TSTP Solution File: PLA053_4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : PLA053_4 : 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 : n026.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 15:41:24 EDT 2023
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 56 ( 10 unt; 11 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 146 ( 56 ~; 47 |; 20 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 (; 45 !; 11 ?; 34 :)
% 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 ) > $i ).
tff(func_def_2,type,
sK1: '$ki_world' > $i ).
tff(func_def_4,type,
sK3: '$ki_world' ).
tff(func_def_6,type,
sK5: '$ki_world' > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
h: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
bomb: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
defused: ( '$ki_world' * $i ) > $o ).
tff(pred_def_5,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f128,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f53,f55,f83,f113,f118,f127]) ).
tff(f127,plain,
( spl6_3
| ~ spl6_1
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f119,f111,f42,f50]) ).
tff(f50,plain,
( spl6_3
<=> defused(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
tff(f42,plain,
( spl6_1
<=> bomb(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
tff(f111,plain,
( spl6_11
<=> ! [X0] :
( ~ bomb(sK3,X0)
| defused(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
tff(f119,plain,
( defused(sK3,sK4)
| ~ spl6_1
| ~ spl6_11 ),
inference(resolution,[],[f112,f44]) ).
tff(f44,plain,
( bomb(sK3,sK4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f112,plain,
( ! [X0: $i] :
( ~ bomb(sK3,X0)
| defused(sK3,X0) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f111]) ).
tff(f118,plain,
( ~ spl6_4
| ~ spl6_10 ),
inference(avatar_split_clause,[],[f117,f108,f71]) ).
tff(f71,plain,
( spl6_4
<=> '$ki_accessible'('$ki_local_world',sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
tff(f108,plain,
( spl6_10
<=> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'('$ki_local_world',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
tff(f117,plain,
( ~ '$ki_accessible'('$ki_local_world',sK3)
| ~ spl6_10 ),
inference(resolution,[],[f109,f27]) ).
tff(f27,plain,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(f109,plain,
( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,sK3) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f108]) ).
tff(f113,plain,
( spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f89,f111,f108]) ).
tff(f89,plain,
! [X0: $i,X1: '$ki_world'] :
( ~ bomb(sK3,X0)
| defused(sK3,X0)
| ~ '$ki_accessible'(X1,sK3)
| ~ '$ki_accessible'('$ki_local_world',X1) ),
inference(resolution,[],[f88,f26]) ).
tff(f26,plain,
! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
inference(cnf_transformation,[],[f10]) ).
tff(f10,plain,
! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: '$ki_world',X3] : '$ki_exists_in_world_$i'(X0,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(f88,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| defused(sK3,X1)
| ~ bomb(sK3,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ '$ki_accessible'(X0,sK3) ),
inference(resolution,[],[f28,f56]) ).
tff(f56,plain,
! [X0: $i] : h(sK3,X0),
inference(resolution,[],[f36,f26]) ).
tff(f36,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X2)
| h(sK3,X2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f20,plain,
? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1] :
( ! [X2] :
( ( h(X0,X2)
& bomb(X0,X1)
& ~ defused(X0,X1) )
| ~ '$ki_exists_in_world_$i'(X0,X2) )
& '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
? [X0: '$ki_world'] :
( ? [X1] :
( ! [X2] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| ( ~ defused(X0,X1)
& h(X0,X2)
& bomb(X0,X1) ) )
& '$ki_exists_in_world_$i'(X0,X1) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,plain,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ( ( h(X0,X2)
& bomb(X0,X1) )
=> defused(X0,X1) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( ( ( bomb(X0,X3)
& h(X0,X7) )
=> defused(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( ( ( bomb(X0,X3)
& h(X0,X7) )
=> defused(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f28,plain,
! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
( ~ h(X3,sK0(X0,X1))
| ~ '$ki_accessible'('$ki_local_world',X0)
| defused(X3,X1)
| ~ '$ki_accessible'(X0,X3)
| ~ bomb(X3,X1)
| ~ '$ki_exists_in_world_$i'(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1] :
( ? [X2] :
( '$ki_exists_in_world_$i'(X0,X2)
& ! [X3: '$ki_world'] :
( ~ '$ki_accessible'(X0,X3)
| defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2) ) )
| ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
inference(flattening,[],[f24]) ).
