%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 11:58:50 AM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 20 unt; 6 def)
% Number of atoms : 91 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 27 |; 0 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 34 ( 0 sgn 32 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f43,conjecture,
equivalence_1,
file('/export/starexec/sandbox/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(f66,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| equivalence_1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f68,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f75,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f78,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f84,plain,
~ equivalence_1,
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
( is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| equivalence_1 ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f89,plain,
! [X0,X1] :
( ~ kn2
| ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f93,plain,
! [X0,X1] :
( op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f72]) ).
fof(f96,plain,
~ op_equiv,
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f103,definition,
( spl2_1
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f104,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,definition,
( spl2_2
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f109,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f93,f106,f103]) ).
fof(f135,definition,
( spl2_9
<=> ! [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f136,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,definition,
( spl2_10
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f141,plain,
( spl2_9
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f89,f138,f135]) ).
fof(f151,definition,
( spl2_13
<=> equivalence_1 ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f155,definition,
( spl2_14
<=> is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f157,plain,
( is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f87,f155,f151]) ).
fof(f175,plain,
~ spl2_13,
inference(avatar_split_clause,[],[f84,f151]) ).
fof(f178,plain,
spl2_10,
inference(avatar_split_clause,[],[f78,f138]) ).
fof(f181,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f96,f106]) ).
fof(f204,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ spl2_1
| ~ spl2_9 ),
inference(superposition,[],[f136,f104]) ).
fof(f207,plain,
( $false
| ~ spl2_1
| ~ spl2_9
| ~ spl2_14 ),
inference(backward_subsumption_resolution,[],[f157,f204]) ).
fof(f210,plain,
( ~ spl2_1
| ~ spl2_9
| ~ spl2_14 ),
inference(avatar_contradiction_clause,[],[f207]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( spl2_9
| ~ spl2_10 ),
inference(sat_conversion,[],[f141]) ).
cnf(s7,plain,
( spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s10,plain,
~ spl2_13,
inference(sat_conversion,[],[f175]) ).
cnf(s13,plain,
spl2_10,
inference(sat_conversion,[],[f178]) ).
cnf(s16,plain,
~ spl2_2,
inference(sat_conversion,[],[f181]) ).
cnf(s22,plain,
( ~ spl2_1
| ~ spl2_9
| ~ spl2_14 ),
inference(sat_conversion,[],[f210]) ).
cnf(s25,plain,
spl2_14,
inference(rat,[],[s7,s10]) ).
cnf(s27,plain,
spl2_9,
inference(rat,[],[s5,s13]) ).
cnf(s28,plain,
~ spl2_1,
inference(rat,[],[s22,s25,s27]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s16,s28]) ).
fof(f211,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n017.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 15:50:36 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.48 % (2761559)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2761565)% WARNING: option uhcvi not known.
% 0.15/0.48 % (2761565)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1928451348:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2761565) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2761559-2761565"...
% 0.15/0.48 % (2761565)...printing done.
% 0.15/0.48 % (2761565)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2761565)------------------------------
% 0.15/0.48 % (2761565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2761565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2761565)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2761565)Termination reason: Refutation
% 0.15/0.48 % (2761565)Time elapsed: 0.002 s
% 0.15/0.48 % (2761565)Peak memory usage: 12 MB
% 0.15/0.48 % (2761565)Instructions burned: 3 (million)
% 0.15/0.48 % (2761559)Success in time 0.038 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------