%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL459+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 : 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 11:58:44 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 28 unt; 8 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 153 ( 71 ~; 62 |; 2 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 13 usr; 13 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 49 !; 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(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
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(f53,conjecture,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f54,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ kn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
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(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(f74,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f71]) ).
fof(f75,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f67]) ).
fof(f83,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f63]) ).
fof(f90,plain,
( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f90]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f94]) ).
fof(f117,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f120,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f124,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f135,plain,
~ kn1,
inference(cnf_transformation,[],[f55]) ).
fof(f136,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(X0)
| is_a_theorem(implies(X0,X1))
| modus_ponens ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f140,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| implies_2 ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f144,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| and_3 ),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f151,plain,
( ~ kn1
| is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f154,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f155,plain,
~ implies_2,
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f156,plain,
~ and_3,
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f161,plain,
kn1,
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f187,definition,
( spl1_7
<=> is_a_theorem(implies(sK0,and(sK0,sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f189,plain,
( is_a_theorem(implies(sK0,and(sK0,sK0)))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl1_8
<=> kn1 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f193,plain,
( ~ kn1
| spl1_8 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f151,f191,f187]) ).
fof(f244,definition,
( spl1_21
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f246,plain,
( and_3
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl1_22
<=> ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f249,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( spl1_21
| spl1_22 ),
inference(avatar_split_clause,[],[f144,f248,f244]) ).
fof(f276,definition,
( spl1_29
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition]) ).
fof(f278,plain,
( implies_2
| ~ spl1_29 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f280,definition,
( spl1_30
<=> ! [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition]) ).
fof(f281,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( spl1_29
| spl1_30 ),
inference(avatar_split_clause,[],[f140,f280,f276]) ).
fof(f308,definition,
( spl1_37
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition]) ).
fof(f310,plain,
( modus_ponens
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f312,definition,
( spl1_38
<=> ! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(X0)
| is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_38])],[avatar_definition]) ).
fof(f313,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f314,plain,
( spl1_37
| spl1_38 ),
inference(avatar_split_clause,[],[f136,f312,f308]) ).
fof(f321,plain,
( $false
| spl1_8 ),
inference(resolution,[],[f193,f161]) ).
fof(f322,plain,
spl1_8,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f335,plain,
( $false
| ~ spl1_21 ),
inference(resolution,[],[f246,f156]) ).
fof(f336,plain,
~ spl1_21,
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f343,plain,
( $false
| ~ spl1_29 ),
inference(resolution,[],[f278,f155]) ).
fof(f344,plain,
~ spl1_29,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f351,plain,
( $false
| ~ spl1_37 ),
inference(resolution,[],[f310,f154]) ).
fof(f352,plain,
~ spl1_37,
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f374,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f281,f313]) ).
fof(f408,plain,
( ! [X0] : ~ is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f374,f249]) ).
fof(f412,plain,
( $false
| ~ spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f408,f189]) ).
fof(f415,plain,
( ~ spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(avatar_contradiction_clause,[],[f412]) ).
cnf(s4,plain,
( spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f194]) ).
cnf(s11,plain,
( spl1_21
| spl1_22 ),
inference(sat_conversion,[],[f250]) ).
cnf(s15,plain,
( spl1_29
| spl1_30 ),
inference(sat_conversion,[],[f282]) ).
cnf(s19,plain,
( spl1_37
| spl1_38 ),
inference(sat_conversion,[],[f314]) ).
cnf(s23,plain,
spl1_8,
inference(sat_conversion,[],[f322]) ).
cnf(s30,plain,
~ spl1_21,
inference(sat_conversion,[],[f336]) ).
cnf(s34,plain,
~ spl1_29,
inference(sat_conversion,[],[f344]) ).
cnf(s38,plain,
~ spl1_37,
inference(sat_conversion,[],[f352]) ).
cnf(s40,plain,
( ~ spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(sat_conversion,[],[f415]) ).
cnf(s41,plain,
spl1_38,
inference(rat,[],[s19,s38]) ).
cnf(s45,plain,
spl1_30,
inference(rat,[],[s15,s34]) ).
cnf(s49,plain,
spl1_22,
inference(rat,[],[s11,s30]) ).
cnf(s50,plain,
~ spl1_7,
inference(rat,[],[s40,s41,s45,s49]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s4,s23,s50]) ).
fof(f416,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:45:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.46 % (2201730)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2201737)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2104539591:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (2201735)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1429220768_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (2201738)dis+10_1_sil=32000:sp=arity:random_seed=846865764:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2201739)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1496947820:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (2201740)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=100543845:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (2201741)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4161086900:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (2201741) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2201730-2201741"...
% 0.10/0.46 % (2201738) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2201730-2201738"...
% 0.10/0.46 % (2201739) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2201730-2201739"...
% 0.10/0.46 % (2201736)% WARNING: option uhcvi not known.
% 0.10/0.46 % (2201741)...printing done.
% 0.10/0.46 % (2201740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2201730-2201740"...
% 0.10/0.46 % (2201739)...printing done.
% 0.10/0.46 % (2201738)...printing done.
% 0.10/0.46 % (2201741)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2201741)------------------------------
% 0.10/0.46 % (2201741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2201741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2201741)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2201741)Termination reason: Refutation
% 0.10/0.46 % (2201741)Time elapsed: 0.006 s
% 0.10/0.46 % (2201741)Peak memory usage: 12 MB
% 0.10/0.46 % (2201741)Instructions burned: 6 (million)
% 0.10/0.46 % (2201730)Success in time 0.044 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------