%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:29 AM UTC 2026
% Result : Theorem 2.66s 1.06s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 24 unt; 8 def)
% Number of atoms : 114 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 92 ( 42 ~; 36 |; 0 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f53,conjecture,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
fof(f54,negated_conjecture,
~ cn2,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn2,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
=> cn2 ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f62,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f85,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f62]) ).
fof(f91,plain,
( cn2
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f92,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f93,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f95,plain,
( cn2
| ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f91]) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f85]) ).
fof(f111,plain,
( cn2
| ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f112,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f92]) ).
fof(f113,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f93]) ).
fof(f115,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f116,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f126,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f135,plain,
~ cn2,
inference(cnf_transformation,[],[f55]) ).
fof(f145,definition,
( spl2_3
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f149,definition,
( spl2_4
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f113,f149,f145]) ).
fof(f153,definition,
( spl2_5
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f157,definition,
( spl2_6
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( ~ spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f112,f157,f153]) ).
fof(f161,definition,
( spl2_7
<=> is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f163,plain,
( ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1)))
| spl2_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl2_8
<=> cn2 ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl2_7
| spl2_8 ),
inference(avatar_split_clause,[],[f111,f165,f161]) ).
fof(f210,definition,
( spl2_19
<=> or_1 ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f214,definition,
( spl2_20
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ spl2_19
| spl2_20 ),
inference(avatar_split_clause,[],[f105,f214,f210]) ).
fof(f289,plain,
~ spl2_8,
inference(avatar_split_clause,[],[f135,f165]) ).
fof(f292,plain,
spl2_5,
inference(avatar_split_clause,[],[f115,f153]) ).
fof(f297,plain,
spl2_3,
inference(avatar_split_clause,[],[f116,f145]) ).
fof(f327,plain,
spl2_19,
inference(avatar_split_clause,[],[f126,f210]) ).
fof(f350,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_4
| ~ spl2_6 ),
inference(superposition,[],[f150,f158]) ).
fof(f357,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| ~ spl2_4
| ~ spl2_6
| spl2_7 ),
inference(superposition,[],[f163,f350]) ).
fof(f370,plain,
( $false
| ~ spl2_4
| ~ spl2_6
| spl2_7
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f357,f215]) ).
fof(f371,plain,
( ~ spl2_4
| ~ spl2_6
| spl2_7
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f370]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f151]) ).
cnf(s3,plain,
( ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f159]) ).
cnf(s4,plain,
( ~ spl2_7
| spl2_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s10,plain,
( ~ spl2_19
| spl2_20 ),
inference(sat_conversion,[],[f216]) ).
cnf(s20,plain,
~ spl2_8,
inference(sat_conversion,[],[f289]) ).
cnf(s22,plain,
spl2_5,
inference(sat_conversion,[],[f292]) ).
cnf(s24,plain,
spl2_3,
inference(sat_conversion,[],[f297]) ).
cnf(s44,plain,
spl2_19,
inference(sat_conversion,[],[f327]) ).
cnf(s57,plain,
( ~ spl2_4
| ~ spl2_6
| spl2_7
| ~ spl2_20 ),
inference(sat_conversion,[],[f371]) ).
cnf(s67,plain,
spl2_20,
inference(rat,[],[s10,s44]) ).
cnf(s73,plain,
~ spl2_7,
inference(rat,[],[s4,s20]) ).
cnf(s74,plain,
spl2_6,
inference(rat,[],[s3,s22]) ).
cnf(s75,plain,
~ spl2_4,
inference(rat,[],[s57,s67,s73,s74]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s2,s75,s24]) ).
fof(f372,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:45:54 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.66/1.06 % (1408969)Detected formulas, will run a generic FOF schedule.
% 2.66/1.06 % (1408994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=831849335:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.06 % (1408991)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1770600914:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.06 % (1408989)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2701168319:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.06 % (1408993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1571007777:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.06 % (1408992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2919194366:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.06 % (1408990)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1807074384:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.06 % (1408993)Refutation not found, incomplete strategy
% 2.66/1.06 % (1408993)------------------------------
% 2.66/1.06 % (1408993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.06 % (1408993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.06 % (1408993)CaDiCaL version: 2.1.3
% 2.66/1.06 % (1408993)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.06 % (1408993)Time elapsed: 0.0000 s
% 2.66/1.06 % (1408993)Peak memory usage: 87 MB
% 2.66/1.06 % (1408992)Refutation not found, incomplete strategy
% 2.66/1.06 % (1408992)------------------------------
% 2.66/1.06 % (1408992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.06 % (1408992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.06 % (1408992)CaDiCaL version: 2.1.3
% 2.66/1.06 % (1408992)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.06 % (1408992)Time elapsed: 0.001 s
% 2.66/1.06 % (1408992)Peak memory usage: 87 MB
% 2.66/1.06 % (1408994)First to succeed.
% 2.66/1.06 % (1408994)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1408969"
% 2.66/1.06 % (1408995)dis-21_1_sil=8000:lcm=predicate:random_seed=3351944767:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.66/1.06 % (1408995)Refutation not found, incomplete strategy
% 2.66/1.06 % (1408995)------------------------------
% 2.66/1.06 % (1408995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.06 % (1408995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.06 % (1408995)CaDiCaL version: 2.1.3
% 2.66/1.06 % (1408995)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.06 % (1408995)Time elapsed: 0.003 s
% 2.66/1.06 % (1408995)Peak memory usage: 88 MB
% 2.66/1.06 % (1408995)Instructions burned: 1 (million)
% 2.66/1.06 % (1408994)Refutation found. Thanks to Tanya!
% 2.66/1.06 % SZS status Theorem for theBenchmark
% 2.66/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.06 % (1408994)------------------------------
% 2.66/1.06 % (1408994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.06 % (1408994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.06 % (1408994)CaDiCaL version: 2.1.3
% 2.66/1.06 % (1408994)Termination reason: Refutation
% 2.66/1.06 % (1408994)Time elapsed: 0.003 s
% 2.66/1.06 % (1408994)Peak memory usage: 90 MB
% 2.66/1.06 % (1408994)Instructions burned: 6 (million)
% 2.66/1.06 % (1408994)------------------------------
% 2.66/1.06 % (1408994)------------------------------
% 2.66/1.06 % (1408969)Success in time 0.329 s
% 2.66/1.06 % Vampire exiting
%------------------------------------------------------------------------------