TSTP Solution File: SYO893_11 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYO893_11 : 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 : n006.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 15:45:52 EDT 2023
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 45 ( 6 unt; 10 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 228 ( 87 ~; 63 |; 57 &)
% ( 4 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 6 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 104 (; 65 !; 39 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK1: '$ki_world' > '$ki_world' ).
tff(func_def_2,type,
sK2: '$ki_world' ).
tff(func_def_3,type,
sK3: '$ki_world' > '$ki_world' ).
tff(func_def_4,type,
sK4: '$ki_world' > '$ki_world' ).
tff(func_def_5,type,
sK5: '$ki_world' ).
tff(func_def_6,type,
sK6: '$ki_world' > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f49,plain,
$false,
inference(subsumption_resolution,[],[f48,f20]) ).
tff(f20,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(f48,plain,
! [X0: '$ki_world'] : ~ '$ki_accessible'(sK5,X0),
inference(subsumption_resolution,[],[f46,f40]) ).
tff(f40,plain,
~ sP0,
inference(subsumption_resolution,[],[f39,f20]) ).
tff(f39,plain,
! [X0: '$ki_world'] :
( ~ sP0
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(subsumption_resolution,[],[f38,f20]) ).
tff(f38,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(sK4(X0),sK3(X1))
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f37]) ).
tff(f37,plain,
! [X0: '$ki_world',X1: '$ki_world'] :
( ~ sP0
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ sP0
| ~ '$ki_accessible'(sK4(X0),sK3(X1)) ),
inference(resolution,[],[f36,f29]) ).
tff(f29,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( p(X2)
| ~ sP0
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK4(X0),X2) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ( '$ki_accessible'(X0,sK4(X0))
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK4(X0),X2) ) ) ) )
& ( sP0
| ( '$ki_accessible'('$ki_local_world',sK5)
& ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X4)
| ( ~ p(sK6(X4))
& '$ki_accessible'(X4,sK6(X4)) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f15,f18,f17,f16]) ).
tff(f16,plain,
! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
=> ( '$ki_accessible'(X0,sK4(X0))
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK4(X0),X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
( ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(X3,X4)
| ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) ) ) )
=> ( '$ki_accessible'('$ki_local_world',sK5)
& ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(sK5,X4)
| ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
=> ( ~ p(sK6(X4))
& '$ki_accessible'(X4,sK6(X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) ) ) )
& ( sP0
| ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& ! [X4: '$ki_world'] :
( ~ '$ki_accessible'(X3,X4)
| ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) ) ) ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,plain,
( ( ~ sP0
| ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ? [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
& ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) ) ) )
& ( sP0
| ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,plain,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) ) )
<~> sP0 ),
inference(definition_folding,[],[f5,f6]) ).
tff(f6,plain,
( sP0
<=> ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f5,plain,
( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X0,X1)
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) ) )
<~> ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f4,plain,
~ ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) ) )
<=> ~ ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ? [X4: '$ki_world'] :
( '$ki_accessible'(X3,X4)
& ! [X5: '$ki_world'] :
( '$ki_accessible'(X4,X5)
=> p(X5) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,negated_conjecture,
~ ( ? [X0: '$ki_world'] :
( ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ? [X3: '$ki_world'] :
( ~ p(X3)
& '$ki_accessible'(X2,X3) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<=> ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X2,X3)
=> p(X3) )
& '$ki_accessible'(X0,X2) ) ) ),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
( ? [X0: '$ki_world'] :
( ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> ? [X3: '$ki_world'] :
( ~ p(X3)
& '$ki_accessible'(X2,X3) ) )
& '$ki_accessible'('$ki_local_world',X0) )
<=> ~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X2: '$ki_world'] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X2,X3)
=> p(X3) )
& '$ki_accessible'(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f36,plain,
! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ sP0 ),
inference(subsumption_resolution,[],[f23,f20]) ).
