detected minimum model sizes of [1,1]
% 0.10/0.33 Detected maximum model sizes of [max,2]
% 0.10/0.33 TRYING [1,1]
% 0.10/0.33 TRYING [2,1]
% 0.10/0.33 TRYING [3,1]
% 0.10/0.33 TRYING [2,2]
% 0.10/0.33 TRYING [3,2]
% 0.10/0.33 TRYING [4,1]
% 0.10/0.33 TRYING [4,2]
% 0.10/0.33 % (2168)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.33 % (2167)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.33 % (2169)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.34 % (2166)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)
% 0.10/0.34 Cannot enumerate next child to try in an incomplete setup
% 0.10/0.34 % (2165)Refutation not found, incomplete strategy% (2165)------------------------------
% 0.10/0.34 % (2165)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34 % (2165)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.34
% 0.10/0.34 % (2165)Memory used [KB]: 785
% 0.10/0.34 % (2165)Time elapsed: 0.007 s
% 0.10/0.34 % (2165)Instructions burned: 19 (million)
% 0.10/0.34 % (2164)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.34 % (2170)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)
% 0.10/0.34 % (2165)------------------------------
% 0.10/0.34 % (2165)------------------------------
% 0.10/0.34 Detected minimum model sizes of [1,1]
% 0.10/0.34 Detected maximum model sizes of [max,2]
% 0.10/0.34 TRYING [1,1]
% 0.10/0.34 % (2169)Also succeeded, but the first one will report.
% 0.10/0.34 % (2168)First to succeed.
% 0.10/0.34 TRYING [2,1]
% 0.10/0.34 % (2166)Also succeeded, but the first one will report.
% 0.10/0.34 Detected minimum model sizes of [1,1]
% 0.10/0.34 Detected maximum model sizes of [max,2]
% 0.10/0.34 TRYING [3,1]
% 0.10/0.34 TRYING [1,1]
% 0.10/0.34 Detected minimum model sizes of [1,1]
% 0.10/0.34 Detected maximum model sizes of [max,2]
% 0.10/0.34 % (2168)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2163"
% 0.10/0.34 TRYING [1,1]
% 0.10/0.34 TRYING [2,1]
% 0.10/0.34 TRYING [2,1]
% 0.10/0.34 TRYING [3,1]
% 0.10/0.34 % (2168)Refutation found. Thanks to Tanya!
% 0.10/0.34 % SZS status Theorem for theBenchmark
% 0.10/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.34 % (2168)------------------------------
% 0.10/0.34 % (2168)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34 % (2168)Termination reason: Refutation
% 0.10/0.34
% 0.10/0.34 % (2168)Memory used [KB]: 749
% 0.10/0.34 % (2168)Time elapsed: 0.003 s
% 0.10/0.34 % (2168)Instructions burned: 3 (million)
% 0.10/0.34 % (2163)Success in time 0.015 s
%------------------------------------------------------------------------------