%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL454+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 : 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 2.47s 1.23s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 85 ( 29 unt; 10 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 76 ~; 72 |; 2 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 16 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 62 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f53,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f54,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
=> r1 ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f60,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f68,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f71,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f72,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f71]) ).
fof(f73,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f68]) ).
fof(f77,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f67]) ).
fof(f84,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f60]) ).
fof(f88,plain,
( r1
| ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f73]) ).
fof(f98,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
( r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f119,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f121,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f129,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f137,plain,
~ r1,
inference(cnf_transformation,[],[f55]) ).
fof(f179,definition,
( spl1_11
<=> is_a_theorem(implies(or(sK0,sK0),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f181,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| spl1_11 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl1_12
<=> r1 ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f186,plain,
( ~ spl1_11
| spl1_12 ),
inference(avatar_split_clause,[],[f110,f183,f179]) ).
fof(f212,definition,
( spl1_19
<=> or_3 ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f216,definition,
( spl1_20
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f217,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( ~ spl1_19
| spl1_20 ),
inference(avatar_split_clause,[],[f106,f216,f212]) ).
fof(f268,definition,
( spl1_33
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_33])],[avatar_definition]) ).
fof(f272,definition,
( spl1_34
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_34])],[avatar_definition]) ).
fof(f273,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( ~ spl1_33
| spl1_34 ),
inference(avatar_split_clause,[],[f99,f272,f268]) ).
fof(f276,definition,
( spl1_35
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition]) ).
fof(f280,definition,
( spl1_36
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition]) ).
fof(f281,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( ~ spl1_35
| spl1_36 ),
inference(avatar_split_clause,[],[f98,f280,f276]) ).
fof(f300,definition,
( spl1_41
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_41])],[avatar_definition]) ).
fof(f304,definition,
( spl1_42
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_42])],[avatar_definition]) ).
fof(f305,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f306,plain,
( ~ spl1_41
| spl1_42 ),
inference(avatar_split_clause,[],[f95,f304,f300]) ).
fof(f307,plain,
~ spl1_12,
inference(avatar_split_clause,[],[f137,f183]) ).
fof(f321,plain,
spl1_41,
inference(avatar_split_clause,[],[f119,f300]) ).
fof(f327,plain,
spl1_35,
inference(avatar_split_clause,[],[f121,f276]) ).
fof(f330,plain,
spl1_33,
inference(avatar_split_clause,[],[f122,f268]) ).
fof(f351,plain,
spl1_19,
inference(avatar_split_clause,[],[f129,f212]) ).
fof(f374,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,implies(or(sK0,sK0),sK0)))
| ~ is_a_theorem(X0) )
| spl1_11
| ~ spl1_42 ),
inference(resolution,[],[f305,f181]) ).
fof(f472,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,implies(or(sK0,sK0),sK0))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| spl1_11
| ~ spl1_42 ),
inference(resolution,[],[f374,f305]) ).
fof(f3267,plain,
( ~ is_a_theorem(implies(sK0,sK0))
| ~ is_a_theorem(implies(sK0,sK0))
| spl1_11
| ~ spl1_20
| ~ spl1_42 ),
inference(resolution,[],[f472,f217]) ).
fof(f3285,plain,
( ~ is_a_theorem(implies(sK0,sK0))
| spl1_11
| ~ spl1_20
| ~ spl1_42 ),
inference(duplicate_literal_removal,[],[f3267]) ).
fof(f3286,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,implies(sK0,sK0)))
| ~ is_a_theorem(X0) )
| spl1_11
| ~ spl1_20
| ~ spl1_42 ),
inference(resolution,[],[f3285,f305]) ).
fof(f3300,plain,
( ~ is_a_theorem(implies(sK0,implies(sK0,sK0)))
| spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f3286,f273]) ).
fof(f3313,plain,
( $false
| spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(forward_subsumption_resolution,[],[f3300,f281]) ).
fof(f3314,plain,
( spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(avatar_contradiction_clause,[],[f3313]) ).
cnf(s6,plain,
( ~ spl1_11
| spl1_12 ),
inference(sat_conversion,[],[f186]) ).
cnf(s10,plain,
( ~ spl1_19
| spl1_20 ),
inference(sat_conversion,[],[f218]) ).
cnf(s17,plain,
( ~ spl1_33
| spl1_34 ),
inference(sat_conversion,[],[f274]) ).
