%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL540+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 : n014.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 11:52:53 AM UTC 2026
% Result : Theorem 3.59s 1.46s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 21 unt; 8 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 64 ~; 64 |; 10 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 12 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 33 !; 4 ?)
% 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(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f52,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f89,conjecture,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f90,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ adjunction,
inference(flattening,[],[f90]) ).
fof(f96,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) )
=> adjunction ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f112,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(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f137,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f138,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(flattening,[],[f137]) ).
fof(f146,plain,
( adjunction
| ( ~ is_a_theorem(and(sK0,sK1))
& is_a_theorem(sK0)
& is_a_theorem(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f138]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f155,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f126]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f175,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f184,plain,
( adjunction
| is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( adjunction
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f205,plain,
~ adjunction,
inference(cnf_transformation,[],[f91]) ).
fof(f263,definition,
( spl2_15
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f265,plain,
( is_a_theorem(sK1)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f267,definition,
( spl2_16
<=> adjunction ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f270,plain,
( spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f184,f267,f263]) ).
fof(f272,definition,
( spl2_17
<=> is_a_theorem(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f274,plain,
( is_a_theorem(sK0)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl2_17
| spl2_16 ),
inference(avatar_split_clause,[],[f185,f267,f272]) ).
fof(f277,definition,
( spl2_18
<=> is_a_theorem(and(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f279,plain,
( ~ is_a_theorem(and(sK0,sK1))
| spl2_18 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
( ~ spl2_18
| spl2_16 ),
inference(avatar_split_clause,[],[f186,f267,f277]) ).
fof(f362,definition,
( spl2_39
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl2_39])],[avatar_definition]) ).
fof(f366,definition,
( spl2_40
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_40])],[avatar_definition]) ).
fof(f367,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f368,plain,
( ~ spl2_39
| spl2_40 ),
inference(avatar_split_clause,[],[f155,f366,f362]) ).
fof(f426,definition,
( spl2_55
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_55])],[avatar_definition]) ).
fof(f430,definition,
( spl2_56
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_56])],[avatar_definition]) ).
fof(f431,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( ~ spl2_55
| spl2_56 ),
inference(avatar_split_clause,[],[f147,f430,f426]) ).
fof(f433,plain,
~ spl2_16,
inference(avatar_split_clause,[],[f205,f267]) ).
fof(f447,plain,
spl2_55,
inference(avatar_split_clause,[],[f168,f426]) ).
fof(f468,plain,
spl2_39,
inference(avatar_split_clause,[],[f175,f362]) ).
fof(f518,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,and(sK0,sK1)))
| ~ is_a_theorem(X0) )
| spl2_18
| ~ spl2_56 ),
inference(resolution,[],[f431,f279]) ).
fof(f536,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,and(sK0,sK1))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| spl2_18
| ~ spl2_56 ),
inference(resolution,[],[f518,f431]) ).
fof(f1090,plain,
( ~ is_a_theorem(sK0)
| ~ is_a_theorem(sK1)
| spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(resolution,[],[f536,f367]) ).
fof(f1110,plain,
( ~ is_a_theorem(sK1)
| ~ spl2_17
| spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(forward_subsumption_resolution,[],[f1090,f274]) ).
fof(f1111,plain,
( $false
| ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(forward_subsumption_resolution,[],[f1110,f265]) ).
fof(f1112,plain,
( ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(avatar_contradiction_clause,[],[f1111]) ).
cnf(s8,plain,
( spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f270]) ).
cnf(s9,plain,
( spl2_16
| spl2_17 ),
inference(sat_conversion,[],[f275]) ).
cnf(s10,plain,
( spl2_16
| ~ spl2_18 ),
inference(sat_conversion,[],[f280]) ).
cnf(s21,plain,
( ~ spl2_39
| spl2_40 ),
inference(sat_conversion,[],[f368]) ).
