%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL451+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 : n018.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 11:52:29 AM UTC 2026
% Result : Theorem 3.68s 1.45s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 42 ( 19 ~; 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(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f53,conjecture,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f54,negated_conjecture,
~ cn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> cn1 ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f66,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f81,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f66]) ).
fof(f91,plain,
( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f95,plain,
( cn1
| ~ 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)],[f91]) ).
fof(f101,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f122,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
~ cn1,
inference(cnf_transformation,[],[f55]) ).
fof(f161,definition,
( spl3_7
<=> is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f163,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| spl3_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl3_8
<=> cn1 ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f111,f165,f161]) ).
fof(f242,definition,
( spl3_27
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[spl3_27])],[avatar_definition]) ).
fof(f246,definition,
( spl3_28
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[spl3_28])],[avatar_definition]) ).
fof(f247,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ spl3_27
| spl3_28 ),
inference(avatar_split_clause,[],[f101,f246,f242]) ).
fof(f289,plain,
~ spl3_8,
inference(avatar_split_clause,[],[f135,f165]) ).
fof(f310,plain,
spl3_27,
inference(avatar_split_clause,[],[f122,f242]) ).
fof(f376,plain,
( $false
| spl3_7
| ~ spl3_28 ),
inference(resolution,[],[f247,f163]) ).
fof(f380,plain,
( spl3_7
| ~ spl3_28 ),
inference(avatar_contradiction_clause,[],[f376]) ).
cnf(s4,plain,
( ~ spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( ~ spl3_27
| spl3_28 ),
inference(sat_conversion,[],[f248]) ).
cnf(s20,plain,
~ spl3_8,
inference(sat_conversion,[],[f289]) ).
cnf(s34,plain,
spl3_27,
inference(sat_conversion,[],[f310]) ).
cnf(s58,plain,
( spl3_7
| ~ spl3_28 ),
inference(sat_conversion,[],[f380]) ).
cnf(s64,plain,
spl3_28,
inference(rat,[],[s14,s34]) ).
cnf(s65,plain,
spl3_7,
inference(rat,[],[s58,s64]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s4,s20,s65]) ).
fof(f383,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n018.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 15:47:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.68/1.45 % (2538060)Detected formulas, will run a generic FOF schedule.
% 3.68/1.45 % (2538068)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1606684494:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.45 % (2538068)Refutation not found, incomplete strategy
% 3.68/1.45 % (2538068)------------------------------
% 3.68/1.45 % (2538068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.45 % (2538068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.45 % (2538068)CaDiCaL version: 2.1.3
% 3.68/1.45 % (2538068)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.45 % (2538068)Time elapsed: 0.0000 s
% 3.68/1.45 % (2538068)Peak memory usage: 86 MB
% 3.68/1.45 % (2538065)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=1271814914:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.45 % (2538066)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=3128579832:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.45 % (2538070)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=376596346:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.45 % (2538069)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2860693236:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.45 % (2538067)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=2411160185:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.45 % (2538071)dis-21_1_sil=8000:lcm=predicate:random_seed=1330157767: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)
% 3.68/1.45 % (2538069)Refutation not found, incomplete strategy
% 3.68/1.45 % (2538069)------------------------------
% 3.68/1.45 % (2538069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.45 % (2538069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.45 % (2538069)CaDiCaL version: 2.1.3
% 3.68/1.45 % (2538069)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.45 % (2538069)Time elapsed: 0.001 s
% 3.68/1.45 % (2538069)Peak memory usage: 86 MB
% 3.68/1.45 % (2538071)Refutation not found, incomplete strategy
% 3.68/1.45 % (2538071)------------------------------
% 3.68/1.45 % (2538071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.45 % (2538071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.45 % (2538071)CaDiCaL version: 2.1.3
% 3.68/1.45 % (2538071)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.45 % (2538071)Time elapsed: 0.002 s
% 3.68/1.45 % (2538071)Peak memory usage: 88 MB
% 3.68/1.45 % (2538071)Instructions burned: 1 (million)
% 3.68/1.45 % (2538070)First to succeed.
% 3.68/1.45 % (2538070)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2538060"
% 3.68/1.45 % (2538068)------------------------------
% 3.68/1.45 % (2538068)------------------------------
% 3.68/1.45 % (2538071)------------------------------
% 3.68/1.45 % (2538071)------------------------------
% 3.68/1.45 % (2538069)------------------------------
% 3.68/1.45 % (2538069)------------------------------
% 3.68/1.45 % (2538079)lrs+10_1_sil=8000:sp=occurrence:random_seed=183025320:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.68/1.45 % (2538079)Refutation not found, incomplete strategy
% 3.68/1.45 % (2538079)------------------------------
% 3.68/1.45 % (2538079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.45 % (2538079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.45 % (2538079)CaDiCaL version: 2.1.3
% 3.68/1.45 % (2538079)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.45 % (2538079)Time elapsed: 0.0000 s
% 3.68/1.45 % (2538079)Peak memory usage: 87 MB
% 3.68/1.45 % (2538070)Refutation found. Thanks to Tanya!
% 3.68/1.45 % SZS status Theorem for theBenchmark
% 3.68/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.45 % (2538070)------------------------------
% 3.68/1.45 % (2538070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.45 % (2538070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.45 % (2538070)CaDiCaL version: 2.1.3
% 3.68/1.45 % (2538070)Termination reason: Refutation
% 3.68/1.45 % (2538070)Time elapsed: 0.006 s
% 3.68/1.45 % (2538070)Peak memory usage: 89 MB
% 3.68/1.45 % (2538070)Instructions burned: 6 (million)
% 3.68/1.45 % (2538070)------------------------------
% 3.68/1.45 % (2538070)------------------------------
% 3.68/1.45 % (2538060)Success in time 0.437 s
% 3.68/1.45 % Vampire exiting
%------------------------------------------------------------------------------