TSTP Solution File: SYO888_10 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---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_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 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 159 ( 53 ~; 41 |; 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 : 55 (; 45 !; 10 ?; 34 :)
% 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(f49,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f44,f48]) ).
tff(f48,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f47]) ).
tff(f47,plain,
( $false
| ~ spl3_2 ),
inference(subsumption_resolution,[],[f45,f27]) ).
tff(f27,plain,
~ h(sK2,sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ! [X0] :
( ~ f('$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) ) )
& ~ h(sK2,sK1)
& '$ki_accessible'('$ki_local_world',sK2)
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& f('$ki_local_world',sK1)
& ! [X4] :
( ~ g('$ki_local_world',X4)
| ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f18,f17]) ).
tff(f17,plain,
( ? [X2] :
( ? [X3: '$ki_world'] :
( ~ h(X3,X2)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X2)
& f('$ki_local_world',X2) )
=> ( ? [X3: '$ki_world'] :
( ~ h(X3,sK1)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& f('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
( ? [X3: '$ki_world'] :
( ~ h(X3,sK1)
& '$ki_accessible'('$ki_local_world',X3) )
=> ( ~ h(sK2,sK1)
& '$ki_accessible'('$ki_local_world',sK2) ) ),
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'('$ki_local_world',X1)
| g(X1,X0) ) )
& ? [X2] :
( ? [X3: '$ki_world'] :
( ~ h(X3,X2)
& '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X2)
& f('$ki_local_world',X2) )
& ! [X4] :
( ~ g('$ki_local_world',X4)
| ! [X5: '$ki_world'] :
( h(X5,X4)
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(rectify,[],[f12]) ).
tff(f12,plain,
( ! [X2] :
( ~ f('$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] :
( ? [X5: '$ki_world'] :
( ~ h(X5,X4)
& '$ki_accessible'('$ki_local_world',X5) )
& '$ki_exists_in_world_$i'('$ki_local_world',X4)
& f('$ki_local_world',X4) )
& ! [X0] :
( ~ g('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( h(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(flattening,[],[f11]) ).
tff(f11,plain,
( ? [X4] :
( ? [X5: '$ki_world'] :
( ~ h(X5,X4)
& '$ki_accessible'('$ki_local_world',X5) )
& f('$ki_local_world',X4)
& '$ki_exists_in_world_$i'('$ki_local_world',X4) )
& ! [X0] :
( ! [X1: '$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) )
& ! [X2] :
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| g(X3,X2) )
| ~ f('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f6,plain,
~ ( ( ! [X0] :
( '$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) ) ) )
& ! [X2] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
=> ( f('$ki_local_world',X2)
=> ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> g(X3,X2) ) ) ) )
=> ! [X4] :
( '$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(f45,plain,
( h(sK2,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f36,f26]) ).
tff(f26,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f19]) ).
tff(f36,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| h(X0,sK1) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f35,plain,
( spl3_2
<=> ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| h(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f44,plain,
spl3_1,
inference(avatar_split_clause,[],[f41,f31]) ).
tff(f31,plain,
( spl3_1
<=> g('$ki_local_world',sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f41,plain,
g('$ki_local_world',sK1),
inference(resolution,[],[f21,f39]) ).
tff(f39,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| g(X0,sK1) ),
inference(subsumption_resolution,[],[f38,f24]) ).
tff(f24,plain,
f('$ki_local_world',sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f38,plain,
! [X0: '$ki_world'] :
( g(X0,sK1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ f('$ki_local_world',sK1) ),
inference(resolution,[],[f28,f25]) ).
tff(f25,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f28,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| g(X1,X0)
| ~ f('$ki_local_world',X0)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(cnf_transformation,[],[f19]) ).
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(f37,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f29,f35,f31]) ).
tff(f29,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ g('$ki_local_world',sK1)
| h(X0,sK1) ),
inference(resolution,[],[f23,f25]) ).
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
% 0.11/0.12 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 13:16:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (31116)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.51 % (31112)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.51 % (31112)First to succeed.
% 0.20/0.51 % (31111)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)
% 0.20/0.51 % (31120)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 % (31123)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51 % (31116)Also succeeded, but the first one will report.
% 0.20/0.52 % (31112)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (31112)------------------------------
% 0.20/0.52 % (31112)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (31112)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (31112)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (31112)Memory used [KB]: 5884
% 0.20/0.52 % (31112)Time elapsed: 0.116 s
% 0.20/0.52 % (31112)Instructions burned: 2 (million)
% 0.20/0.52 % (31112)------------------------------
% 0.20/0.52 % (31112)------------------------------
% 0.20/0.52 % (31107)Success in time 0.164 s
%------------------------------------------------------------------------------