tff(f24,plain,
! [X0: '$ki_world'] :
( ! [X1] :
( ? [X2] :
( ! [X3: '$ki_world'] :
( defused(X3,X1)
| ~ bomb(X3,X1)
| ~ h(X3,X2)
| ~ '$ki_accessible'(X0,X3) )
& '$ki_exists_in_world_$i'(X0,X2) )
| ~ '$ki_exists_in_world_$i'(X0,X1) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2] :
( ! [X3: '$ki_world'] :
( '$ki_accessible'(X0,X3)
=> ( ( bomb(X3,X1)
& h(X3,X2) )
=> defused(X3,X1) ) )
& '$ki_exists_in_world_$i'(X0,X2) ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X0,X3)
=> ? [X7] :
( '$ki_exists_in_world_$i'(X0,X7)
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X0,X6)
=> ( ( bomb(X6,X3)
& h(X6,X7) )
=> defused(X6,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f83,plain,
spl6_4,
inference(avatar_contradiction_clause,[],[f82]) ).
tff(f82,plain,
( $false
| spl6_4 ),
inference(resolution,[],[f73,f38]) ).
tff(f38,plain,
'$ki_accessible'('$ki_local_world',sK3),
inference(cnf_transformation,[],[f20]) ).
tff(f73,plain,
( ~ '$ki_accessible'('$ki_local_world',sK3)
| spl6_4 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f55,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f54]) ).
tff(f54,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f26,f47]) ).
tff(f47,plain,
( ! [X2: $i] : ~ '$ki_exists_in_world_$i'(sK3,X2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f46,plain,
( spl6_2
<=> ! [X2] : ~ '$ki_exists_in_world_$i'(sK3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
tff(f53,plain,
( spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f34,f50,f46]) ).
tff(f34,plain,
! [X2: $i] :
( ~ defused(sK3,sK4)
| ~ '$ki_exists_in_world_$i'(sK3,X2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f48,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f35,f46,f42]) ).
tff(f35,plain,
! [X2: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X2)
| bomb(sK3,sK4) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.13 % 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 : n026.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 12:42:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % (1450)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 % (1456)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51 % (1456)First to succeed.
% 0.19/0.51 % (1469)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.51 % (1460)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 % (1468)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 (2999ds/498Mi)
% 0.19/0.51 % (1449)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (1454)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (1448)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)
% 0.19/0.52 % (1459)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)
% 0.19/0.52 % (1447)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52 % (1452)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (1451)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (1455)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 % (1446)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)
% 0.19/0.52 % (1457)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 TRYING [2]
% 0.19/0.52 TRYING [3]
% 0.19/0.52 TRYING [4]
% 0.19/0.52 % (1467)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.52 % (1464)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (1466)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.52 % (1453)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.53 % (1472)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)
% 0.19/0.53 % (1453)Instruction limit reached!
% 0.19/0.53 % (1453)------------------------------
% 0.19/0.53 % (1453)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (1453)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (1453)Termination reason: Unknown
% 0.19/0.53 % (1453)Termination phase: Blocked clause elimination
% 0.19/0.53
% 0.19/0.53 % (1453)Memory used [KB]: 895
% 0.19/0.53 % (1453)Time elapsed: 0.002 s
% 0.19/0.53 % (1453)Instructions burned: 2 (million)
% 0.19/0.53 % (1453)------------------------------
% 0.19/0.53 % (1453)------------------------------
% 0.19/0.53 % (1456)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (1456)------------------------------
% 0.19/0.53 % (1456)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (1456)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (1456)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (1456)Memory used [KB]: 5500
% 0.19/0.53 % (1456)Time elapsed: 0.113 s
% 0.19/0.53 % (1456)Instructions burned: 2 (million)
% 0.19/0.53 % (1456)------------------------------
% 0.19/0.53 % (1456)------------------------------
% 0.19/0.53 % (1444)Success in time 0.183 s
%------------------------------------------------------------------------------