TSTP Solution File: SYO888_10 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYO888_10 : 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_sat --cores 0 -t %d %s
% Computer : n023.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 15:45:51 EDT 2023
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 41 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 162 ( 54 ~; 43 |; 31 &)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 54 (; 44 !; 10 ?; 33 :)
% 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' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
f: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
g: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f72,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f67,f71]) ).
tff(f71,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f70]) ).
tff(f70,plain,
( $false
| ~ spl3_1 ),
inference(subsumption_resolution,[],[f68,f25]) ).
tff(f25,plain,
~ h(sK2,sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ! [X0] :
( ~ f('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| g(X1,X0) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& '$ki_accessible'('$ki_local_world',sK2)
& ~ h(sK2,sK1)
& f('$ki_local_world',sK1)
& ! [X4] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
| ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ g('$ki_local_world',X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f18,f17]) ).
tff(f17,plain,
( ? [X2] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ~ h(X3,X2) )
& f('$ki_local_world',X2) )
=> ( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ~ h(X3,sK1) )
& f('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ~ h(X3,sK1) )
=> ( '$ki_accessible'('$ki_local_world',sK2)
& ~ h(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
( ! [X0] :
( ~ f('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| g(X1,X0) ) )
& ? [X2] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ~ h(X3,X2) )
& f('$ki_local_world',X2) )
& ! [X4] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
| ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ g('$ki_local_world',X4) ) ),
inference(rectify,[],[f10]) ).
tff(f10,plain,
( ! [X2] :
( ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2)
| ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| g(X3,X2) ) )
& ? [X4] :
( '$ki_exists_in_world_$i'('$ki_local_world',X4)
& ? [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
& ~ h(X5,X4) )
& f('$ki_local_world',X4) )
& ! [X0] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( h(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ g('$ki_local_world',X0) ) ),
inference(flattening,[],[f9]) ).
tff(f9,plain,
( ? [X4] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
& ~ h(X5,X4) )
& f('$ki_local_world',X4)
& '$ki_exists_in_world_$i'('$ki_local_world',X4) )
& ! [X2] :
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| g(X3,X2) )
| ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) )
& ! [X0] :
( ! [X1: '$ki_world'] :
( h(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ g('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f6,plain,
~ ( ( ! [X2] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
=> ( f('$ki_local_world',X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> g(X3,X2) ) ) )
& ! [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ( g('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> h(X1,X0) ) ) ) )
=> ! [X4] :
( '$ki_exists_in_world_$i'('$ki_local_world',X4)
=> ( f('$ki_local_world',X4)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
=> h(X5,X4) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,negated_conjecture,
~ ( ( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( g('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> h(X0,X3) ) ) )
& ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( f('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> g(X0,X3) ) ) ) )
=> ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( f('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> h(X0,X3) ) ) ) ),
inference(negated_conjecture,[],[f4]) ).
tff(f4,conjecture,
( ( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( g('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> h(X0,X3) ) ) )
& ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( f('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> g(X0,X3) ) ) ) )
=> ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ( f('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> h(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f68,plain,
( h(sK2,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f32,f26]) ).
tff(f26,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f19]) ).
tff(f32,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| h(X0,sK1) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f31,plain,
( spl3_1
<=> ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| h(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f67,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f66]) ).
tff(f66,plain,
( $false
| spl3_2 ),
inference(subsumption_resolution,[],[f65,f36]) ).
tff(f36,plain,
( ~ g('$ki_local_world',sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f34,plain,
( spl3_2
<=> g('$ki_local_world',sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f65,plain,
g('$ki_local_world',sK1),
inference(subsumption_resolution,[],[f64,f27]) ).
tff(f27,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f64,plain,
( ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1)
| g('$ki_local_world',sK1) ),
inference(resolution,[],[f48,f24]) ).
tff(f24,plain,
f('$ki_local_world',sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f48,plain,
! [X1: $i] :
( ~ f('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X1)
| g('$ki_local_world',X1) ),
inference(resolution,[],[f28,f21]) ).
tff(f21,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f28,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| g(X1,X0)
| ~ f('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f37,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f29,f34,f31]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( ~ g('$ki_local_world',sK1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| h(X0,sK1) ),
inference(resolution,[],[f23,f27]) ).
tff(f23,plain,
! [X4: $i,X5: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
| ~ g('$ki_local_world',X4)
| ~ '$ki_accessible'('$ki_local_world',X5)
| h(X5,X4) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.31 % Computer : n023.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 22 13:27:12 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.45 % (4995)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.46 % (5012)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.17/0.46 % (4995)First to succeed.
% 0.17/0.46 % (4995)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (4995)------------------------------
% 0.17/0.46 % (4995)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.46 % (4995)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.46 % (4995)Termination reason: Refutation
% 0.17/0.46
% 0.17/0.46 % (4995)Memory used [KB]: 5373
% 0.17/0.46 % (4995)Time elapsed: 0.082 s
% 0.17/0.46 % (4995)Instructions burned: 2 (million)
% 0.17/0.46 % (4995)------------------------------
% 0.17/0.46 % (4995)------------------------------
% 0.17/0.46 % (4986)Success in time 0.135 s
%------------------------------------------------------------------------------