%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL455+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 : n005.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 3.19s 1.11s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 14 unt; 4 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 15 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f53,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f54,negated_conjecture,
~ r2,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r2,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f61,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f83,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f61]) ).
fof(f88,plain,
( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f88]) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f94]) ).
fof(f128,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f137,plain,
~ r2,
inference(cnf_transformation,[],[f55]) ).
fof(f179,definition,
( spl2_11
<=> is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f181,plain,
( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
| spl2_11 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl2_12
<=> r2 ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f186,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f110,f183,f179]) ).
fof(f220,definition,
( spl2_21
<=> or_2 ),
introduced(definition,[new_symbols(definition,[spl2_21])],[avatar_definition]) ).
fof(f224,definition,
( spl2_22
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl2_22])],[avatar_definition]) ).
fof(f225,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( ~ spl2_21
| spl2_22 ),
inference(avatar_split_clause,[],[f105,f224,f220]) ).
fof(f307,plain,
~ spl2_12,
inference(avatar_split_clause,[],[f137,f183]) ).
fof(f348,plain,
spl2_21,
inference(avatar_split_clause,[],[f128,f220]) ).
fof(f370,plain,
( $false
| spl2_11
| ~ spl2_22 ),
inference(resolution,[],[f225,f181]) ).
fof(f371,plain,
( spl2_11
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f370]) ).
cnf(s6,plain,
( ~ spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f186]) ).
cnf(s11,plain,
( ~ spl2_21
| spl2_22 ),
inference(sat_conversion,[],[f226]) ).
cnf(s22,plain,
~ spl2_12,
inference(sat_conversion,[],[f307]) ).
cnf(s48,plain,
spl2_21,
inference(sat_conversion,[],[f348]) ).
cnf(s63,plain,
( spl2_11
| ~ spl2_22 ),
inference(sat_conversion,[],[f371]) ).
cnf(s74,plain,
spl2_22,
inference(rat,[],[s11,s48]) ).
cnf(s75,plain,
spl2_11,
inference(rat,[],[s63,s74]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s6,s22,s75]) ).
fof(f372,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:44:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.19/1.11 % (4163400)Detected formulas, will run a generic FOF schedule.
% 3.19/1.11 % (4163409)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3529204969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.19/1.11 % (4163406)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=1584826232:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.19/1.11 % (4163410)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2979625572:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.19/1.11 % (4163407)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=1460782844:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.19/1.11 % (4163405)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=4022221703:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.19/1.11 % (4163411)dis-21_1_sil=8000:lcm=predicate:random_seed=2188898441: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)
% 3.19/1.11 % (4163408)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2744037193:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.19/1.11 % (4163409)Refutation not found, incomplete strategy
% 3.19/1.11 % (4163409)------------------------------
% 3.19/1.11 % (4163409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.11 % (4163409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.11 % (4163409)CaDiCaL version: 2.1.3
% 3.19/1.11 % (4163408)Refutation not found, incomplete strategy
% 3.19/1.11 % (4163408)------------------------------
% 3.19/1.11 % (4163408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.11 % (4163409)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.11 % (4163409)Time elapsed: 0.001 s
% 3.19/1.11 % (4163409)Peak memory usage: 86 MB
% 3.19/1.11 % (4163408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.11 % (4163408)CaDiCaL version: 2.1.3
% 3.19/1.11 % (4163408)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.11 % (4163408)Time elapsed: 0.001 s
% 3.19/1.11 % (4163408)Peak memory usage: 86 MB
% 3.19/1.11 % (4163411)Refutation not found, incomplete strategy
% 3.19/1.11 % (4163411)------------------------------
% 3.19/1.11 % (4163411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.11 % (4163411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.11 % (4163411)CaDiCaL version: 2.1.3
% 3.19/1.11 % (4163411)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.11 % (4163411)Time elapsed: 0.002 s
% 3.19/1.11 % (4163411)Peak memory usage: 88 MB
% 3.19/1.11 % (4163411)Instructions burned: 2 (million)
% 3.19/1.11 % (4163410)First to succeed.
% 3.19/1.11 % (4163410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4163400"
% 3.19/1.11 % (4163411)------------------------------
% 3.19/1.11 % (4163411)------------------------------
% 3.19/1.11 % (4163409)------------------------------
% 3.19/1.11 % (4163409)------------------------------
% 3.19/1.11 % (4163408)------------------------------
% 3.19/1.11 % (4163408)------------------------------
% 3.19/1.11 % (4163410)Refutation found. Thanks to Tanya!
% 3.19/1.11 % SZS status Theorem for theBenchmark
% 3.19/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.19/1.11 % (4163410)------------------------------
% 3.19/1.11 % (4163410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.11 % (4163410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.11 % (4163410)CaDiCaL version: 2.1.3
% 3.19/1.11 % (4163410)Termination reason: Refutation
% 3.19/1.11 % (4163410)Time elapsed: 0.004 s
% 3.19/1.11 % (4163410)Peak memory usage: 89 MB
% 3.19/1.11 % (4163410)Instructions burned: 4 (million)
% 3.19/1.11 % (4163410)------------------------------
% 3.19/1.11 % (4163410)------------------------------
% 3.19/1.11 % (4163400)Success in time 0.417 s
% 3.19/1.11 % Vampire exiting
%------------------------------------------------------------------------------