TSTP Solution File: SYO890_16 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYO890_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 : n029.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 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 86 ( 28 ~; 19 |; 23 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 49 (; 37 !; 12 ?; 30 :)
% 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' ) > $o ).
tff(pred_def_2,type,
e: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
f: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f46,plain,
$false,
inference(subsumption_resolution,[],[f44,f33]) ).
tff(f33,plain,
f(sK2,sK1),
inference(resolution,[],[f30,f29]) ).
tff(f29,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X1: '$ki_world'] :
( f(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1) )
& '$ki_accessible'('$ki_local_world',sK2)
& ! [X3] :
( ~ '$ki_exists_in_world_$i'(sK2,X3)
| ~ f(sK2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f14,f22,f21]) ).
tff(f21,plain,
( ? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( f(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) ) )
=> ( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& ! [X1: '$ki_world'] :
( f(X1,sK1)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
( ? [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
& ! [X3] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ f(X2,X3) ) )
=> ( '$ki_accessible'('$ki_local_world',sK2)
& ! [X3] :
( ~ '$ki_exists_in_world_$i'(sK2,X3)
| ~ f(sK2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f14,plain,
( ? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( f(X1,X0)
| ~ '$ki_accessible'('$ki_local_world',X1) ) )
& ? [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
& ! [X3] :
( ~ '$ki_exists_in_world_$i'(X2,X3)
| ~ f(X2,X3) ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
~ ( ? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> f(X1,X0) ) )
=> ! [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
=> ? [X3] :
( f(X2,X3)
& '$ki_exists_in_world_$i'(X2,X3) ) ) ),
inference(pure_predicate_removal,[],[f9]) ).
tff(f9,plain,
~ ( ? [X0] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( f(X1,X0)
& e(X1,X0) ) ) )
=> ! [X2: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X2)
=> ? [X3] :
( f(X2,X3)
& '$ki_exists_in_world_$i'(X2,X3) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ( ? [X3] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( e(X0,X3)
& f(X0,X3) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& f(X0,X3) ) ) ),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
( ? [X3] :
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( e(X0,X3)
& f(X0,X3) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X3) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
& f(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f30,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| f(X1,sK1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f44,plain,
~ f(sK2,sK1),
inference(resolution,[],[f39,f28]) ).
tff(f28,plain,
! [X3: $i] :
( ~ '$ki_exists_in_world_$i'(sK2,X3)
| ~ f(sK2,X3) ),
inference(cnf_transformation,[],[f23]) ).
tff(f39,plain,
'$ki_exists_in_world_$i'(sK2,sK1),
inference(resolution,[],[f35,f29]) ).
tff(f35,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| '$ki_exists_in_world_$i'(X0,sK1) ),
inference(resolution,[],[f25,f31]) ).
tff(f31,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X2,X1)
| ~ '$ki_accessible'(X2,X0)
| '$ki_exists_in_world_$i'(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
! [X0: '$ki_world',X1,X2: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X2,X1)
| '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'(X2,X0) ),
inference(rectify,[],[f13]) ).
tff(f13,plain,
! [X0: '$ki_world',X2,X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X1,X2)
| '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X1,X0) ),
inference(flattening,[],[f12]) ).
tff(f12,plain,
! [X2,X1: '$ki_world',X0: '$ki_world'] :
( '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X1,X0)
| ~ '$ki_exists_in_world_$i'(X1,X2) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
! [X2,X1: '$ki_world',X0: '$ki_world'] :
( ( '$ki_accessible'(X1,X0)
& '$ki_exists_in_world_$i'(X1,X2) )
=> '$ki_exists_in_world_$i'(X0,X2) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X1: '$ki_world',X0: '$ki_world',X3] :
( ( '$ki_accessible'(X0,X1)
& '$ki_exists_in_world_$i'(X0,X3) )
=> '$ki_exists_in_world_$i'(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 22 13:25:31 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % (1206)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (1204)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50 % (1207)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (1210)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50 % (1203)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.50 % (1208)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)
% 0.19/0.51 % (1218)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51 % (1210)First to succeed.
% 0.19/0.51 % (1210)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (1210)------------------------------
% 0.19/0.51 % (1210)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (1210)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (1210)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (1210)Memory used [KB]: 5373
% 0.19/0.51 % (1210)Time elapsed: 0.101 s
% 0.19/0.51 % (1210)Instructions burned: 1 (million)
% 0.19/0.51 % (1210)------------------------------
% 0.19/0.51 % (1210)------------------------------
% 0.19/0.51 % (1202)Success in time 0.166 s
%------------------------------------------------------------------------------