%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL483+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 : n002.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 1.37s 1.80s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 29 unt; 10 def)
% Number of atoms : 141 ( 16 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 115 ( 52 ~; 46 |; 0 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
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(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f45,conjecture,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f46,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ modus_tollens,
inference(flattening,[],[f46]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> modus_tollens ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f59,plain,
( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f62,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f65,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f67,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f73,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f79,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f65]) ).
fof(f81,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f67]) ).
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(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f97,plain,
~ modus_tollens,
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(f115,definition,
( spl2_5
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f119,definition,
( spl2_6
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f120,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f121,plain,
( ~ spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f81,f119,f115]) ).
fof(f131,definition,
( spl2_9
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f135,definition,
( spl2_10
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f136,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f79,f135,f131]) ).
fof(f155,definition,
( spl2_15
<=> r3 ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f159,definition,
( spl2_16
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f160,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f161,plain,
( ~ spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f76,f159,f155]) ).
fof(f179,definition,
( spl2_21
<=> is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_21])],[avatar_definition]) ).
fof(f181,plain,
( ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1)))
| spl2_21 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl2_22
<=> modus_tollens ),
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(f225,plain,
spl2_15,
inference(avatar_split_clause,[],[f90,f155]) ).
fof(f237,plain,
spl2_9,
inference(avatar_split_clause,[],[f94,f131]) ).
fof(f240,plain,
spl2_5,
inference(avatar_split_clause,[],[f95,f115]) ).
fof(f244,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1)))
| ~ spl2_4
| ~ spl2_16 ),
inference(superposition,[],[f160,f112]) ).
fof(f258,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_6
| ~ spl2_10 ),
inference(forward_demodulation,[],[f136,f120]) ).
fof(f261,plain,
( ~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1)))
| ~ spl2_6
| ~ spl2_10
| spl2_21 ),
inference(superposition,[],[f181,f258]) ).
fof(f299,plain,
( $false
| ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| ~ spl2_16
| spl2_21 ),
inference(forward_subsumption_resolution,[],[f261,f244]) ).
fof(f300,plain,
( ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| ~ spl2_16
| spl2_21 ),
inference(avatar_contradiction_clause,[],[f299]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f137]) ).
cnf(s8,plain,
( ~ spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f161]) ).
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(s28,plain,
spl2_15,
inference(sat_conversion,[],[f225]) ).
cnf(s36,plain,
spl2_9,
inference(sat_conversion,[],[f237]) ).
cnf(s38,plain,
spl2_5,
inference(sat_conversion,[],[f240]) ).
cnf(s39,plain,
( ~ spl2_4
| ~ spl2_6
| ~ spl2_10
| ~ spl2_16
| spl2_21 ),
inference(sat_conversion,[],[f300]) ).
cnf(s42,plain,
~ spl2_21,
inference(rat,[],[s11,s14]) ).
cnf(s45,plain,
spl2_16,
inference(rat,[],[s8,s28]) ).
cnf(s48,plain,
spl2_10,
inference(rat,[],[s5,s36]) ).
cnf(s50,plain,
spl2_6,
inference(rat,[],[s3,s38]) ).
cnf(s51,plain,
~ spl2_4,
inference(rat,[],[s39,s42,s45,s48,s50]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s2,s51,s16]) ).
fof(f301,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 15:52:06 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 1.37/1.79 % (3701842)Detected formulas, will run a generic FOF schedule.
% 1.37/1.79 % (3701849)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=1853291356:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.37/1.79 % (3701855)dis-21_1_sil=8000:lcm=predicate:random_seed=2783886456: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)
% 1.37/1.79 % (3701855)Refutation not found, incomplete strategy
% 1.37/1.79 % (3701855)------------------------------
% 1.37/1.79 % (3701855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.37/1.79 % (3701855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/1.79 % (3701855)CaDiCaL version: 2.1.3
% 1.37/1.79 % (3701855)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.79 % (3701855)Time elapsed: 0.002 s
% 1.37/1.79 % (3701855)Peak memory usage: 88 MB
% 1.37/1.79 % (3701855)Instructions burned: 1 (million)
% 1.37/1.79 % (3701851)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=1303709247:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.37/1.80 % (3701853)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=205602432:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.37/1.80 % (3701852)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2554621047:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.37/1.80 % (3701850)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=2551708933:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.37/1.80 % (3701853)Refutation not found, incomplete strategy
% 1.37/1.80 % (3701853)------------------------------
% 1.37/1.80 % (3701853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.37/1.80 % (3701853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/1.80 % (3701852)Refutation not found, incomplete strategy
% 1.37/1.80 % (3701852)------------------------------
% 1.37/1.80 % (3701852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.37/1.80 % (3701853)CaDiCaL version: 2.1.3
% 1.37/1.80 % (3701853)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.80 % (3701853)Time elapsed: 0.001 s
% 1.37/1.80 % (3701852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/1.80 % (3701853)Peak memory usage: 86 MB
% 1.37/1.80 % (3701852)CaDiCaL version: 2.1.3
% 1.37/1.80 % (3701852)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.80 % (3701852)Time elapsed: 0.001 s
% 1.37/1.80 % (3701852)Peak memory usage: 87 MB
% 1.37/1.80 % (3701854)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1270451788:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.37/1.80 % (3701854)First to succeed.
% 1.37/1.80 % (3701854)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3701842"
% 1.37/1.80 % (3701855)------------------------------
% 1.37/1.80 % (3701855)------------------------------
% 1.37/1.80 % (3701852)------------------------------
% 1.37/1.80 % (3701852)------------------------------
% 1.37/1.80 % (3701853)------------------------------
% 1.37/1.80 % (3701853)------------------------------
% 1.37/1.80 % (3701854)Refutation found. Thanks to Tanya!
% 1.37/1.80 % SZS status Theorem for theBenchmark
% 1.37/1.80 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/2.12 % (3701854)------------------------------
% 6.10/2.12 % (3701854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.12 % (3701854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.12 % (3701854)CaDiCaL version: 2.1.3
% 6.10/2.12 % (3701854)Termination reason: Refutation
% 6.10/2.12 % (3701854)Time elapsed: 0.010 s
% 6.10/2.12 % (3701854)Peak memory usage: 90 MB
% 6.10/2.12 % (3701854)Instructions burned: 7 (million)
% 6.10/2.12 % (3701854)------------------------------
% 6.10/2.12 % (3701854)------------------------------
% 6.10/2.12 % (3701842)Success in time 0.736 s
% 6.10/2.12 % Vampire exiting
%------------------------------------------------------------------------------