%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL529+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 11:58:52 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 28 unt; 8 def)
% Number of atoms : 151 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 129 ( 59 ~; 53 |; 0 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f64,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f89,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m2,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
=> axiom_m2 ),
inference(unused_predicate_definition_removal,[],[f64]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f104,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f104]) ).
fof(f134,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f95]) ).
fof(f138,plain,
( axiom_m2
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f91]) ).
fof(f140,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f142,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f138]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f169,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f179,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f134]) ).
fof(f183,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f185,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m2,
inference(cnf_transformation,[],[f90]) ).
fof(f201,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| and_1 ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f213,plain,
~ and_1,
inference(consistent_polarity_flipping,[],[f169]) ).
fof(f218,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| necessitation ),
inference(consistent_polarity_flipping,[],[f179]) ).
fof(f219,plain,
( ~ axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(consistent_polarity_flipping,[],[f183]) ).
fof(f221,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| op_strict_implies ),
inference(consistent_polarity_flipping,[],[f185]) ).
fof(f224,plain,
~ necessitation,
inference(consistent_polarity_flipping,[],[f188]) ).
fof(f227,plain,
~ op_strict_implies,
inference(consistent_polarity_flipping,[],[f194]) ).
fof(f229,plain,
axiom_m2,
inference(consistent_polarity_flipping,[],[f197]) ).
fof(f239,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f241,plain,
( op_strict_implies
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f244,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f221,f243,f239]) ).
fof(f255,definition,
( spl2_7
<=> is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f257,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| spl2_7 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl2_8
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f261,plain,
( ~ axiom_m2
| spl2_8 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f219,f259,f255]) ).
fof(f288,definition,
( spl2_15
<=> necessitation ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f290,plain,
( necessitation
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f292,definition,
( spl2_16
<=> ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f293,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f218,f292,f288]) ).
fof(f384,definition,
( spl2_39
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl2_39])],[avatar_definition]) ).
fof(f386,plain,
( and_1
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f388,definition,
( spl2_40
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_40])],[avatar_definition]) ).
fof(f389,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f390,plain,
( spl2_39
| spl2_40 ),
inference(avatar_split_clause,[],[f201,f388,f384]) ).
fof(f439,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f241,f227]) ).
fof(f440,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f443,plain,
( $false
| spl2_8 ),
inference(resolution,[],[f261,f229]) ).
fof(f444,plain,
spl2_8,
inference(avatar_contradiction_clause,[],[f443]) ).
fof(f451,plain,
( $false
| ~ spl2_15 ),
inference(resolution,[],[f290,f224]) ).
fof(f452,plain,
~ spl2_15,
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f475,plain,
( $false
| ~ spl2_39 ),
inference(resolution,[],[f386,f213]) ).
fof(f476,plain,
~ spl2_39,
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f490,plain,
( ~ is_a_theorem(necessarily(implies(and(sK0,sK1),sK0)))
| ~ spl2_4
| spl2_7 ),
inference(superposition,[],[f257,f244]) ).
fof(f504,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| ~ spl2_4
| spl2_7
| ~ spl2_16 ),
inference(resolution,[],[f490,f293]) ).
fof(f505,plain,
( $false
| ~ spl2_4
| spl2_7
| ~ spl2_16
| ~ spl2_40 ),
inference(resolution,[],[f504,f389]) ).
fof(f507,plain,
( ~ spl2_4
| spl2_7
| ~ spl2_16
| ~ spl2_40 ),
inference(avatar_contradiction_clause,[],[f505]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s4,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(sat_conversion,[],[f262]) ).
cnf(s8,plain,
( spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f294]) ).
cnf(s20,plain,
( spl2_39
| spl2_40 ),
inference(sat_conversion,[],[f390]) ).
cnf(s27,plain,
~ spl2_3,
inference(sat_conversion,[],[f440]) ).
cnf(s29,plain,
spl2_8,
inference(sat_conversion,[],[f444]) ).
cnf(s33,plain,
~ spl2_15,
inference(sat_conversion,[],[f452]) ).
cnf(s45,plain,
~ spl2_39,
inference(sat_conversion,[],[f476]) ).
cnf(s52,plain,
( ~ spl2_4
| spl2_7
| ~ spl2_16
| ~ spl2_40 ),
inference(sat_conversion,[],[f507]) ).
cnf(s59,plain,
spl2_40,
inference(rat,[],[s20,s45]) ).
cnf(s71,plain,
spl2_16,
inference(rat,[],[s8,s33]) ).
cnf(s75,plain,
~ spl2_7,
inference(rat,[],[s4,s29]) ).
cnf(s76,plain,
~ spl2_4,
inference(rat,[],[s52,s59,s71,s75]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s2,s76,s27]) ).
fof(f508,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL529+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n002.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 15:58:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % (3705812)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3705831)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3146406394:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (3705831) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3705812-3705831"...
% 0.12/0.45 % (3705831)...printing done.
% 0.12/0.45 % (3705826)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3705831)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3705831)------------------------------
% 0.12/0.45 % (3705831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3705831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3705831)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3705831)Termination reason: Refutation
% 0.12/0.45 % (3705831)Time elapsed: 0.003 s
% 0.12/0.45 % (3705831)Peak memory usage: 12 MB
% 0.12/0.45 % (3705831)Instructions burned: 6 (million)
% 0.12/0.45 % (3705812)Success in time 0.034 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------