cnf(s18,plain,
( ~ spl1_35
| spl1_36 ),
inference(sat_conversion,[],[f282]) ).
cnf(s21,plain,
( ~ spl1_41
| spl1_42 ),
inference(sat_conversion,[],[f306]) ).
cnf(s22,plain,
~ spl1_12,
inference(sat_conversion,[],[f307]) ).
cnf(s30,plain,
spl1_41,
inference(sat_conversion,[],[f321]) ).
cnf(s34,plain,
spl1_35,
inference(sat_conversion,[],[f327]) ).
cnf(s36,plain,
spl1_33,
inference(sat_conversion,[],[f330]) ).
cnf(s50,plain,
spl1_19,
inference(sat_conversion,[],[f351]) ).
cnf(s64,plain,
( spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(sat_conversion,[],[f3314]) ).
cnf(s65,plain,
spl1_42,
inference(rat,[],[s21,s30]) ).
cnf(s68,plain,
spl1_36,
inference(rat,[],[s18,s34]) ).
cnf(s69,plain,
spl1_34,
inference(rat,[],[s17,s36]) ).
cnf(s76,plain,
spl1_20,
inference(rat,[],[s10,s50]) ).
cnf(s77,plain,
spl1_11,
inference(rat,[],[s64,s65,s68,s69,s76]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s6,s22,s77]) ).
fof(f3315,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 15:45:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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
% 2.47/1.23 % (1408162)Detected formulas, will run a generic FOF schedule.
% 2.47/1.23 % (1408191)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2770550009:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.47/1.23 % (1408183)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=1343638283:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.47/1.23 % (1408184)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=3230685274:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.47/1.23 % (1408186)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=175185762:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.47/1.23 % (1408188)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=741610665:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.47/1.23 % (1408189)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2817098896:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.47/1.23 % (1408189)Refutation not found, incomplete strategy
% 2.47/1.23 % (1408189)------------------------------
% 2.47/1.23 % (1408189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.23 % (1408189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.23 % (1408189)CaDiCaL version: 2.1.3
% 2.47/1.23 % (1408188)Refutation not found, incomplete strategy
% 2.47/1.23 % (1408188)------------------------------
% 2.47/1.23 % (1408188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.23 % (1408189)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.23 % (1408189)Time elapsed: 0.001 s
% 2.47/1.23 % (1408189)Peak memory usage: 86 MB
% 2.47/1.23 % (1408188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.23 % (1408188)CaDiCaL version: 2.1.3
% 2.47/1.23 % (1408188)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.23 % (1408188)Time elapsed: 0.001 s
% 2.47/1.23 % (1408188)Peak memory usage: 86 MB
% 2.47/1.23 % (1408191)First to succeed.
% 2.47/1.23 % (1408191)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1408162"
% 2.47/1.23 % (1408193)dis-21_1_sil=8000:lcm=predicate:random_seed=990975637: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)
% 2.47/1.23 % (1408193)Refutation not found, incomplete strategy
% 2.47/1.23 % (1408193)------------------------------
% 2.47/1.23 % (1408193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.23 % (1408193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.23 % (1408193)CaDiCaL version: 2.1.3
% 2.47/1.23 % (1408193)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.23 % (1408193)Time elapsed: 0.002 s
% 2.47/1.23 % (1408193)Peak memory usage: 88 MB
% 2.47/1.23 % (1408193)Instructions burned: 2 (million)
% 2.47/1.23 % (1408191)Refutation found. Thanks to Tanya!
% 2.47/1.23 % SZS status Theorem for theBenchmark
% 2.47/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.87/1.42 % (1408191)------------------------------
% 2.87/1.42 % (1408191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.42 % (1408191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.42 % (1408191)CaDiCaL version: 2.1.3
% 2.87/1.42 % (1408191)Termination reason: Refutation
% 2.87/1.42 % (1408191)Time elapsed: 0.042 s
% 2.87/1.42 % (1408191)Peak memory usage: 92 MB
% 2.87/1.42 % (1408191)Instructions burned: 108 (million)
% 2.87/1.42 % (1408191)------------------------------
% 2.87/1.42 % (1408191)------------------------------
% 2.87/1.42 % (1408162)Success in time 0.305 s
% 2.87/1.42 % Vampire exiting
%------------------------------------------------------------------------------