tff(f23,plain,
! [X4: '$ki_world'] :
( ~ p(sK3(X4))
| ~ '$ki_accessible'(sK2,X4)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK1(X0),X2) )
& '$ki_accessible'(X0,sK1(X0)) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( ( ! [X4: '$ki_world'] :
( ( ~ p(sK3(X4))
& '$ki_accessible'(X4,sK3(X4)) )
| ~ '$ki_accessible'(sK2,X4) )
& '$ki_accessible'('$ki_local_world',sK2) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f12,f11,f10]) ).
tff(f10,plain,
! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
& '$ki_accessible'(X0,X1) )
=> ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK1(X0),X2) )
& '$ki_accessible'(X0,sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f11,plain,
( ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
=> ( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(sK2,X4) )
& '$ki_accessible'('$ki_local_world',sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f12,plain,
! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
=> ( ~ p(sK3(X4))
& '$ki_accessible'(X4,sK3(X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f9,plain,
( ( sP0
| ! [X0: '$ki_world'] :
( ? [X1: '$ki_world'] :
( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
& '$ki_accessible'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) )
& ( ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
( ( sP0
| ! [X3: '$ki_world'] :
( ? [X4: '$ki_world'] :
( ! [X5: '$ki_world'] :
( p(X5)
| ~ '$ki_accessible'(X4,X5) )
& '$ki_accessible'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) ) )
& ( ? [X3: '$ki_world'] :
( ! [X4: '$ki_world'] :
( ? [X5: '$ki_world'] :
( ~ p(X5)
& '$ki_accessible'(X4,X5) )
| ~ '$ki_accessible'(X3,X4) )
& '$ki_accessible'('$ki_local_world',X3) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f46,plain,
! [X0: '$ki_world'] :
( sP0
| ~ '$ki_accessible'(sK5,X0) ),
inference(resolution,[],[f45,f27]) ).
tff(f27,plain,
! [X4: '$ki_world'] :
( ~ p(sK6(X4))
| sP0
| ~ '$ki_accessible'(sK5,X4) ),
inference(cnf_transformation,[],[f19]) ).
tff(f45,plain,
! [X2: '$ki_world'] : p(X2),
inference(subsumption_resolution,[],[f44,f40]) ).
tff(f44,plain,
! [X2: '$ki_world'] :
( sP0
| p(X2) ),
inference(subsumption_resolution,[],[f43,f20]) ).
tff(f43,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(sK1(X0),X2)
| sP0 ),
inference(subsumption_resolution,[],[f25,f20]) ).
tff(f25,plain,
! [X2: '$ki_world',X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(sK1(X0),X2)
| sP0
| p(X2) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO893_11 : 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
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 22 13:08:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % (10882)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.42 TRYING [1]
% 0.19/0.42 TRYING [2]
% 0.19/0.43 % (10898)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.19/0.43 TRYING [3]
% 0.19/0.43 TRYING [4]
% 0.19/0.43 TRYING [5]
% 0.19/0.43 TRYING [6]
% 0.19/0.43 TRYING [7]
% 0.19/0.44 % (10890)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 (3000ds/68Mi)
% 0.19/0.44 TRYING [8]
% 0.19/0.44 % (10898)First to succeed.
% 0.19/0.44 TRYING [9]
% 0.19/0.45 % (10898)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45 % (10898)------------------------------
% 0.19/0.45 % (10898)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45 % (10898)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45 % (10898)Termination reason: Refutation
% 0.19/0.45
% 0.19/0.45 % (10898)Memory used [KB]: 895
% 0.19/0.45 % (10898)Time elapsed: 0.070 s
% 0.19/0.45 % (10898)Instructions burned: 1 (million)
% 0.19/0.45 % (10898)------------------------------
% 0.19/0.45 % (10898)------------------------------
% 0.19/0.45 % (10875)Success in time 0.104 s
%------------------------------------------------------------------------------