%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL544+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 : n004.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 11:58:54 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 103 ( 37 unt; 12 def)
% Number of atoms : 215 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 203 ( 91 ~; 83 |; 2 &)
% ( 17 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 67 !; 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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f66,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f90,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m4,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f108,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
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(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f108]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f136,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f97]) ).
fof(f141,plain,
( axiom_m4
| ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f149,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f153,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f126]) ).
fof(f166,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f169,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f173,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f181,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f186,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(cnf_transformation,[],[f141]) ).
fof(f188,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f191,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f198,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f201,plain,
~ axiom_m4,
inference(cnf_transformation,[],[f91]) ).
fof(f202,plain,
! [X0,X1] :
( modus_ponens
| is_a_theorem(implies(X0,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(consistent_polarity_flipping,[],[f145]) ).
fof(f206,plain,
! [X0,X1] :
( implies_2
| ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f210,plain,
! [X0,X1] :
( and_3
| ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(consistent_polarity_flipping,[],[f153]) ).
fof(f221,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f166]) ).
fof(f223,plain,
~ implies_2,
inference(consistent_polarity_flipping,[],[f169]) ).
fof(f226,plain,
~ and_3,
inference(consistent_polarity_flipping,[],[f173]) ).
fof(f231,plain,
! [X0] :
( ~ necessitation
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ),
inference(consistent_polarity_flipping,[],[f181]) ).
fof(f236,plain,
( is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(consistent_polarity_flipping,[],[f186]) ).
fof(f251,definition,
( spl1_3
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f252,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,definition,
( spl1_4
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f257,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f188,f254,f251]) ).
fof(f267,definition,
( spl1_7
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f271,definition,
( spl1_8
<=> is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f273,plain,
( is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f236,f271,f267]) ).
fof(f308,definition,
( spl1_17
<=> ! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f309,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,definition,
( spl1_18
<=> necessitation ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f314,plain,
( spl1_17
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f231,f311,f308]) ).
fof(f388,definition,
( spl1_37
<=> ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition]) ).
fof(f389,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f391,definition,
( spl1_38
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_38])],[avatar_definition]) ).
fof(f394,plain,
( spl1_37
| spl1_38 ),
inference(avatar_split_clause,[],[f210,f391,f388]) ).
fof(f420,definition,
( spl1_45
<=> ! [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_45])],[avatar_definition]) ).
fof(f421,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_45 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f423,definition,
( spl1_46
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_46])],[avatar_definition]) ).
fof(f426,plain,
( spl1_45
| spl1_46 ),
inference(avatar_split_clause,[],[f206,f423,f420]) ).
fof(f452,definition,
( spl1_53
<=> ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_53])],[avatar_definition]) ).
fof(f453,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1)
| is_a_theorem(X0) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f455,definition,
( spl1_54
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_54])],[avatar_definition]) ).
fof(f458,plain,
( spl1_53
| spl1_54 ),
inference(avatar_split_clause,[],[f202,f455,f452]) ).
fof(f459,plain,
~ spl1_7,
inference(avatar_split_clause,[],[f201,f267]) ).
fof(f467,plain,
spl1_18,
inference(avatar_split_clause,[],[f191,f311]) ).
fof(f470,plain,
spl1_4,
inference(avatar_split_clause,[],[f198,f254]) ).
fof(f473,plain,
~ spl1_54,
inference(avatar_split_clause,[],[f221,f455]) ).
fof(f475,plain,
~ spl1_46,
inference(avatar_split_clause,[],[f223,f423]) ).
fof(f478,plain,
~ spl1_38,
inference(avatar_split_clause,[],[f226,f391]) ).
fof(f488,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_3
| ~ spl1_17 ),
inference(superposition,[],[f309,f252]) ).
fof(f520,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,implies(X0,X1))) )
| ~ spl1_45
| ~ spl1_53 ),
inference(resolution,[],[f421,f453]) ).
