%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL506+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 : n013.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 11:52:38 AM UTC 2026
% Result : Theorem 3.38s 1.35s
% Output : Refutation 3.38s
% 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/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f43,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f44,negated_conjecture,
~ and_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ and_1,
inference(flattening,[],[f44]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> and_1 ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f54,plain,
( and_1
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f57,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f59,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f54]) ).
fof(f63,plain,
~ and_1,
inference(cnf_transformation,[],[f45]) ).
fof(f70,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f57]) ).
fof(f77,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f94,definition,
( spl3_3
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f95,plain,
( ~ kn2
| spl3_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl3_4
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f98,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f73,f97,f94]) ).
fof(f115,definition,
( spl3_9
<=> is_a_theorem(implies(and(sK0,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f116,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| spl3_9 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl3_10
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f119,plain,
( and_1
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( ~ spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f70,f118,f115]) ).
fof(f152,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f77,f95]) ).
fof(f153,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f154,plain,
( $false
| ~ spl3_4
| spl3_9 ),
inference(resolution,[],[f98,f116]) ).
fof(f155,plain,
( ~ spl3_4
| spl3_9 ),
inference(avatar_contradiction_clause,[],[f154]) ).
fof(f156,plain,
( $false
| ~ spl3_10 ),
inference(resolution,[],[f119,f63]) ).
fof(f157,plain,
~ spl3_10,
inference(avatar_contradiction_clause,[],[f156]) ).
cnf(s2,plain,
( ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f99]) ).
cnf(s5,plain,
( ~ spl3_9
| spl3_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s14,plain,
spl3_3,
inference(sat_conversion,[],[f153]) ).
cnf(s15,plain,
( ~ spl3_4
| spl3_9 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
~ spl3_10,
inference(sat_conversion,[],[f157]) ).
cnf(s20,plain,
~ spl3_9,
inference(rat,[],[s5,s16]) ).
cnf(s21,plain,
~ spl3_4,
inference(rat,[],[s15,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s2,s21,s14]) ).
fof(f158,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.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 15:53:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 3.38/1.35 % (376154)Detected formulas, will run a generic FOF schedule.
% 3.38/1.35 % (376159)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=802559394:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.35 % (376165)dis-21_1_sil=8000:lcm=predicate:random_seed=1311269927: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)
% 3.38/1.35 % (376165)First to succeed.
% 3.38/1.35 % (376164)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3121202756:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.35 % (376163)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1708871937:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.35 % (376161)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=2065527949:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.35 % (376162)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1571102850:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.35 % (376160)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=1160267770:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.35 % (376165)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-376154"
% 3.38/1.35 % (376163)Refutation not found, incomplete strategy
% 3.38/1.35 % (376163)------------------------------
% 3.38/1.35 % (376163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.35 % (376163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.35 % (376163)CaDiCaL version: 2.1.3
% 3.38/1.35 % (376163)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.35 % (376163)Time elapsed: 0.0000 s
% 3.38/1.35 % (376163)Peak memory usage: 86 MB
% 3.38/1.35 % (376162)Refutation not found, incomplete strategy
% 3.38/1.35 % (376162)------------------------------
% 3.38/1.35 % (376162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.35 % (376162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.35 % (376162)CaDiCaL version: 2.1.3
% 3.38/1.35 % (376162)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.35 % (376162)Time elapsed: 0.001 s
% 3.38/1.35 % (376162)Peak memory usage: 86 MB
% 3.38/1.35 % (376164)Also succeeded, but the first one will report.
% 3.38/1.35 % (376162)------------------------------
% 3.38/1.35 % (376162)------------------------------
% 3.38/1.35 % (376163)------------------------------
% 3.38/1.35 % (376163)------------------------------
% 3.38/1.35 % (376165)Refutation found. Thanks to Tanya!
% 3.38/1.35 % SZS status Theorem for theBenchmark
% 3.38/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.35 % (376165)------------------------------
% 3.38/1.35 % (376165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.35 % (376165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.35 % (376165)CaDiCaL version: 2.1.3
% 3.38/1.35 % (376165)Termination reason: Refutation
% 3.38/1.35 % (376165)Time elapsed: 0.003 s
% 3.38/1.35 % (376165)Peak memory usage: 89 MB
% 3.38/1.35 % (376165)Instructions burned: 2 (million)
% 3.38/1.35 % (376165)------------------------------
% 3.38/1.35 % (376165)------------------------------
% 3.38/1.35 % (376154)Success in time 0.409 s
% 3.38/1.35 % Vampire exiting
%------------------------------------------------------------------------------