TSTP Solution File: LCL962_16 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : LCL962_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n026.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 : Mon May 22 15:38:39 EDT 2023
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 49 ( 8 unt; 9 typ; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 55 ~; 41 |; 8 &)
% ( 3 <=>; 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 : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 39 (; 35 !; 4 ?; 39 :)
% 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' > '$ki_world' ).
tff(func_def_4,type,
sK1: '$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(f83,plain,
$false,
inference(avatar_sat_refutation,[],[f44,f48,f56,f82]) ).
tff(f82,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f81]) ).
tff(f81,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(subsumption_resolution,[],[f69,f35]) ).
tff(f35,plain,
p(sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
( '$ki_accessible'('#idx(a)','$ki_local_world',sK1)
& p(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f26]) ).
tff(f26,plain,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
& p(X0) )
=> ( '$ki_accessible'('#idx(a)','$ki_local_world',sK1)
& p(sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
? [X0: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
& p(X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$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)','$ki_local_world',X0)
=> ~ p(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f69,plain,
( ~ p(sK1)
| ~ spl2_1
| ~ spl2_3 ),
inference(unit_resulting_resolution,[],[f57,f59,f36,f32]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)',X0,X1)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f20]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( p(X1)
| ~ '$ki_accessible'('#idx(b)',X0,X1) )
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
| ~ p(X0) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
! [X0: '$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,[],[f10]) ).
tff(f10,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(f36,plain,
'$ki_accessible'('#idx(a)','$ki_local_world',sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f59,plain,
( '$ki_accessible'('#idx(b)',sK1,sK0(sK1))
| ~ spl2_3 ),
inference(unit_resulting_resolution,[],[f36,f47]) ).
tff(f47,plain,
( ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,sK0(X1))
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f46,plain,
( spl2_3
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,sK0(X1))
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f57,plain,
( ~ p(sK0(sK1))
| ~ spl2_1 ),
inference(unit_resulting_resolution,[],[f36,f40]) ).
tff(f40,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(sK0(X1)) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f39,plain,
( spl2_1
<=> ! [X1: '$ki_world'] :
( ~ p(sK0(X1))
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f56,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f55]) ).
tff(f55,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f50,f33]) ).
tff(f33,plain,
~ p('$ki_local_world'),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
~ p('$ki_local_world'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).
tff(f50,plain,
( p('$ki_local_world')
| ~ spl2_2 ),
inference(unit_resulting_resolution,[],[f30,f43]) ).
tff(f43,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f42,plain,
( spl2_2
<=> ! [X0: '$ki_world'] :
( p(X0)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f30,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(f48,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f29,f46,f42]) ).
tff(f29,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,sK0(X1))
| p(X0)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| p(X0) )
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ( '$ki_accessible'('#idx(b)',X1,sK0(X1))
& ~ p(sK0(X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
tff(f22,plain,
! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,X2)
& ~ p(X2) )
=> ( '$ki_accessible'('#idx(b)',X1,sK0(X1))
& ~ p(sK0(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f21,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(ennf_transformation,[],[f11]) ).
tff(f11,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(f44,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f28,f42,f39]) ).
tff(f28,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( p(X0)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
| ~ p(sK0(X1))
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) ),
inference(cnf_transformation,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL962_16 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 22 12:18:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.50 % (6309)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.50 % (6317)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (6327)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.51 % (6316)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.51 % (6333)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.51 % (6317)First to succeed.
% 0.20/0.51 % (6317)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (6317)------------------------------
% 0.20/0.51 % (6317)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (6317)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (6317)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (6317)Memory used [KB]: 5884
% 0.20/0.51 % (6317)Time elapsed: 0.102 s
% 0.20/0.51 % (6317)Instructions burned: 2 (million)
% 0.20/0.51 % (6317)------------------------------
% 0.20/0.51 % (6317)------------------------------
% 0.20/0.51 % (6300)Success in time 0.164 s
%------------------------------------------------------------------------------