fof(f545,plain,
( is_a_theorem(implies(sK0,and(sK0,sK0)))
| ~ spl1_3
| ~ spl1_8
| ~ spl1_17 ),
inference(resolution,[],[f488,f273]) ).
fof(f642,plain,
( is_a_theorem(implies(sK0,implies(sK0,and(sK0,sK0))))
| ~ spl1_3
| ~ spl1_8
| ~ spl1_17
| ~ spl1_45
| ~ spl1_53 ),
inference(resolution,[],[f520,f545]) ).
fof(f645,plain,
( $false
| ~ spl1_3
| ~ spl1_8
| ~ spl1_17
| ~ spl1_37
| ~ spl1_45
| ~ spl1_53 ),
inference(forward_subsumption_resolution,[],[f642,f389]) ).
fof(f646,plain,
( ~ spl1_3
| ~ spl1_8
| ~ spl1_17
| ~ spl1_37
| ~ spl1_45
| ~ spl1_53 ),
inference(avatar_contradiction_clause,[],[f645]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f257]) ).
cnf(s4,plain,
( spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f274]) ).
cnf(s9,plain,
( spl1_17
| ~ spl1_18 ),
inference(sat_conversion,[],[f314]) ).
cnf(s19,plain,
( spl1_37
| spl1_38 ),
inference(sat_conversion,[],[f394]) ).
cnf(s23,plain,
( spl1_45
| spl1_46 ),
inference(sat_conversion,[],[f426]) ).
cnf(s27,plain,
( spl1_53
| spl1_54 ),
inference(sat_conversion,[],[f458]) ).
cnf(s28,plain,
~ spl1_7,
inference(sat_conversion,[],[f459]) ).
cnf(s36,plain,
spl1_18,
inference(sat_conversion,[],[f467]) ).
cnf(s40,plain,
spl1_4,
inference(sat_conversion,[],[f470]) ).
cnf(s44,plain,
~ spl1_54,
inference(sat_conversion,[],[f473]) ).
cnf(s46,plain,
~ spl1_46,
inference(sat_conversion,[],[f475]) ).
cnf(s49,plain,
~ spl1_38,
inference(sat_conversion,[],[f478]) ).
cnf(s59,plain,
( ~ spl1_3
| ~ spl1_8
| ~ spl1_17
| ~ spl1_37
| ~ spl1_45
| ~ spl1_53 ),
inference(sat_conversion,[],[f646]) ).
cnf(s60,plain,
spl1_53,
inference(rat,[],[s27,s44]) ).
cnf(s64,plain,
spl1_45,
inference(rat,[],[s23,s46]) ).
cnf(s68,plain,
spl1_37,
inference(rat,[],[s19,s49]) ).
cnf(s78,plain,
spl1_17,
inference(rat,[],[s9,s36]) ).
cnf(s83,plain,
spl1_8,
inference(rat,[],[s4,s28]) ).
cnf(s84,plain,
~ spl1_3,
inference(rat,[],[s59,s60,s64,s68,s78,s83]) ).
cnf(s86,plain,
$false,
inference(rat,[],[s2,s40,s84]) ).
fof(f647,plain,
$false,
inference(avatar_sat_refutation,[],[s86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:58:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.44 % (3696387)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3696393)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3696393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3667210530:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % (3696393) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3696387-3696393"...
% 0.11/0.44 % (3696393)...printing done.
% 0.11/0.44 % (3696392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4140294291_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % (3696394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1243772615:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (3696395)dis+10_1_sil=32000:sp=arity:random_seed=4078088692:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (3696397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2126029288:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (3696398)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2217173054:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (3696393)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3696393)------------------------------
% 0.11/0.45 % (3696393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3696393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3696393)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3696393)Termination reason: Refutation
% 0.11/0.45 % (3696393)Time elapsed: 0.006 s
% 0.11/0.45 % (3696393)Peak memory usage: 13 MB
% 0.11/0.45 % (3696393)Instructions burned: 13 (million)
% 0.11/0.45 % (3696387)Success in time 0.036 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------