TSTP Solution File: SYO891_16 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --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 15:45:48 EDT 2023
% Result : Theorem 1.24s 0.52s
% Output : Refutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 32 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 122 ( 34 ~; 26 |; 45 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 10 ( 10 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 : 73 (; 44 !; 29 ?; 39 :)
% 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_2,type,
sK1: ( $i * '$ki_world' ) > $i ).
tff(func_def_4,type,
sK3: '$ki_world' ).
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(f65,plain,
$false,
inference(subsumption_resolution,[],[f62,f59]) ).
tff(f59,plain,
'$ki_exists_in_world_$i'(sK3,sK2),
inference(unit_resulting_resolution,[],[f44,f46,f53]) ).
tff(f53,plain,
! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,X0)
| ~ '$ki_accessible'(X1,X2)
| '$ki_exists_in_world_$i'(X2,X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0,X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,X0)
| ~ '$ki_accessible'(X1,X2)
| '$ki_exists_in_world_$i'(X2,X0) ),
inference(rectify,[],[f26]) ).
tff(f26,plain,
! [X1,X0: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X0,X2)
| '$ki_exists_in_world_$i'(X2,X1) ),
inference(flattening,[],[f25]) ).
tff(f25,plain,
! [X1,X2: '$ki_world',X0: '$ki_world'] :
( '$ki_exists_in_world_$i'(X2,X1)
| ~ '$ki_accessible'(X0,X2)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
! [X1,X2: '$ki_world',X0: '$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_exists_in_world_$i'(X0,X3)
& '$ki_accessible'(X0,X1) )
=> '$ki_exists_in_world_$i'(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
tff(f46,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
( ! [X0] :
( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
| ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ( qmltpeq(X1,X0,sK1(X0,X1))
& '$ki_exists_in_world_$i'(X1,sK1(X0,X1)) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4] :
( ~ p(X3,X4)
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK2)
& p(sK3,sK2)
& '$ki_accessible'('$ki_local_world',sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f35,f38,f37,f36]) ).
tff(f36,plain,
! [X0,X1: '$ki_world'] :
( ? [X2] :
( qmltpeq(X1,X0,X2)
& '$ki_exists_in_world_$i'(X1,X2) )
=> ( qmltpeq(X1,X0,sK1(X0,X1))
& '$ki_exists_in_world_$i'(X1,sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f37,plain,
( ? [X5] :
( '$ki_exists_in_world_$i'('$ki_local_world',X5)
& ? [X6: '$ki_world'] :
( p(X6,X5)
& '$ki_accessible'('$ki_local_world',X6) ) )
=> ( '$ki_exists_in_world_$i'('$ki_local_world',sK2)
& ? [X6: '$ki_world'] :
( p(X6,sK2)
& '$ki_accessible'('$ki_local_world',X6) ) ) ),
introduced(choice_axiom,[]) ).
tff(f38,plain,
( ? [X6: '$ki_world'] :
( p(X6,sK2)
& '$ki_accessible'('$ki_local_world',X6) )
=> ( p(sK3,sK2)
& '$ki_accessible'('$ki_local_world',sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f35,plain,
( ! [X0] :
( ~ '$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_$i'(X1,X2) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4] :
( ~ p(X3,X4)
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) )
& ? [X5] :
( '$ki_exists_in_world_$i'('$ki_local_world',X5)
& ? [X6: '$ki_world'] :
( p(X6,X5)
& '$ki_accessible'('$ki_local_world',X6) ) ) ),
inference(rectify,[],[f28]) ).
tff(f28,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) ) ) )
& ! [X5: '$ki_world'] :
( ! [X6] :
( ~ p(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
& ? [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) ) ) ),
inference(flattening,[],[f27]) ).
tff(f27,plain,
( ! [X5: '$ki_world'] :
( ! [X6] :
( ~ p(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
& ? [X3] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) ) )
& ! [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) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,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] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( p(X4,X3)
& '$ki_accessible'('$ki_local_world',X4) ) )
=> ? [X5: '$ki_world'] :
( ? [X6] :
( '$ki_exists_in_world_$i'(X5,X6)
& p(X5,X6) )
& '$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'] :
( p(X0,X3)
& '$ki_accessible'('$ki_local_world',X0) )
& '$ki_exists_in_world_$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: '$ki_world'] :
( p(X0,X3)
& '$ki_accessible'('$ki_local_world',X0) )
& '$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'('$ki_local_world',X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f44,plain,
'$ki_accessible'('$ki_local_world',sK3),
inference(cnf_transformation,[],[f39]) ).
tff(f62,plain,
~ '$ki_exists_in_world_$i'(sK3,sK2),
inference(unit_resulting_resolution,[],[f45,f44,f47]) ).
tff(f47,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_exists_in_world_$i'(X3,X4)
| ~ p(X3,X4)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f39]) ).
tff(f45,plain,
p(sK3,sK2),
inference(cnf_transformation,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO891_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 : n023.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 13:27:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (8464)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 % (8463)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.24/0.52 % (8471)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.24/0.52 % (8480)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.24/0.52 % (8464)First to succeed.
% 1.24/0.52 % (8463)Instruction limit reached!
% 1.24/0.52 % (8463)------------------------------
% 1.24/0.52 % (8463)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.24/0.52 % (8463)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.24/0.52 % (8463)Termination reason: Unknown
% 1.24/0.52 % (8463)Termination phase: Saturation
% 1.24/0.52
% 1.24/0.52 % (8463)Memory used [KB]: 5884
% 1.24/0.52 % (8463)Time elapsed: 0.105 s
% 1.24/0.52 % (8463)Instructions burned: 3 (million)
% 1.24/0.52 % (8463)------------------------------
% 1.24/0.52 % (8463)------------------------------
% 1.24/0.52 % (8464)Refutation found. Thanks to Tanya!
% 1.24/0.52 % SZS status Theorem for theBenchmark
% 1.24/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.24/0.52 % (8464)------------------------------
% 1.24/0.52 % (8464)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.24/0.52 % (8464)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.24/0.52 % (8464)Termination reason: Refutation
% 1.24/0.52
% 1.24/0.52 % (8464)Memory used [KB]: 5884
% 1.24/0.52 % (8464)Time elapsed: 0.112 s
% 1.24/0.52 % (8464)Instructions burned: 1 (million)
% 1.24/0.52 % (8464)------------------------------
% 1.24/0.52 % (8464)------------------------------
% 1.24/0.52 % (8457)Success in time 0.165 s
%------------------------------------------------------------------------------