%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL525+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 : 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 11:52:51 AM UTC 2026
% Result : Theorem 2.90s 1.29s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 26 unt; 10 def)
% Number of atoms : 189 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 183 ( 76 ~; 76 |; 10 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 40 !; 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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f51,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f89,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f89]) ).
fof(f92,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f94,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) )
=> modus_ponens_strict_implies ),
inference(unused_predicate_definition_removal,[],[f51]) ).
fof(f110,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(f115,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f115]) ).
fof(f135,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f136,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(flattening,[],[f135]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f92]) ).
fof(f141,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f143,plain,
( modus_ponens_strict_implies
| ( ~ is_a_theorem(sK1)
& is_a_theorem(sK0)
& is_a_theorem(strict_implies(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f136]) ).
fof(f144,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f116]) ).
fof(f165,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f181,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f182,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f183,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f185,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f141]) ).
fof(f193,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f197,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f200,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f90]) ).
fof(f210,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f214,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f188,f214,f210]) ).
fof(f234,definition,
( spl2_9
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f238,definition,
( spl2_10
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f239,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f185,f238,f234]) ).
fof(f250,definition,
( spl2_13
<=> is_a_theorem(strict_implies(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f252,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl2_14
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f257,plain,
( spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f181,f254,f250]) ).
fof(f259,definition,
( spl2_15
<=> is_a_theorem(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f261,plain,
( is_a_theorem(sK0)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl2_15
| spl2_14 ),
inference(avatar_split_clause,[],[f182,f254,f259]) ).
fof(f264,definition,
( spl2_16
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f266,plain,
( ~ is_a_theorem(sK1)
| spl2_16 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( ~ spl2_16
| spl2_14 ),
inference(avatar_split_clause,[],[f183,f254,f264]) ).
fof(f413,definition,
( spl2_53
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_53])],[avatar_definition]) ).
fof(f417,definition,
( spl2_54
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_54])],[avatar_definition]) ).
fof(f418,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( ~ spl2_53
| spl2_54 ),
inference(avatar_split_clause,[],[f144,f417,f413]) ).
fof(f420,plain,
~ spl2_14,
inference(avatar_split_clause,[],[f200,f254]) ).
fof(f423,plain,
spl2_53,
inference(avatar_split_clause,[],[f165,f413]) ).
fof(f474,plain,
spl2_9,
inference(avatar_split_clause,[],[f193,f234]) ).
fof(f480,plain,
spl2_3,
inference(avatar_split_clause,[],[f197,f210]) ).
fof(f494,plain,
( ! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1)))
| ~ spl2_4
| ~ spl2_10 ),
inference(superposition,[],[f239,f215]) ).
fof(f498,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,sK1))
| ~ is_a_theorem(X0) )
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f418,f266]) ).
fof(f503,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,sK1)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f498,f418]) ).
fof(f663,plain,
( ! [X0] :
( ~ is_a_theorem(strict_implies(X0,sK1))
| ~ is_a_theorem(X0) )
| ~ spl2_4
| ~ spl2_10
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f503,f494]) ).
fof(f703,plain,
( ~ is_a_theorem(sK0)
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f663,f252]) ).
fof(f707,plain,
( $false
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_54 ),
inference(forward_subsumption_resolution,[],[f703,f261]) ).
fof(f708,plain,
( ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_54 ),
inference(avatar_contradiction_clause,[],[f707]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f216]) ).
cnf(s5,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f240]) ).
cnf(s7,plain,
( spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f257]) ).
cnf(s8,plain,
( spl2_14
| spl2_15 ),
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( spl2_14
| ~ spl2_16 ),
inference(sat_conversion,[],[f267]) ).
cnf(s28,plain,
( ~ spl2_53
| spl2_54 ),
inference(sat_conversion,[],[f419]) ).
cnf(s29,plain,
~ spl2_14,
inference(sat_conversion,[],[f420]) ).
cnf(s31,plain,
spl2_53,
inference(sat_conversion,[],[f423]) ).
cnf(s65,plain,
spl2_9,
inference(sat_conversion,[],[f474]) ).
cnf(s69,plain,
spl2_3,
inference(sat_conversion,[],[f480]) ).
