%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL527+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 11:52:51 AM UTC 2026
% Result : Theorem 2.94s 1.33s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 21 unt; 8 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 64 ~; 64 |; 10 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 12 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 33 !; 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(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f52,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f88,conjecture,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f89,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ adjunction,
inference(flattening,[],[f89]) ).
fof(f94,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) )
=> adjunction ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
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(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f102]) ).
fof(f135,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f136,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(flattening,[],[f135]) ).
fof(f143,plain,
( adjunction
| ( ~ is_a_theorem(and(sK0,sK1))
& is_a_theorem(sK0)
& is_a_theorem(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(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f165,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f172,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f181,plain,
( adjunction
| is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f182,plain,
( adjunction
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f183,plain,
( adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f200,plain,
~ adjunction,
inference(cnf_transformation,[],[f90]) ).
fof(f250,definition,
( spl2_13
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f252,plain,
( is_a_theorem(sK1)
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl2_14
<=> adjunction ),
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(and(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f266,plain,
( ~ is_a_theorem(and(sK0,sK1))
| spl2_16 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( ~ spl2_16
| spl2_14 ),
inference(avatar_split_clause,[],[f183,f254,f264]) ).
fof(f349,definition,
( spl2_37
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl2_37])],[avatar_definition]) ).
fof(f353,definition,
( spl2_38
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_38])],[avatar_definition]) ).
fof(f354,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( ~ spl2_37
| spl2_38 ),
inference(avatar_split_clause,[],[f152,f353,f349]) ).
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(f432,plain,
spl2_53,
inference(avatar_split_clause,[],[f165,f413]) ).
fof(f453,plain,
spl2_37,
inference(avatar_split_clause,[],[f172,f349]) ).
fof(f497,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,and(sK0,sK1)))
| ~ is_a_theorem(X0) )
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f418,f266]) ).
fof(f538,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,and(sK0,sK1))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| spl2_16
| ~ spl2_54 ),
inference(resolution,[],[f497,f418]) ).
fof(f990,plain,
( ~ is_a_theorem(sK0)
| ~ is_a_theorem(sK1)
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(resolution,[],[f538,f354]) ).
fof(f1008,plain,
( ~ is_a_theorem(sK1)
| ~ spl2_15
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(forward_subsumption_resolution,[],[f990,f261]) ).
fof(f1009,plain,
( $false
| ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(forward_subsumption_resolution,[],[f1008,f252]) ).
fof(f1010,plain,
( ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(avatar_contradiction_clause,[],[f1009]) ).
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(s20,plain,
( ~ spl2_37
| spl2_38 ),
inference(sat_conversion,[],[f355]) ).
cnf(s28,plain,
( ~ spl2_53
| spl2_54 ),
inference(sat_conversion,[],[f419]) ).
cnf(s29,plain,
~ spl2_14,
inference(sat_conversion,[],[f420]) ).
cnf(s37,plain,
spl2_53,
inference(sat_conversion,[],[f432]) ).
cnf(s51,plain,
spl2_37,
inference(sat_conversion,[],[f453]) ).
cnf(s81,plain,
( ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s82,plain,
spl2_54,
inference(rat,[],[s28,s37]) ).
cnf(s90,plain,
spl2_38,
inference(rat,[],[s20,s51]) ).
cnf(s101,plain,
~ spl2_16,
inference(rat,[],[s9,s29]) ).
cnf(s102,plain,
spl2_15,
inference(rat,[],[s8,s29]) ).
cnf(s103,plain,
~ spl2_13,
inference(rat,[],[s81,s82,s90,s101,s102]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s7,s29,s103]) ).
fof(f1011,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.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 15:56:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.94/1.33 % (4167632)Detected formulas, will run a generic FOF schedule.
% 2.94/1.33 % (4167641)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1960777928:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.33 % (4167641)Refutation not found, incomplete strategy
% 2.94/1.33 % (4167641)------------------------------
% 2.94/1.33 % (4167641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.33 % (4167641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.33 % (4167641)CaDiCaL version: 2.1.3
% 2.94/1.33 % (4167641)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.33 % (4167641)Time elapsed: 0.001 s
% 2.94/1.33 % (4167641)Peak memory usage: 87 MB
% 2.94/1.33 % (4167638)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=2622349028:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.33 % (4167637)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=2273429903:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.33 % (4167639)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=2706489776:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.33 % (4167640)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2324362505:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.33 % (4167640)Refutation not found, incomplete strategy
% 2.94/1.33 % (4167640)------------------------------
% 2.94/1.33 % (4167640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.33 % (4167640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.33 % (4167640)CaDiCaL version: 2.1.3
% 2.94/1.33 % (4167640)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.33 % (4167640)Time elapsed: 0.001 s
% 2.94/1.33 % (4167640)Peak memory usage: 87 MB
% 2.94/1.33 % (4167643)dis-21_1_sil=8000:lcm=predicate:random_seed=2008614388: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)
% 2.94/1.33 % (4167642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=118939421:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.33 % (4167643)Refutation not found, incomplete strategy
% 2.94/1.33 % (4167643)------------------------------
% 2.94/1.33 % (4167643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.33 % (4167643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.33 % (4167643)CaDiCaL version: 2.1.3
% 2.94/1.33 % (4167643)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.33 % (4167643)Time elapsed: 0.002 s
% 2.94/1.33 % (4167643)Peak memory usage: 88 MB
% 2.94/1.33 % (4167643)Instructions burned: 1 (million)
% 2.94/1.33 % (4167642)First to succeed.
% 2.94/1.33 % (4167642)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4167632"
% 2.94/1.33 % (4167641)------------------------------
% 2.94/1.33 % (4167641)------------------------------
% 2.94/1.33 % (4167651)lrs+10_1_sil=8000:sp=occurrence:random_seed=1724761354:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.94/1.33 % (4167651)Refutation not found, incomplete strategy
% 2.94/1.33 % (4167651)------------------------------
% 2.94/1.33 % (4167651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.33 % (4167651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.33 % (4167651)CaDiCaL version: 2.1.3
% 2.94/1.33 % (4167651)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.33 % (4167651)Time elapsed: 0.001 s
% 2.94/1.33 % (4167651)Peak memory usage: 88 MB
% 2.94/1.33 % (4167640)------------------------------
% 2.94/1.33 % (4167640)------------------------------
% 2.94/1.33 % (4167643)------------------------------
% 2.94/1.33 % (4167643)------------------------------
% 2.94/1.33 % (4167642)Refutation found. Thanks to Tanya!
% 2.94/1.33 % SZS status Theorem for theBenchmark
% 2.94/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.54 % (4167642)------------------------------
% 3.93/1.54 % (4167642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.54 % (4167642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.54 % (4167642)CaDiCaL version: 2.1.3
% 3.93/1.54 % (4167642)Termination reason: Refutation
% 3.93/1.54 % (4167642)Time elapsed: 0.021 s
% 3.93/1.54 % (4167642)Peak memory usage: 90 MB
% 3.93/1.54 % (4167642)Instructions burned: 27 (million)
% 3.93/1.54 % (4167642)------------------------------
% 3.93/1.54 % (4167642)------------------------------
% 3.93/1.54 % (4167632)Success in time 0.469 s
% 3.93/1.54 % Vampire exiting
%------------------------------------------------------------------------------