%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL512+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 : n009.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 11:52:49 AM UTC 2026
% Result : Theorem 3.34s 1.36s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 19 unt; 6 def)
% Number of atoms : 86 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 31 ~; 25 |; 0 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f43,conjecture,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f44,negated_conjecture,
~ equivalence_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ equivalence_1,
inference(flattening,[],[f44]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
=> equivalence_1 ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f57,plain,
( equivalence_1
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f63,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f67,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f63]) ).
fof(f76,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f85,plain,
~ equivalence_1,
inference(cnf_transformation,[],[f45]) ).
fof(f87,definition,
( spl2_1
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f91,definition,
( spl2_2
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f92,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f73,f91,f87]) ).
fof(f119,definition,
( spl2_9
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f123,definition,
( spl2_10
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f69,f123,f119]) ).
fof(f135,definition,
( spl2_13
<=> is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f137,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| spl2_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl2_14
<=> equivalence_1 ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f142,plain,
( ~ spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f67,f139,f135]) ).
fof(f159,plain,
~ spl2_14,
inference(avatar_split_clause,[],[f85,f139]) ).
fof(f165,plain,
spl2_1,
inference(avatar_split_clause,[],[f76,f87]) ).
fof(f174,plain,
spl2_9,
inference(avatar_split_clause,[],[f79,f119]) ).
fof(f187,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ spl2_2
| ~ spl2_10 ),
inference(superposition,[],[f124,f92]) ).
fof(f197,plain,
( $false
| ~ spl2_2
| ~ spl2_10
| spl2_13 ),
inference(resolution,[],[f187,f137]) ).
fof(f199,plain,
( ~ spl2_2
| ~ spl2_10
| spl2_13 ),
inference(avatar_contradiction_clause,[],[f197]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f93]) ).
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(s14,plain,
spl2_1,
inference(sat_conversion,[],[f165]) ).
cnf(s20,plain,
spl2_9,
inference(sat_conversion,[],[f174]) ).
cnf(s27,plain,
( ~ spl2_2
| ~ spl2_10
| spl2_13 ),
inference(sat_conversion,[],[f199]) ).
cnf(s30,plain,
~ spl2_13,
inference(rat,[],[s7,s10]) ).
cnf(s32,plain,
spl2_10,
inference(rat,[],[s5,s20]) ).
cnf(s33,plain,
~ spl2_2,
inference(rat,[],[s27,s30,s32]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s33,s14]) ).
fof(f200,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:55:15 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.34/1.36 % (2210928)Detected formulas, will run a generic FOF schedule.
% 3.34/1.36 % (2210939)dis-21_1_sil=8000:lcm=predicate:random_seed=2815130330: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)
% 3.34/1.36 % (2210939)Refutation not found, incomplete strategy
% 3.34/1.36 % (2210939)------------------------------
% 3.34/1.36 % (2210939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (2210939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (2210939)CaDiCaL version: 2.1.3
% 3.34/1.36 % (2210939)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.36 % (2210939)Time elapsed: 0.001 s
% 3.34/1.36 % (2210939)Peak memory usage: 88 MB
% 3.34/1.36 % (2210939)Instructions burned: 1 (million)
% 3.34/1.36 % (2210935)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=1298248868:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.36 % (2210936)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1970350784:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.36 % (2210937)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2127632974:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.36 % (2210934)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=926957046:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.36 % (2210933)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=2966649203:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.36 % (2210938)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1385838839:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.36 % (2210937)Refutation not found, incomplete strategy
% 3.34/1.36 % (2210937)------------------------------
% 3.34/1.36 % (2210937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (2210937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (2210936)Refutation not found, incomplete strategy
% 3.34/1.36 % (2210936)------------------------------
% 3.34/1.36 % (2210936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (2210937)CaDiCaL version: 2.1.3
% 3.34/1.36 % (2210937)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.36 % (2210937)Time elapsed: 0.001 s
% 3.34/1.36 % (2210936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (2210937)Peak memory usage: 86 MB
% 3.34/1.36 % (2210936)CaDiCaL version: 2.1.3
% 3.34/1.36 % (2210936)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.36 % (2210936)Time elapsed: 0.001 s
% 3.34/1.36 % (2210936)Peak memory usage: 87 MB
% 3.34/1.36 % (2210938)First to succeed.
% 3.34/1.36 % (2210938)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2210928"
% 3.34/1.36 % (2210939)------------------------------
% 3.34/1.36 % (2210939)------------------------------
% 3.34/1.36 % (2210947)lrs+10_1_sil=8000:sp=occurrence:random_seed=1247037025:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.34/1.36 % (2210947)Refutation not found, incomplete strategy
% 3.34/1.36 % (2210947)------------------------------
% 3.34/1.36 % (2210947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (2210947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (2210947)CaDiCaL version: 2.1.3
% 3.34/1.36 % (2210947)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.36 % (2210947)Time elapsed: 0.001 s
% 3.34/1.36 % (2210947)Peak memory usage: 88 MB
% 3.34/1.36 % (2210937)------------------------------
% 3.34/1.36 % (2210937)------------------------------
% 3.34/1.36 % (2210936)------------------------------
% 3.34/1.36 % (2210936)------------------------------
% 3.34/1.36 % (2210938)Refutation found. Thanks to Tanya!
% 3.34/1.36 % SZS status Theorem for theBenchmark
% 3.34/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.36 % (2210938)------------------------------
% 3.34/1.36 % (2210938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.36 % (2210938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.36 % (2210938)CaDiCaL version: 2.1.3
% 3.34/1.36 % (2210938)Termination reason: Refutation
% 3.34/1.36 % (2210938)Time elapsed: 0.005 s
% 3.34/1.36 % (2210938)Peak memory usage: 89 MB
% 3.34/1.36 % (2210938)Instructions burned: 4 (million)
% 3.34/1.36 % (2210938)------------------------------
% 3.34/1.36 % (2210938)------------------------------
% 3.34/1.36 % (2210928)Success in time 0.399 s
% 3.34/1.36 % Vampire exiting
%------------------------------------------------------------------------------