TSTP Solution File: SYO893_11 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYO893_11 : 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 : n018.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 15:45:48 EDT 2023
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 54 ( 3 unt; 10 typ; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 245 ( 93 ~; 71 |; 57 &)
% ( 7 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 6 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 102 (; 63 !; 39 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' > '$ki_world' ).
tff(func_def_2,type,
sK2: '$ki_world' ).
tff(func_def_3,type,
sK3: '$ki_world' > '$ki_world' ).
tff(func_def_4,type,
sK4: '$ki_world' > '$ki_world' ).
tff(func_def_5,type,
sK5: '$ki_world' ).
tff(func_def_6,type,
sK6: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f56,plain,
$false,
inference(avatar_sat_refutation,[],[f39,f45,f50,f52,f55]) ).
tff(f55,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f53,f36,f43]) ).
tff(f43,plain,
( spl7_3
<=> ! [X2: '$ki_world'] : p(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
tff(f36,plain,
( spl7_2
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
tff(f53,plain,
( ! [X0: '$ki_world'] : p(X0)
| spl7_2 ),
inference(unit_resulting_resolution,[],[f20,f20,f37,f25]) ).
tff(f25,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1(X0),X2)
| sP0
| ~ '$ki_accessible'('$ki_local_world',X0)
| p(X2) ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK1(X0),X2) )
& '$ki_accessible'(X0,sK1(X0)) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( ( ! [X4: '$ki_world'] :
( ( ~ p(sK3(X4))
& '$ki_accessible'(X4,sK3(X4)) )
| ~ '$ki_accessible'(sK2,X4) )
& '$ki_accessible'('$ki_local_world',sK2) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f12,f11,f10]) ).
tff(f10,plain,
! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
& '$ki_accessible'(X0,X1) )
=> ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK1(X0),X2) )
& '$ki_accessible'(X0,sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f11,plain,
( ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
=> ( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(sK2,X4) )
& '$ki_accessible'('$ki_local_world',sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f12,plain,
! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
=> ( ~ p(sK3(X4))
& '$ki_accessible'(X4,sK3(X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f9,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
& '$ki_accessible'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
& '$ki_accessible'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) )
| ~ '$ki_accessible'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f6,plain,
( sP0
<=> ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) )
| ~ '$ki_accessible'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f37,plain,
( ~ sP0
| spl7_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f20,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f52,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f51]) ).
tff(f51,plain,
( $false
| ~ spl7_1
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f34,f44]) ).
tff(f44,plain,
( ! [X2: '$ki_world'] : p(X2)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f34,plain,
( ! [X4: '$ki_world'] : ~ p(sK6(X4))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f33]) ).
tff(f33,plain,
( spl7_1
<=> ! [X4: '$ki_world'] : ~ p(sK6(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
tff(f50,plain,
( ~ spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f49]) ).
tff(f49,plain,
( $false
| ~ spl7_2
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f47,f44]) ).
tff(f47,plain,
( ! [X0: '$ki_world'] : ~ p(sK3(X0))
| ~ spl7_2 ),
inference(unit_resulting_resolution,[],[f20,f38,f23]) ).
tff(f23,plain,
! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ sP0
| ~ '$ki_accessible'(sK2,X4) ),
inference(cnf_transformation,[],[f13]) ).
tff(f38,plain,
( sP0
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f45,plain,
( spl7_3
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f41,f36,f43]) ).
tff(f41,plain,
! [X2: '$ki_world'] :
( ~ sP0
| p(X2) ),
inference(subsumption_resolution,[],[f40,f20]) ).
tff(f40,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ sP0
| p(X2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f30,f20]) ).
tff(f30,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'(sK4(X0),X2)
| p(X2)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK4(X0),X2)
| p(X2) )
& '$ki_accessible'(X0,sK4(X0)) ) ) )
& ( sP0
| ( '$ki_accessible'('$ki_local_world',sK5)
& ! [X4: '$ki_world'] :
( ( '$ki_accessible'(X4,sK6(X4))
& ~ p(sK6(X4)) )
| ~ '$ki_accessible'(sK5,X4) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f15,f18,f17,f16]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| p(X2) )
& '$ki_accessible'(X0,X1) )
=> ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK4(X0),X2)
| p(X2) )
& '$ki_accessible'(X0,sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
=> ( '$ki_accessible'('$ki_local_world',sK5)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(sK5,X4) ) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
=> ( '$ki_accessible'(X4,sK6(X4))
& ~ p(sK6(X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| p(X2) )
& '$ki_accessible'(X0,X1) ) ) )
& ( sP0
| ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,plain,
( ( ~ sP0
| ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X4,X5)
| p(X5) )
& '$ki_accessible'(X3,X4) ) ) )
& ( sP0
| ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,plain,
( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
<~> sP0 ),
inference(definition_folding,[],[f5,f6]) ).
tff(f5,plain,
( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
& ~ p(X5) )
| ~ '$ki_accessible'(X3,X4) ) )
<~> ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) )
| ~ '$ki_accessible'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f4,plain,
~ ( ~ ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ? [X4: '$ki_world'] :
( '$ki_accessible'(X3,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> p(X5) ) ) )
<=> ? [X0: '$ki_world'] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
inference(rectify,[],[f3]) ).
tff(f3,negated_conjecture,
~ ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ? [X3: '$ki_world'] :
( ~ p(X3)
& '$ki_accessible'(X2,X3) ) ) )
<=> ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X2,X3)
=> p(X3) )
& '$ki_accessible'(X0,X2) ) ) ),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ? [X3: '$ki_world'] :
( ~ p(X3)
& '$ki_accessible'(X2,X3) ) ) )
<=> ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X2,X3)
=> p(X3) )
& '$ki_accessible'(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f39,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f31,f36,f33]) ).
tff(f31,plain,
! [X4: '$ki_world'] :
( sP0
| ~ p(sK6(X4)) ),
inference(subsumption_resolution,[],[f26,f20]) ).
tff(f26,plain,
! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X4)
| ~ p(sK6(X4))
| sP0 ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO893_11 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 22 13:19:01 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.45 % (4481)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.47 % (4481)First to succeed.
% 0.18/0.48 % (4481)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (4481)------------------------------
% 0.18/0.48 % (4481)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.48 % (4481)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.48 % (4481)Termination reason: Refutation
% 0.18/0.48
% 0.18/0.48 % (4481)Memory used [KB]: 5884
% 0.18/0.48 % (4481)Time elapsed: 0.110 s
% 0.18/0.48 % (4481)Instructions burned: 1 (million)
% 0.18/0.48 % (4481)------------------------------
% 0.18/0.48 % (4481)------------------------------
% 0.18/0.48 % (4477)Success in time 0.144 s
%------------------------------------------------------------------------------