%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:52:31 AM UTC 2026
% Result : Theorem 2.37s 0.93s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 14 unt; 4 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 15 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f19,axiom,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f43,conjecture,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f44,negated_conjecture,
~ implies_3,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_3,
inference(flattening,[],[f44]) ).
fof(f48,plain,
( cn1
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f49,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> implies_3 ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f58,plain,
( implies_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f65,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f58]) ).
fof(f68,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f69,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f78,plain,
cn1,
inference(cnf_transformation,[],[f36]) ).
fof(f85,plain,
~ implies_3,
inference(cnf_transformation,[],[f45]) ).
fof(f127,definition,
( spl3_11
<=> cn1 ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f131,definition,
( spl3_12
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f132,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( ~ spl3_11
| spl3_12 ),
inference(avatar_split_clause,[],[f69,f131,f127]) ).
fof(f135,definition,
( spl3_13
<=> is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f137,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| spl3_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl3_14
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f142,plain,
( ~ spl3_13
| spl3_14 ),
inference(avatar_split_clause,[],[f68,f139,f135]) ).
fof(f159,plain,
~ spl3_14,
inference(avatar_split_clause,[],[f85,f139]) ).
fof(f168,plain,
spl3_11,
inference(avatar_split_clause,[],[f78,f127]) ).
fof(f192,plain,
( $false
| ~ spl3_12
| spl3_13 ),
inference(resolution,[],[f132,f137]) ).
fof(f195,plain,
( ~ spl3_12
| spl3_13 ),
inference(avatar_contradiction_clause,[],[f192]) ).
cnf(s6,plain,
( ~ spl3_11
| spl3_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
( ~ spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s10,plain,
~ spl3_14,
inference(sat_conversion,[],[f159]) ).
cnf(s16,plain,
spl3_11,
inference(sat_conversion,[],[f168]) ).
cnf(s27,plain,
( ~ spl3_12
| spl3_13 ),
inference(sat_conversion,[],[f195]) ).
cnf(s30,plain,
~ spl3_13,
inference(rat,[],[s7,s10]) ).
cnf(s31,plain,
~ spl3_12,
inference(rat,[],[s27,s30]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s6,s31,s16]) ).
fof(f196,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 15:48:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.37/0.93 % (2541084)Detected formulas, will run a generic FOF schedule.
% 2.37/0.93 % (2541093)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3084289060:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.37/0.93 % (2541094)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4022083783:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.37/0.93 % (2541091)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=3476855419:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.37/0.93 % (2541092)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1728114488:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.37/0.93 % (2541095)dis-21_1_sil=8000:lcm=predicate:random_seed=2693343411: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)
% 2.37/0.93 % (2541090)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=2244816991:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.37/0.93 % (2541089)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=4019970810:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.37/0.93 % (2541093)Refutation not found, incomplete strategy
% 2.37/0.93 % (2541093)------------------------------
% 2.37/0.93 % (2541093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.93 % (2541092)Refutation not found, incomplete strategy
% 2.37/0.93 % (2541092)------------------------------
% 2.37/0.93 % (2541092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.93 % (2541093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.93 % (2541092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.93 % (2541093)CaDiCaL version: 2.1.3
% 2.37/0.93 % (2541093)Termination reason: Refutation not found, incomplete strategy
% 2.37/0.93 % (2541093)Time elapsed: 0.0000 s
% 2.37/0.93 % (2541092)CaDiCaL version: 2.1.3
% 2.37/0.93 % (2541092)Termination reason: Refutation not found, incomplete strategy
% 2.37/0.93 % (2541092)Time elapsed: 0.0000 s
% 2.37/0.93 % (2541093)Peak memory usage: 86 MB
% 2.37/0.93 % (2541092)Peak memory usage: 86 MB
% 2.37/0.93 % (2541095)Refutation not found, incomplete strategy
% 2.37/0.93 % (2541095)------------------------------
% 2.37/0.93 % (2541095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.93 % (2541095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.93 % (2541095)CaDiCaL version: 2.1.3
% 2.37/0.93 % (2541095)Termination reason: Refutation not found, incomplete strategy
% 2.37/0.93 % (2541095)Time elapsed: 0.001 s
% 2.37/0.93 % (2541095)Peak memory usage: 88 MB
% 2.37/0.93 % (2541095)Instructions burned: 1 (million)
% 2.37/0.93 % (2541094)First to succeed.
% 2.37/0.93 % (2541094)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2541084"
% 2.37/0.93 % (2541092)------------------------------
% 2.37/0.93 % (2541092)------------------------------
% 2.37/0.93 % (2541093)------------------------------
% 2.37/0.93 % (2541093)------------------------------
% 2.37/0.93 % (2541095)------------------------------
% 2.37/0.93 % (2541095)------------------------------
% 2.37/0.93 % (2541094)Refutation found. Thanks to Tanya!
% 2.37/0.93 % SZS status Theorem for theBenchmark
% 2.37/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.93 % (2541094)------------------------------
% 2.37/0.93 % (2541094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.93 % (2541094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.93 % (2541094)CaDiCaL version: 2.1.3
% 2.37/0.93 % (2541094)Termination reason: Refutation
% 2.37/0.93 % (2541094)Time elapsed: 0.002 s
% 2.37/0.93 % (2541094)Peak memory usage: 89 MB
% 2.37/0.93 % (2541094)Instructions burned: 3 (million)
% 2.37/0.93 % (2541094)------------------------------
% 2.37/0.93 % (2541094)------------------------------
% 2.37/0.93 % (2541084)Success in time 0.303 s
% 2.37/0.93 % Vampire exiting
%------------------------------------------------------------------------------