%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL538+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 : n005.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 11:52:53 AM UTC 2026
% Result : Theorem 2.89s 1.28s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 26 unt; 10 def)
% Number of atoms : 192 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 189 ( 79 ~; 79 |; 10 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 43 ( 0 sgn 39 !; 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',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f90,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f90]) ).
fof(f94,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,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(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(f137,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,[],[f96]) ).
fof(f138,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(flattening,[],[f137]) ).
fof(f140,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f94]) ).
fof(f144,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f146,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)],[f138]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f184,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f188,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f140]) ).
fof(f192,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f144]) ).
fof(f197,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f202,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f205,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f91]) ).
fof(f215,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f219,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f220,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f192,f219,f215]) ).
fof(f247,definition,
( spl2_11
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f251,definition,
( spl2_12
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f252,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f188,f251,f247]) ).
fof(f263,definition,
( spl2_15
<=> is_a_theorem(strict_implies(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f265,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f267,definition,
( spl2_16
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f270,plain,
( spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f184,f267,f263]) ).
fof(f272,definition,
( spl2_17
<=> is_a_theorem(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f274,plain,
( is_a_theorem(sK0)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl2_17
| spl2_16 ),
inference(avatar_split_clause,[],[f185,f267,f272]) ).
fof(f277,definition,
( spl2_18
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f279,plain,
( ~ is_a_theorem(sK1)
| spl2_18 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
( ~ spl2_18
| spl2_16 ),
inference(avatar_split_clause,[],[f186,f267,f277]) ).
fof(f426,definition,
( spl2_55
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_55])],[avatar_definition]) ).
fof(f430,definition,
( spl2_56
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_56])],[avatar_definition]) ).
fof(f431,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( ~ spl2_55
| spl2_56 ),
inference(avatar_split_clause,[],[f147,f430,f426]) ).
fof(f433,plain,
~ spl2_16,
inference(avatar_split_clause,[],[f205,f267]) ).
fof(f436,plain,
spl2_55,
inference(avatar_split_clause,[],[f168,f426]) ).
fof(f487,plain,
spl2_11,
inference(avatar_split_clause,[],[f197,f247]) ).
fof(f496,plain,
spl2_3,
inference(avatar_split_clause,[],[f202,f215]) ).
fof(f500,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_12
| ~ spl2_56 ),
inference(resolution,[],[f252,f431]) ).
fof(f528,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ spl2_4
| ~ spl2_12
| ~ spl2_56 ),
inference(superposition,[],[f500,f220]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_4
| ~ spl2_12
| ~ spl2_56 ),
inference(resolution,[],[f528,f431]) ).
fof(f639,plain,
( ~ is_a_theorem(sK0)
| is_a_theorem(sK1)
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_56 ),
inference(resolution,[],[f558,f265]) ).
fof(f643,plain,
( is_a_theorem(sK1)
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17
| ~ spl2_56 ),
inference(forward_subsumption_resolution,[],[f639,f274]) ).
fof(f644,plain,
( $false
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_56 ),
inference(forward_subsumption_resolution,[],[f643,f279]) ).
fof(f645,plain,
( ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_56 ),
inference(avatar_contradiction_clause,[],[f644]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f221]) ).
cnf(s6,plain,
( ~ spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f253]) ).
cnf(s8,plain,
( spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f270]) ).
cnf(s9,plain,
( spl2_16
| spl2_17 ),
inference(sat_conversion,[],[f275]) ).
cnf(s10,plain,
( spl2_16
| ~ spl2_18 ),
inference(sat_conversion,[],[f280]) ).
cnf(s29,plain,
( ~ spl2_55
| spl2_56 ),
inference(sat_conversion,[],[f432]) ).
cnf(s30,plain,
~ spl2_16,
inference(sat_conversion,[],[f433]) ).
cnf(s32,plain,
spl2_55,
inference(sat_conversion,[],[f436]) ).
cnf(s66,plain,
spl2_11,
inference(sat_conversion,[],[f487]) ).
cnf(s72,plain,
spl2_3,
inference(sat_conversion,[],[f496]) ).
cnf(s83,plain,
( ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17
| spl2_18
| ~ spl2_56 ),
inference(sat_conversion,[],[f645]) ).
cnf(s84,plain,
spl2_56,
inference(rat,[],[s29,s32]) ).
cnf(s103,plain,
~ spl2_18,
inference(rat,[],[s10,s30]) ).
