TSTP Solution File: SYO889_16 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYO889_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 : n015.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 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 33 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 187 ( 67 ~; 53 |; 52 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 83 (; 51 !; 32 ?; 59 :)
% 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' * $i ) > '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_4,type,
sK3: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
a: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
b: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f45,plain,
$false,
inference(subsumption_resolution,[],[f44,f29]) ).
tff(f29,plain,
'$ki_exists_in_world_$i'(sK1,sK2),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ( b(sK0(X0,X1),X1)
& '$ki_accessible'(X0,sK0(X0,X1)) )
| ~ '$ki_exists_in_world_$i'(X0,X1) ) )
& ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X5)
| a(X5,sK2) )
& '$ki_exists_in_world_$i'(sK1,sK2)
& '$ki_accessible'('$ki_local_world',sK1)
& ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ b(X8,X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f21,f20,f19]) ).
tff(f19,plain,
! [X0: '$ki_world',X1] :
( ? [X2: '$ki_world'] :
( b(X2,X1)
& '$ki_accessible'(X0,X2) )
=> ( b(sK0(X0,X1),X1)
& '$ki_accessible'(X0,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f20,plain,
( ? [X3: '$ki_world'] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X3,X5)
| a(X5,X4) )
& '$ki_exists_in_world_$i'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
=> ( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X5)
| a(X5,X4) )
& '$ki_exists_in_world_$i'(sK1,X4) )
& '$ki_accessible'('$ki_local_world',sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f21,plain,
( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X5)
| a(X5,X4) )
& '$ki_exists_in_world_$i'(sK1,X4) )
=> ( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X5)
| a(X5,sK2) )
& '$ki_exists_in_world_$i'(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ? [X2: '$ki_world'] :
( b(X2,X1)
& '$ki_accessible'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) ) )
& ? [X3: '$ki_world'] :
( ? [X4] :
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'(X3,X5)
| a(X5,X4) )
& '$ki_exists_in_world_$i'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
& ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ b(X8,X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) ) ),
inference(rectify,[],[f12]) ).
tff(f12,plain,
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( b(X5,X4)
& '$ki_accessible'(X3,X5) )
| ~ '$ki_exists_in_world_$i'(X3,X4) ) )
& ? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| a(X2,X1) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ b(X8,X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) ) ),
inference(flattening,[],[f11]) ).
tff(f11,plain,
( ! [X6: '$ki_world'] :
( ! [X7] :
( ! [X8: '$ki_world'] :
( ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ b(X8,X7) )
| ~ '$ki_exists_in_world_$i'(X6,X7) )
| ~ '$ki_accessible'('$ki_local_world',X6) )
& ? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'(X0,X2)
| a(X2,X1) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ! [X4] :
( ? [X5: '$ki_world'] :
( b(X5,X4)
& '$ki_accessible'(X3,X5) )
| ~ '$ki_exists_in_world_$i'(X3,X4) ) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,plain,
~ ( ( ? [X0: '$ki_world'] :
( ? [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ? [X5: '$ki_world'] :
( b(X5,X4)
& '$ki_accessible'(X3,X5) ) ) ) )
=> ? [X6: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X6)
& ? [X7] :
( ? [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
& b(X8,X7)
& a(X8,X7) )
& '$ki_exists_in_world_$i'(X6,X7) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ( ( ? [X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> a(X4,X3) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4) ) ) ) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4)
& a(X4,X3) ) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
( ( ? [X0: '$ki_world'] :
( ? [X3] :
( ! [X4: '$ki_world'] :
( '$ki_accessible'(X0,X4)
=> a(X4,X3) )
& '$ki_exists_in_world_$i'(X0,X3) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4) ) ) ) )
=> ? [X0: '$ki_world'] :
( ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& ? [X4: '$ki_world'] :
( b(X4,X3)
& '$ki_accessible'(X0,X4)
& a(X4,X3) ) )
& '$ki_accessible'('$ki_local_world',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f44,plain,
~ '$ki_exists_in_world_$i'(sK1,sK2),
inference(subsumption_resolution,[],[f43,f28]) ).
tff(f28,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f22]) ).
tff(f43,plain,
( ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_exists_in_world_$i'(sK1,sK2) ),
inference(duplicate_literal_removal,[],[f42]) ).
tff(f42,plain,
( ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_exists_in_world_$i'(sK1,sK2)
| ~ '$ki_exists_in_world_$i'(sK1,sK2) ),
inference(resolution,[],[f41,f31]) ).
tff(f31,plain,
! [X0: '$ki_world',X1: $i] :
( '$ki_accessible'(X0,sK0(X0,X1))
| ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f22]) ).
tff(f41,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1,sK0(X0,sK2))
| ~ '$ki_exists_in_world_$i'(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f40,f32]) ).
tff(f32,plain,
! [X0: '$ki_world',X1: $i] :
( b(sK0(X0,X1),X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f40,plain,
! [X0: '$ki_world'] :
( ~ b(X0,sK2)
| ~ '$ki_accessible'(sK1,X0) ),
inference(subsumption_resolution,[],[f39,f30]) ).
tff(f30,plain,
! [X5: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X5)
| a(X5,sK2) ),
inference(cnf_transformation,[],[f22]) ).
tff(f39,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X0)
| ~ a(X0,sK2)
| ~ b(X0,sK2) ),
inference(subsumption_resolution,[],[f38,f28]) ).
tff(f38,plain,
! [X0: '$ki_world'] :
( ~ a(X0,sK2)
| ~ '$ki_accessible'(sK1,X0)
| ~ b(X0,sK2)
| ~ '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f27,f29]) ).
tff(f27,plain,
! [X8: '$ki_world',X6: '$ki_world',X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ '$ki_accessible'('$ki_local_world',X6)
| ~ b(X8,X7) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % 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 : n015.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 13:24:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.44 % (7858)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)
% 0.19/0.47 % (7858)First to succeed.
% 0.19/0.47 % (7858)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (7858)------------------------------
% 0.19/0.47 % (7858)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47 % (7858)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47 % (7858)Termination reason: Refutation
% 0.19/0.47
% 0.19/0.47 % (7858)Memory used [KB]: 5884
% 0.19/0.47 % (7858)Time elapsed: 0.087 s
% 0.19/0.47 % (7858)Instructions burned: 2 (million)
% 0.19/0.47 % (7858)------------------------------
% 0.19/0.47 % (7858)------------------------------
% 0.19/0.47 % (7850)Success in time 0.12 s
%------------------------------------------------------------------------------