cnf(s80,plain,
( ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_54 ),
inference(sat_conversion,[],[f708]) ).
cnf(s81,plain,
spl2_54,
inference(rat,[],[s28,s31]) ).
cnf(s100,plain,
~ spl2_16,
inference(rat,[],[s9,s29]) ).
cnf(s101,plain,
spl2_15,
inference(rat,[],[s8,s29]) ).
cnf(s102,plain,
spl2_13,
inference(rat,[],[s7,s29]) ).
cnf(s104,plain,
spl2_10,
inference(rat,[],[s5,s65]) ).
cnf(s105,plain,
~ spl2_4,
inference(rat,[],[s80,s81,s100,s101,s102,s104]) ).
cnf(s108,plain,
$false,
inference(rat,[],[s2,s105,s69]) ).
fof(f709,plain,
$false,
inference(avatar_sat_refutation,[],[s108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL525+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:51:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.90/1.29 % (2763371)Detected formulas, will run a generic FOF schedule.
% 2.90/1.29 % (2763376)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=3605903737:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.90/1.29 % (2763380)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1177096119:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.90/1.29 % (2763377)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=2141799256:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.90/1.29 % (2763379)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2274452026:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.90/1.29 % (2763378)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=2457070151:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.90/1.29 % (2763381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1877201533:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.90/1.29 % (2763379)Refutation not found, incomplete strategy
% 2.90/1.29 % (2763379)------------------------------
% 2.90/1.29 % (2763379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.29 % (2763380)Refutation not found, incomplete strategy
% 2.90/1.29 % (2763380)------------------------------
% 2.90/1.29 % (2763380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.29 % (2763379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.29 % (2763380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.29 % (2763379)CaDiCaL version: 2.1.3
% 2.90/1.29 % (2763380)CaDiCaL version: 2.1.3
% 2.90/1.29 % (2763379)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.29 % (2763379)Time elapsed: 0.001 s
% 2.90/1.29 % (2763380)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.29 % (2763380)Time elapsed: 0.001 s
% 2.90/1.29 % (2763380)Peak memory usage: 87 MB
% 2.90/1.29 % (2763379)Peak memory usage: 87 MB
% 2.90/1.29 % (2763381)First to succeed.
% 2.90/1.29 % (2763381)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2763371"
% 2.90/1.29 % (2763382)dis-21_1_sil=8000:lcm=predicate:random_seed=2224800156: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)
% 2.90/1.29 % (2763382)Refutation not found, incomplete strategy
% 2.90/1.29 % (2763382)------------------------------
% 2.90/1.29 % (2763382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.29 % (2763382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.29 % (2763382)CaDiCaL version: 2.1.3
% 2.90/1.29 % (2763382)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.29 % (2763382)Time elapsed: 0.002 s
% 2.90/1.29 % (2763382)Peak memory usage: 88 MB
% 2.90/1.29 % (2763382)Instructions burned: 1 (million)
% 2.90/1.29 % (2763379)------------------------------
% 2.90/1.29 % (2763379)------------------------------
% 2.90/1.29 % (2763380)------------------------------
% 2.90/1.29 % (2763380)------------------------------
% 2.90/1.29 % (2763382)------------------------------
% 2.90/1.29 % (2763382)------------------------------
% 2.90/1.29 % (2763381)Refutation found. Thanks to Tanya!
% 2.90/1.29 % SZS status Theorem for theBenchmark
% 2.90/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.38 % (2763381)------------------------------
% 3.58/1.38 % (2763381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.38 % (2763381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.38 % (2763381)CaDiCaL version: 2.1.3
% 3.58/1.38 % (2763381)Termination reason: Refutation
% 3.58/1.38 % (2763381)Time elapsed: 0.015 s
% 3.58/1.38 % (2763381)Peak memory usage: 90 MB
% 3.58/1.38 % (2763381)Instructions burned: 17 (million)
% 3.58/1.38 % (2763381)------------------------------
% 3.58/1.38 % (2763381)------------------------------
% 3.58/1.38 % (2763371)Success in time 0.443 s
% 3.58/1.38 % Vampire exiting
%------------------------------------------------------------------------------