%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL484+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 : n006.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 11:52:35 AM UTC 2026
% Result : Theorem 4.86s 1.89s
% Output : Refutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 19 unt; 6 def)
% Number of atoms : 86 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 31 ~; 25 |; 0 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f45,conjecture,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f46,negated_conjecture,
~ implies_1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ implies_1,
inference(flattening,[],[f46]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
=> implies_1 ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f59,plain,
( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f61,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f51]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f73,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f82,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f97,plain,
~ implies_1,
inference(cnf_transformation,[],[f47]) ).
fof(f107,definition,
( spl2_3
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f111,definition,
( spl2_4
<=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f112,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f82,f111,f107]) ).
fof(f163,definition,
( spl2_17
<=> r2 ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f167,definition,
( spl2_18
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f168,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( ~ spl2_17
| spl2_18 ),
inference(avatar_split_clause,[],[f75,f167,f163]) ).
fof(f179,definition,
( spl2_21
<=> is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_21])],[avatar_definition]) ).
fof(f181,plain,
( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| spl2_21 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl2_22
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[spl2_22])],[avatar_definition]) ).
fof(f186,plain,
( ~ spl2_21
| spl2_22 ),
inference(avatar_split_clause,[],[f73,f183,f179]) ).
fof(f203,plain,
~ spl2_22,
inference(avatar_split_clause,[],[f97,f183]) ).
fof(f206,plain,
spl2_3,
inference(avatar_split_clause,[],[f84,f107]) ).
fof(f218,plain,
spl2_17,
inference(avatar_split_clause,[],[f89,f163]) ).
fof(f234,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1)))
| ~ spl2_4
| ~ spl2_18 ),
inference(superposition,[],[f168,f112]) ).
fof(f249,plain,
( $false
| ~ spl2_4
| ~ spl2_18
| spl2_21 ),
inference(resolution,[],[f234,f181]) ).
fof(f250,plain,
( ~ spl2_4
| ~ spl2_18
| spl2_21 ),
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
( ~ spl2_17
| spl2_18 ),
inference(sat_conversion,[],[f169]) ).
cnf(s11,plain,
( ~ spl2_21
| spl2_22 ),
inference(sat_conversion,[],[f186]) ).
cnf(s14,plain,
~ spl2_22,
inference(sat_conversion,[],[f203]) ).
cnf(s16,plain,
spl2_3,
inference(sat_conversion,[],[f206]) ).
cnf(s24,plain,
spl2_17,
inference(sat_conversion,[],[f218]) ).
cnf(s39,plain,
( ~ spl2_4
| ~ spl2_18
| spl2_21 ),
inference(sat_conversion,[],[f250]) ).
cnf(s42,plain,
~ spl2_21,
inference(rat,[],[s11,s14]) ).
cnf(s44,plain,
spl2_18,
inference(rat,[],[s9,s24]) ).
cnf(s45,plain,
~ spl2_4,
inference(rat,[],[s39,s42,s44]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s2,s45,s16]) ).
fof(f251,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL484+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 : n006.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 15:49:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 4.86/1.89 % (3128318)Detected formulas, will run a generic FOF schedule.
% 4.86/1.89 % (3128336)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=1670863732:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.86/1.89 % (3128340)dis-21_1_sil=8000:lcm=predicate:random_seed=2867032347: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)
% 4.86/1.89 % (3128340)Refutation not found, incomplete strategy
% 4.86/1.89 % (3128340)------------------------------
% 4.86/1.89 % (3128340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.89 % (3128340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.89 % (3128340)CaDiCaL version: 2.1.3
% 4.86/1.89 % (3128340)Termination reason: Refutation not found, incomplete strategy
% 4.86/1.89 % (3128340)Time elapsed: 0.002 s
% 4.86/1.89 % (3128340)Peak memory usage: 88 MB
% 4.86/1.89 % (3128340)Instructions burned: 1 (million)
% 4.86/1.89 % (3128334)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=2043897378:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.86/1.89 % (3128339)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3188072728:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.86/1.89 % (3128335)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=101245262:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.86/1.89 % (3128338)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2027306023:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.86/1.89 % (3128337)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1828673734:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.86/1.89 % (3128338)Refutation not found, incomplete strategy
% 4.86/1.89 % (3128338)------------------------------
% 4.86/1.89 % (3128338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.89 % (3128338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.89 % (3128338)CaDiCaL version: 2.1.3
% 4.86/1.89 % (3128338)Termination reason: Refutation not found, incomplete strategy
% 4.86/1.89 % (3128338)Time elapsed: 0.001 s
% 4.86/1.89 % (3128338)Peak memory usage: 86 MB
% 4.86/1.89 % (3128337)Refutation not found, incomplete strategy
% 4.86/1.89 % (3128337)------------------------------
% 4.86/1.89 % (3128337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.89 % (3128337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.89 % (3128337)CaDiCaL version: 2.1.3
% 4.86/1.89 % (3128337)Termination reason: Refutation not found, incomplete strategy
% 4.86/1.89 % (3128337)Time elapsed: 0.001 s
% 4.86/1.89 % (3128337)Peak memory usage: 86 MB
% 4.86/1.89 % (3128339)First to succeed.
% 4.86/1.89 % (3128339)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3128318"
% 4.86/1.89 % (3128338)------------------------------
% 4.86/1.89 % (3128338)------------------------------
% 4.86/1.89 % (3128339)Refutation found. Thanks to Tanya!
% 4.86/1.89 % SZS status Theorem for theBenchmark
% 4.86/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 4.86/1.89 % (3128339)------------------------------
% 4.86/1.89 % (3128339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.89 % (3128339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.89 % (3128339)CaDiCaL version: 2.1.3
% 4.86/1.89 % (3128339)Termination reason: Refutation
% 4.86/1.89 % (3128339)Time elapsed: 0.006 s
% 4.86/1.89 % (3128339)Peak memory usage: 90 MB
% 4.86/1.89 % (3128339)Instructions burned: 4 (million)
% 4.86/1.89 % (3128339)------------------------------
% 4.86/1.89 % (3128339)------------------------------
% 4.86/1.89 % (3128318)Success in time 0.569 s
% 4.86/1.89 % Vampire exiting
%------------------------------------------------------------------------------