cnf(s104,plain,
spl2_17,
inference(rat,[],[s9,s30]) ).
cnf(s105,plain,
spl2_15,
inference(rat,[],[s8,s30]) ).
cnf(s107,plain,
spl2_12,
inference(rat,[],[s6,s66]) ).
cnf(s108,plain,
~ spl2_4,
inference(rat,[],[s83,s84,s103,s104,s105,s107]) ).
cnf(s112,plain,
$false,
inference(rat,[],[s2,s108,s72]) ).
fof(f646,plain,
$false,
inference(avatar_sat_refutation,[],[s112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:57:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.89/1.28 % (4169442)Detected formulas, will run a generic FOF schedule.
% 2.89/1.28 % (4169451)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1441892130:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.89/1.28 % (4169451)Refutation not found, incomplete strategy
% 2.89/1.28 % (4169451)------------------------------
% 2.89/1.28 % (4169451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (4169451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (4169451)CaDiCaL version: 2.1.3
% 2.89/1.28 % (4169451)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.28 % (4169451)Time elapsed: 0.001 s
% 2.89/1.28 % (4169451)Peak memory usage: 87 MB
% 2.89/1.28 % (4169447)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=1392869720:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.89/1.28 % (4169453)dis-21_1_sil=8000:lcm=predicate:random_seed=3737428321: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)
% 2.89/1.28 % (4169449)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=3974856567:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.89/1.28 % (4169448)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=1316890179:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.89/1.28 % (4169450)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3965599091:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.89/1.28 % (4169452)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1370873652:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.89/1.28 % (4169450)Refutation not found, incomplete strategy
% 2.89/1.28 % (4169450)------------------------------
% 2.89/1.28 % (4169450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (4169450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (4169450)CaDiCaL version: 2.1.3
% 2.89/1.28 % (4169450)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.28 % (4169450)Time elapsed: 0.001 s
% 2.89/1.28 % (4169450)Peak memory usage: 87 MB
% 2.89/1.28 % (4169453)Refutation not found, incomplete strategy
% 2.89/1.28 % (4169453)------------------------------
% 2.89/1.28 % (4169453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (4169453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (4169453)CaDiCaL version: 2.1.3
% 2.89/1.28 % (4169453)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.28 % (4169453)Time elapsed: 0.002 s
% 2.89/1.28 % (4169453)Peak memory usage: 88 MB
% 2.89/1.28 % (4169453)Instructions burned: 1 (million)
% 2.89/1.28 % (4169452)First to succeed.
% 2.89/1.28 % (4169452)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4169442"
% 2.89/1.28 % (4169451)------------------------------
% 2.89/1.28 % (4169451)------------------------------
% 2.89/1.28 % (4169453)------------------------------
% 2.89/1.28 % (4169453)------------------------------
% 2.89/1.28 % (4169450)------------------------------
% 2.89/1.28 % (4169450)------------------------------
% 2.89/1.28 % (4169461)lrs+10_1_sil=8000:sp=occurrence:random_seed=2980842002:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.89/1.28 % (4169461)Refutation not found, incomplete strategy
% 2.89/1.28 % (4169461)------------------------------
% 2.89/1.28 % (4169461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.28 % (4169461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.28 % (4169461)CaDiCaL version: 2.1.3
% 2.89/1.28 % (4169461)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.28 % (4169461)Time elapsed: 0.001 s
% 2.89/1.28 % (4169461)Peak memory usage: 88 MB
% 2.89/1.28 % (4169452)Refutation found. Thanks to Tanya!
% 2.89/1.28 % SZS status Theorem for theBenchmark
% 2.89/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.48 % (4169452)------------------------------
% 3.71/1.48 % (4169452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.48 % (4169452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.48 % (4169452)CaDiCaL version: 2.1.3
% 3.71/1.48 % (4169452)Termination reason: Refutation
% 3.71/1.48 % (4169452)Time elapsed: 0.012 s
% 3.71/1.48 % (4169452)Peak memory usage: 90 MB
% 3.71/1.48 % (4169452)Instructions burned: 14 (million)
% 3.71/1.48 % (4169452)------------------------------
% 3.71/1.48 % (4169452)------------------------------
% 3.71/1.48 % (4169442)Success in time 0.448 s
% 3.71/1.48 % Vampire exiting
%------------------------------------------------------------------------------