cnf(s29,plain,
( ~ spl2_55
| spl2_56 ),
inference(sat_conversion,[],[f432]) ).
cnf(s30,plain,
~ spl2_16,
inference(sat_conversion,[],[f433]) ).
cnf(s38,plain,
spl2_55,
inference(sat_conversion,[],[f447]) ).
cnf(s52,plain,
spl2_39,
inference(sat_conversion,[],[f468]) ).
cnf(s84,plain,
( ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s85,plain,
spl2_56,
inference(rat,[],[s29,s38]) ).
cnf(s93,plain,
spl2_40,
inference(rat,[],[s21,s52]) ).
cnf(s104,plain,
~ spl2_18,
inference(rat,[],[s10,s30]) ).
cnf(s105,plain,
spl2_17,
inference(rat,[],[s9,s30]) ).
cnf(s106,plain,
~ spl2_15,
inference(rat,[],[s84,s85,s93,s104,s105]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s8,s30,s106]) ).
fof(f1113,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:58:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.59/1.46 % (968811)Detected formulas, will run a generic FOF schedule.
% 3.59/1.46 % (968818)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=2806275666:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.46 % (968821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=362745091:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.46 % (968816)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=2139918853:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.46 % (968817)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=481125324:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.46 % (968819)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=376502643:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.46 % (968820)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2480272454:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.46 % (968822)dis-21_1_sil=8000:lcm=predicate:random_seed=2101356946: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)
% 3.59/1.46 % (968819)Refutation not found, incomplete strategy
% 3.59/1.46 % (968819)------------------------------
% 3.59/1.46 % (968819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (968819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (968820)Refutation not found, incomplete strategy
% 3.59/1.46 % (968820)------------------------------
% 3.59/1.46 % (968820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (968819)CaDiCaL version: 2.1.3
% 3.59/1.46 % (968820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (968819)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (968819)Time elapsed: 0.001 s
% 3.59/1.46 % (968819)Peak memory usage: 87 MB
% 3.59/1.46 % (968820)CaDiCaL version: 2.1.3
% 3.59/1.46 % (968820)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (968820)Time elapsed: 0.001 s
% 3.59/1.46 % (968820)Peak memory usage: 87 MB
% 3.59/1.46 % (968822)Refutation not found, incomplete strategy
% 3.59/1.46 % (968822)------------------------------
% 3.59/1.46 % (968822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (968822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (968822)CaDiCaL version: 2.1.3
% 3.59/1.46 % (968822)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (968822)Time elapsed: 0.002 s
% 3.59/1.46 % (968822)Peak memory usage: 88 MB
% 3.59/1.46 % (968822)Instructions burned: 1 (million)
% 3.59/1.46 % (968821)First to succeed.
% 3.59/1.46 % (968821)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-968811"
% 3.59/1.46 % (968822)------------------------------
% 3.59/1.46 % (968822)------------------------------
% 3.59/1.46 % (968819)------------------------------
% 3.59/1.46 % (968819)------------------------------
% 3.59/1.46 % (968820)------------------------------
% 3.59/1.46 % (968820)------------------------------
% 3.59/1.46 % (968821)Refutation found. Thanks to Tanya!
% 3.59/1.46 % SZS status Theorem for theBenchmark
% 3.59/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.46 % (968821)------------------------------
% 3.59/1.46 % (968821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (968821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (968821)CaDiCaL version: 2.1.3
% 3.59/1.46 % (968821)Termination reason: Refutation
% 3.59/1.46 % (968821)Time elapsed: 0.025 s
% 3.59/1.46 % (968821)Peak memory usage: 90 MB
% 3.59/1.46 % (968821)Instructions burned: 31 (million)
% 3.59/1.46 % (968821)------------------------------
% 3.59/1.46 % (968821)------------------------------
% 3.59/1.46 % (968811)Success in time 0.427 s
% 3.59/1.46 % Vampire exiting
%------------------------------------------------------------------------------