%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL460+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 : n008.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 11:52:30 AM UTC 2026
% Result : Theorem 3.55s 1.52s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 14 unt; 4 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 19 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f53,conjecture,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f54,negated_conjecture,
~ kn2,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ kn2,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> kn2 ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f62,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f68,plain,
( kn2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f73,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f62]) ).
fof(f77,plain,
( kn2
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f68]) ).
fof(f81,plain,
~ kn2,
inference(cnf_transformation,[],[f55]) ).
fof(f88,plain,
( kn2
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f93,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f101,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f134,definition,
( spl3_7
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f135,plain,
( ~ and_1
| spl3_7 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl3_8
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( ~ spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f93,f137,f134]) ).
fof(f169,definition,
( spl3_17
<=> is_a_theorem(implies(and(sK0,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f170,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| spl3_17 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,definition,
( spl3_18
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl3_18])],[avatar_definition]) ).
fof(f173,plain,
( kn2
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( ~ spl3_17
| spl3_18 ),
inference(avatar_split_clause,[],[f88,f172,f169]) ).
fof(f210,plain,
( $false
| spl3_7 ),
inference(resolution,[],[f101,f135]) ).
fof(f211,plain,
spl3_7,
inference(avatar_contradiction_clause,[],[f210]) ).
fof(f212,plain,
( $false
| ~ spl3_8
| spl3_17 ),
inference(resolution,[],[f138,f170]) ).
fof(f213,plain,
( ~ spl3_8
| spl3_17 ),
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f214,plain,
( $false
| ~ spl3_18 ),
inference(resolution,[],[f173,f81]) ).
fof(f215,plain,
~ spl3_18,
inference(avatar_contradiction_clause,[],[f214]) ).
cnf(s4,plain,
( ~ spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f139]) ).
cnf(s9,plain,
( ~ spl3_17
| spl3_18 ),
inference(sat_conversion,[],[f174]) ).
cnf(s20,plain,
spl3_7,
inference(sat_conversion,[],[f211]) ).
cnf(s21,plain,
( ~ spl3_8
| spl3_17 ),
inference(sat_conversion,[],[f213]) ).
cnf(s22,plain,
~ spl3_18,
inference(sat_conversion,[],[f215]) ).
cnf(s26,plain,
~ spl3_17,
inference(rat,[],[s9,s22]) ).
cnf(s27,plain,
~ spl3_8,
inference(rat,[],[s21,s26]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s4,s27,s20]) ).
fof(f216,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:45:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.55/1.52 % (1409005)Detected formulas, will run a generic FOF schedule.
% 3.55/1.52 % (1409049)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1223226781:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.52 % (1409049)Refutation not found, incomplete strategy
% 3.55/1.52 % (1409049)------------------------------
% 3.55/1.52 % (1409049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.52 % (1409049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.52 % (1409049)CaDiCaL version: 2.1.3
% 3.55/1.52 % (1409049)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.52 % (1409049)Time elapsed: 0.003 s
% 3.55/1.52 % (1409049)Peak memory usage: 86 MB
% 3.55/1.52 % (1409051)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2493869082:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.52 % (1409052)dis-21_1_sil=8000:lcm=predicate:random_seed=2275707276: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)
% 3.55/1.52 % (1409043)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=2657581274:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.52 % (1409046)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=3883325355:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.52 % (1409045)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=1268100732:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.52 % (1409052)First to succeed.
% 3.55/1.52 % (1409052)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1409005"
% 3.55/1.52 % (1409051)Also succeeded, but the first one will report.
% 3.55/1.52 % (1409048)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=745491270:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.52 % (1409048)Refutation not found, incomplete strategy
% 3.55/1.52 % (1409048)------------------------------
% 3.55/1.52 % (1409048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.52 % (1409048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.52 % (1409048)CaDiCaL version: 2.1.3
% 3.55/1.52 % (1409048)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.52 % (1409048)Time elapsed: 0.0000 s
% 3.55/1.52 % (1409048)Peak memory usage: 86 MB
% 3.55/1.52 % (1409048)------------------------------
% 3.55/1.52 % (1409048)------------------------------
% 3.55/1.52 % (1409049)------------------------------
% 3.55/1.52 % (1409049)------------------------------
% 3.55/1.52 % (1409137)lrs+10_1_sil=8000:sp=occurrence:random_seed=1930052241:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.55/1.52 % (1409137)Refutation not found, incomplete strategy
% 3.55/1.52 % (1409137)------------------------------
% 3.55/1.52 % (1409137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.52 % (1409137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.52 % (1409137)CaDiCaL version: 2.1.3
% 3.55/1.52 % (1409137)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.52 % (1409137)Time elapsed: 0.0000 s
% 3.55/1.52 % (1409137)Peak memory usage: 87 MB
% 3.55/1.52 % (1409052)Refutation found. Thanks to Tanya!
% 3.55/1.52 % SZS status Theorem for theBenchmark
% 3.55/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.52 % (1409052)------------------------------
% 3.55/1.52 % (1409052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.52 % (1409052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.52 % (1409052)CaDiCaL version: 2.1.3
% 3.55/1.52 % (1409052)Termination reason: Refutation
% 3.55/1.52 % (1409052)Time elapsed: 0.003 s
% 3.55/1.52 % (1409052)Peak memory usage: 89 MB
% 3.55/1.52 % (1409052)Instructions burned: 2 (million)
% 3.55/1.52 % (1409052)------------------------------
% 3.55/1.52 % (1409052)------------------------------
% 3.55/1.52 % (1409005)Success in time 0.395 s
% 3.55/1.52 % Vampire exiting
%------------------------------------------------------------------------------