%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 11:52:32 AM UTC 2026
% Result : Theorem 3.14s 1.12s
% Output : Refutation 3.14s
% 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 : 42 ( 0 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn2) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f43,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ or_1,
inference(flattening,[],[f44]) ).
fof(f47,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f58,plain,
( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f62,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f68,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f63]) ).
fof(f75,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f79,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
~ or_1,
inference(cnf_transformation,[],[f45]) ).
fof(f95,definition,
( spl2_3
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f99,definition,
( spl2_4
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f73,f99,f95]) ).
fof(f103,definition,
( spl2_5
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f107,definition,
( spl2_6
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( ~ spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f72,f107,f103]) ).
fof(f119,definition,
( spl2_9
<=> cn2 ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f123,definition,
( spl2_10
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f70,f123,f119]) ).
fof(f135,definition,
( spl2_13
<=> is_a_theorem(implies(sK0,or(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f137,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| spl2_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl2_14
<=> or_1 ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f142,plain,
( ~ spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f68,f139,f135]) ).
fof(f159,plain,
~ spl2_14,
inference(avatar_split_clause,[],[f85,f139]) ).
fof(f162,plain,
spl2_5,
inference(avatar_split_clause,[],[f75,f103]) ).
fof(f176,plain,
spl2_9,
inference(avatar_split_clause,[],[f79,f119]) ).
fof(f186,plain,
spl2_3,
inference(avatar_split_clause,[],[f83,f95]) ).
fof(f193,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_4
| ~ spl2_6 ),
inference(superposition,[],[f100,f108]) ).
fof(f207,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl2_4
| ~ spl2_6
| ~ spl2_10 ),
inference(superposition,[],[f124,f193]) ).
fof(f230,plain,
( $false
| ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| spl2_13 ),
inference(resolution,[],[f207,f137]) ).
fof(f234,plain,
( ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| spl2_13 ),
inference(avatar_contradiction_clause,[],[f230]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f101]) ).
cnf(s3,plain,
( ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f125]) ).
cnf(s7,plain,
( ~ spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s10,plain,
~ spl2_14,
inference(sat_conversion,[],[f159]) ).
cnf(s12,plain,
spl2_5,
inference(sat_conversion,[],[f162]) ).
cnf(s20,plain,
spl2_9,
inference(sat_conversion,[],[f176]) ).
cnf(s26,plain,
spl2_3,
inference(sat_conversion,[],[f186]) ).
cnf(s27,plain,
( ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| spl2_13 ),
inference(sat_conversion,[],[f234]) ).
cnf(s30,plain,
~ spl2_13,
inference(rat,[],[s7,s10]) ).
cnf(s32,plain,
spl2_10,
inference(rat,[],[s5,s20]) ).
cnf(s34,plain,
spl2_6,
inference(rat,[],[s3,s12]) ).
cnf(s35,plain,
~ spl2_4,
inference(rat,[],[s27,s30,s32,s34]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s2,s35,s26]) ).
fof(f236,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:48:31 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.12 % (2582681)Detected formulas, will run a generic FOF schedule.
% 3.14/1.12 % (2582689)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3310437863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.14/1.12 % (2582690)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3440950608:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.14/1.12 % (2582687)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=632105487:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.14/1.12 % (2582691)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1722434747:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.14/1.12 % (2582692)dis-21_1_sil=8000:lcm=predicate:random_seed=959042890: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)
% 3.14/1.12 % (2582686)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=171147344:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.14/1.12 % (2582688)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=1610676116:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.14/1.12 % (2582690)Refutation not found, incomplete strategy
% 3.14/1.12 % (2582690)------------------------------
% 3.14/1.12 % (2582690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.12 % (2582690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.12 % (2582690)CaDiCaL version: 2.1.3
% 3.14/1.12 % (2582690)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.12 % (2582690)Time elapsed: 0.001 s
% 3.14/1.12 % (2582689)Refutation not found, incomplete strategy
% 3.14/1.12 % (2582689)------------------------------
% 3.14/1.12 % (2582689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.12 % (2582690)Peak memory usage: 86 MB
% 3.14/1.12 % (2582689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.12 % (2582689)CaDiCaL version: 2.1.3
% 3.14/1.12 % (2582689)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.12 % (2582689)Time elapsed: 0.001 s
% 3.14/1.12 % (2582689)Peak memory usage: 86 MB
% 3.14/1.12 % (2582692)Refutation not found, incomplete strategy
% 3.14/1.12 % (2582692)------------------------------
% 3.14/1.12 % (2582692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.12 % (2582692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.12 % (2582692)CaDiCaL version: 2.1.3
% 3.14/1.12 % (2582692)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.12 % (2582692)Time elapsed: 0.002 s
% 3.14/1.12 % (2582692)Peak memory usage: 88 MB
% 3.14/1.12 % (2582692)Instructions burned: 1 (million)
% 3.14/1.12 % (2582691)First to succeed.
% 3.14/1.12 % (2582691)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2582681"
% 3.14/1.12 % (2582690)------------------------------
% 3.14/1.12 % (2582690)------------------------------
% 3.14/1.12 % (2582689)------------------------------
% 3.14/1.12 % (2582689)------------------------------
% 3.14/1.12 % (2582692)------------------------------
% 3.14/1.12 % (2582692)------------------------------
% 3.14/1.12 % (2582691)Refutation found. Thanks to Tanya!
% 3.14/1.12 % SZS status Theorem for theBenchmark
% 3.14/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.14/1.12 % (2582691)------------------------------
% 3.14/1.12 % (2582691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.12 % (2582691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.12 % (2582691)CaDiCaL version: 2.1.3
% 3.14/1.12 % (2582691)Termination reason: Refutation
% 3.14/1.12 % (2582691)Time elapsed: 0.005 s
% 3.14/1.12 % (2582691)Peak memory usage: 89 MB
% 3.14/1.12 % (2582691)Instructions burned: 5 (million)
% 3.14/1.12 % (2582691)------------------------------
% 3.14/1.12 % (2582691)------------------------------
% 3.14/1.12 % (2582681)Success in time 0.412 s
% 3.14/1.12 % Vampire exiting
%------------------------------------------------------------------------------