TSTP Solution File: LCL455+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.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 : Sun May 5 07:46:03 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 49
% Syntax : Number of formulae : 112 ( 66 unt; 0 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 20 ~; 15 |; 0 &)
% ( 28 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 47 ( 46 usr; 46 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f270,plain,
$false,
inference(avatar_sat_refutation,[],[f154,f159,f164,f169,f174,f179,f184,f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f259,f263,f267,f269]) ).
fof(f269,plain,
( spl2_22
| ~ spl2_24 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f268,plain,
( $false
| spl2_22
| ~ spl2_24 ),
inference(resolution,[],[f266,f258]) ).
fof(f258,plain,
( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
| spl2_22 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f256,plain,
( spl2_22
<=> is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f266,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_24 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl2_24
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f267,plain,
( ~ spl2_10
| spl2_24 ),
inference(avatar_split_clause,[],[f136,f265,f196]) ).
fof(f196,plain,
( spl2_10
<=> or_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
fof(f263,plain,
( ~ spl2_11
| spl2_23 ),
inference(avatar_split_clause,[],[f135,f261,f201]) ).
fof(f201,plain,
( spl2_11
<=> or_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f261,plain,
( spl2_23
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f135,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f259,plain,
( ~ spl2_22
| spl2_1 ),
inference(avatar_split_clause,[],[f134,f151,f256]) ).
fof(f151,plain,
( spl2_1
<=> r2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f134,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f88,f105]) ).
fof(f105,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f254,plain,
spl2_21,
inference(avatar_split_clause,[],[f127,f251]) ).
fof(f251,plain,
( spl2_21
<=> op_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f127,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f249,plain,
spl2_20,
inference(avatar_split_clause,[],[f126,f246]) ).
fof(f246,plain,
( spl2_20
<=> op_implies_and ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f126,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f244,plain,
spl2_19,
inference(avatar_split_clause,[],[f125,f241]) ).
fof(f241,plain,
( spl2_19
<=> op_or ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f125,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f239,plain,
spl2_18,
inference(avatar_split_clause,[],[f124,f236]) ).
fof(f236,plain,
( spl2_18
<=> op_and ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f124,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f234,plain,
spl2_17,
inference(avatar_split_clause,[],[f123,f231]) ).
fof(f231,plain,
( spl2_17
<=> op_implies_or ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f123,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f229,plain,
spl2_16,
inference(avatar_split_clause,[],[f122,f226]) ).
fof(f226,plain,
( spl2_16
<=> implies_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f224,plain,
spl2_15,
inference(avatar_split_clause,[],[f121,f221]) ).
fof(f221,plain,
( spl2_15
<=> implies_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f121,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f219,plain,
spl2_14,
inference(avatar_split_clause,[],[f120,f216]) ).
fof(f216,plain,
( spl2_14
<=> and_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f120,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f214,plain,
spl2_13,
inference(avatar_split_clause,[],[f119,f211]) ).
fof(f211,plain,
( spl2_13
<=> and_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f119,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f209,plain,
spl2_12,
inference(avatar_split_clause,[],[f118,f206]) ).
fof(f206,plain,
( spl2_12
<=> and_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f118,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f204,plain,
spl2_11,
inference(avatar_split_clause,[],[f117,f201]) ).
fof(f117,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f199,plain,
spl2_10,
inference(avatar_split_clause,[],[f116,f196]) ).
fof(f116,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f194,plain,
spl2_9,
inference(avatar_split_clause,[],[f115,f191]) ).
fof(f191,plain,
( spl2_9
<=> or_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f115,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f189,plain,
spl2_8,
inference(avatar_split_clause,[],[f114,f186]) ).
fof(f186,plain,
( spl2_8
<=> equivalence_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f114,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f184,plain,
spl2_7,
inference(avatar_split_clause,[],[f113,f181]) ).
fof(f181,plain,
( spl2_7
<=> equivalence_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f113,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f179,plain,
spl2_6,
inference(avatar_split_clause,[],[f112,f176]) ).
fof(f176,plain,
( spl2_6
<=> equivalence_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f112,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f174,plain,
spl2_5,
inference(avatar_split_clause,[],[f111,f171]) ).
fof(f171,plain,
( spl2_5
<=> substitution_of_equivalents ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f111,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f169,plain,
spl2_4,
inference(avatar_split_clause,[],[f110,f166]) ).
fof(f166,plain,
( spl2_4
<=> implies_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f110,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f164,plain,
spl2_3,
inference(avatar_split_clause,[],[f109,f161]) ).
fof(f161,plain,
( spl2_3
<=> modus_tollens ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f109,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f159,plain,
spl2_2,
inference(avatar_split_clause,[],[f108,f156]) ).
fof(f156,plain,
( spl2_2
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f108,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f154,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f107,f151]) ).
fof(f107,plain,
~ r2,
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
~ r2,
inference(flattening,[],[f54]) ).
fof(f54,negated_conjecture,
~ r2,
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 13:23:57 EDT 2024
% 0.22/0.36 % CPUTime :
% 0.22/0.36 % (22926)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (22939)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (22941)WARNING: value z3 for option sas not known
% 0.22/0.39 % (22943)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (22940)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (22942)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (22941)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39 % (22944)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39 % (22945)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 % (22943)First to succeed.
% 0.22/0.39 % (22944)Also succeeded, but the first one will report.
% 0.22/0.39 % (22945)Also succeeded, but the first one will report.
% 0.22/0.39 % (22943)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22926"
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 % (22941)Also succeeded, but the first one will report.
% 0.22/0.39 % (22943)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (22943)------------------------------
% 0.22/0.39 % (22943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39 % (22943)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (22943)Memory used [KB]: 916
% 0.22/0.39 % (22943)Time elapsed: 0.005 s
% 0.22/0.39 % (22943)Instructions burned: 5 (million)
% 0.22/0.39 % (22926)Success in time 0.029 s
%------------------------------------------------------------------------------