TSTP Solution File: SYO891_16 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYO891_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_sat --cores 0 -t %d %s
% Computer : n024.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 0.16s 0.45s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 33 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 113 ( 32 ~; 24 |; 40 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 (; 41 !; 26 ?; 37 :)
% 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: ( $i * '$ki_world' ) > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_4,type,
sK3: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
p: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f81,plain,
$false,
inference(subsumption_resolution,[],[f77,f54]) ).
tff(f54,plain,
~ '$ki_exists_in_world_$i'(sK2,sK1),
inference(subsumption_resolution,[],[f53,f42]) ).
tff(f42,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
( ! [X0] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ( qmltpeq(X1,X0,sK0(X0,X1))
& '$ki_exists_in_world_$i'(X1,sK0(X0,X1)) ) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) )
& p(sK2,sK1)
& '$ki_accessible'('$ki_local_world',sK2)
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f28,f34,f33,f32]) ).
tff(f32,plain,
! [X0,X1: '$ki_world'] :
( ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) )
=> ( qmltpeq(X1,X0,sK0(X0,X1))
& '$ki_exists_in_world_$i'(X1,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
( ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ( ? [X4: '$ki_world'] :
( p(X4,sK1)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f34,plain,
( ? [X4: '$ki_world'] :
( p(X4,sK1)
& '$ki_accessible'('$ki_local_world',X4) )
=> ( p(sK2,sK1)
& '$ki_accessible'('$ki_local_world',sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
( ! [X0] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) ) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) )
& ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
& ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) ) ),
inference(flattening,[],[f27]) ).
tff(f27,plain,
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) )
& ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
& ! [X0] :
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) ) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
~ ( ! [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) ) ) )
=> ( ? [X3] :
( ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X5: '$ki_world'] :
( ? [X6] :
( p(X5,X6)
& '$ki_exists_in_world_$i'(X5,X6) )
& '$ki_accessible'('$ki_local_world',X5) ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,negated_conjecture,
~ ( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( qmltpeq(X0,X3,X4)
& '$ki_exists_in_world_$i'(X0,X4) ) ) )
=> ( ? [X3] :
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0,X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& p(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(negated_conjecture,[],[f9]) ).
tff(f9,conjecture,
( ! [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X4] :
( qmltpeq(X0,X3,X4)
& '$ki_exists_in_world_$i'(X0,X4) ) ) )
=> ( ? [X3] :
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0,X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& p(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f53,plain,
( ~ '$ki_accessible'('$ki_local_world',sK2)
| ~ '$ki_exists_in_world_$i'(sK2,sK1) ),
inference(resolution,[],[f40,f43]) ).
tff(f43,plain,
p(sK2,sK1),
inference(cnf_transformation,[],[f35]) ).
tff(f40,plain,
! [X6: $i,X5: '$ki_world'] :
( ~ p(X5,X6)
| ~ '$ki_accessible'('$ki_local_world',X5)
| ~ '$ki_exists_in_world_$i'(X5,X6) ),
inference(cnf_transformation,[],[f35]) ).
tff(f77,plain,
'$ki_exists_in_world_$i'(sK2,sK1),
inference(resolution,[],[f68,f42]) ).
tff(f68,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| '$ki_exists_in_world_$i'(X0,sK1) ),
inference(resolution,[],[f52,f41]) ).
tff(f41,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f35]) ).
tff(f52,plain,
! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1)
| '$ki_exists_in_world_$i'(X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: '$ki_world',X1: '$ki_world',X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(rectify,[],[f20]) ).
tff(f20,plain,
! [X0: '$ki_world',X2: '$ki_world',X1] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| '$ki_exists_in_world_$i'(X2,X1)
| ~ '$ki_accessible'(X0,X2) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
! [X0: '$ki_world',X1,X2: '$ki_world'] :
( '$ki_exists_in_world_$i'(X2,X1)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,plain,
! [X0: '$ki_world',X1,X2: '$ki_world'] :
( ( '$ki_accessible'(X0,X2)
& '$ki_exists_in_world_$i'(X0,X1) )
=> '$ki_exists_in_world_$i'(X2,X1) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: '$ki_world',X3,X1: '$ki_world'] :
( ( '$ki_accessible'(X0,X1)
& '$ki_exists_in_world_$i'(X0,X3) )
=> '$ki_exists_in_world_$i'(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 22 13:10:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.44 % (20248)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.16/0.45 % (20248)First to succeed.
% 0.16/0.45 % (20270)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.16/0.45 % (20248)Refutation found. Thanks to Tanya!
% 0.16/0.45 % SZS status Theorem for theBenchmark
% 0.16/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.45 % (20248)------------------------------
% 0.16/0.45 % (20248)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.45 % (20248)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.45 % (20248)Termination reason: Refutation
% 0.16/0.45
% 0.16/0.45 % (20248)Memory used [KB]: 5373
% 0.16/0.45 % (20248)Time elapsed: 0.074 s
% 0.16/0.45 % (20248)Instructions burned: 3 (million)
% 0.16/0.45 % (20248)------------------------------
% 0.16/0.45 % (20248)------------------------------
% 0.16/0.45 % (20235)Success in time 0.12 s
%------------------------------------------------------------------------------