%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL542+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 : n014.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 11:52:54 AM UTC 2026
% Result : Theorem 3.77s 1.49s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 24 unt; 8 def)
% Number of atoms : 123 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 47 ~; 41 |; 0 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 36 ( 0 sgn 34 !; 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(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f64,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f90,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m2,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
=> axiom_m2 ),
inference(unused_predicate_definition_removal,[],[f64]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f106,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f136,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f97]) ).
fof(f141,plain,
( axiom_m2
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f92]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,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)],[f141]) ).
fof(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f172,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f136]) ).
fof(f187,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f189,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f143]) ).
fof(f192,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f199,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
~ axiom_m2,
inference(cnf_transformation,[],[f91]) ).
fof(f212,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f216,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f217,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f189,f216,f212]) ).
fof(f228,definition,
( spl2_7
<=> is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f230,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| spl2_7 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl2_8
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f235,plain,
( ~ spl2_7
| spl2_8 ),
inference(avatar_split_clause,[],[f187,f232,f228]) ).
fof(f269,definition,
( spl2_17
<=> necessitation ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f273,definition,
( spl2_18
<=> ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f274,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ spl2_17
| spl2_18 ),
inference(avatar_split_clause,[],[f182,f273,f269]) ).
fof(f365,definition,
( spl2_41
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl2_41])],[avatar_definition]) ).
fof(f369,definition,
( spl2_42
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_42])],[avatar_definition]) ).
fof(f370,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f371,plain,
( ~ spl2_41
| spl2_42 ),
inference(avatar_split_clause,[],[f152,f369,f365]) ).
fof(f420,plain,
~ spl2_8,
inference(avatar_split_clause,[],[f202,f232]) ).
fof(f447,plain,
spl2_41,
inference(avatar_split_clause,[],[f172,f365]) ).
fof(f477,plain,
spl2_17,
inference(avatar_split_clause,[],[f192,f269]) ).
fof(f492,plain,
spl2_3,
inference(avatar_split_clause,[],[f199,f212]) ).
fof(f501,plain,
( ! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_4
| ~ spl2_18 ),
inference(superposition,[],[f274,f217]) ).
fof(f505,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| ~ spl2_4
| spl2_7
| ~ spl2_18 ),
inference(resolution,[],[f501,f230]) ).
fof(f506,plain,
( $false
| ~ spl2_4
| spl2_7
| ~ spl2_18
| ~ spl2_42 ),
inference(forward_subsumption_resolution,[],[f505,f370]) ).
fof(f507,plain,
( ~ spl2_4
| spl2_7
| ~ spl2_18
| ~ spl2_42 ),
inference(avatar_contradiction_clause,[],[f506]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f218]) ).
cnf(s4,plain,
( ~ spl2_7
| spl2_8 ),
inference(sat_conversion,[],[f235]) ).
cnf(s9,plain,
( ~ spl2_17
| spl2_18 ),
inference(sat_conversion,[],[f275]) ).
cnf(s21,plain,
( ~ spl2_41
| spl2_42 ),
inference(sat_conversion,[],[f371]) ).
cnf(s28,plain,
~ spl2_8,
inference(sat_conversion,[],[f420]) ).
cnf(s46,plain,
spl2_41,
inference(sat_conversion,[],[f447]) ).
cnf(s66,plain,
spl2_17,
inference(sat_conversion,[],[f477]) ).
cnf(s76,plain,
spl2_3,
inference(sat_conversion,[],[f492]) ).
cnf(s81,plain,
( ~ spl2_4
| spl2_7
| ~ spl2_18
| ~ spl2_42 ),
inference(sat_conversion,[],[f507]) ).
cnf(s88,plain,
spl2_42,
inference(rat,[],[s21,s46]) ).
cnf(s100,plain,
spl2_18,
inference(rat,[],[s9,s66]) ).
cnf(s105,plain,
~ spl2_7,
inference(rat,[],[s4,s28]) ).
cnf(s106,plain,
~ spl2_4,
inference(rat,[],[s81,s88,s100,s105]) ).
cnf(s108,plain,
$false,
inference(rat,[],[s2,s106,s76]) ).
fof(f508,plain,
$false,
inference(avatar_sat_refutation,[],[s108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n014.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 15:58:16 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.77/1.49 % (969264)Detected formulas, will run a generic FOF schedule.
% 3.77/1.49 % (969269)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=2830648994:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.77/1.49 % (969273)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2075556672:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.77/1.49 % (969271)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=1926220342:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.77/1.49 % (969270)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=2153456421:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.77/1.49 % (969275)dis-21_1_sil=8000:lcm=predicate:random_seed=1052345021: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)
% 3.77/1.49 % (969272)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3173460672:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.77/1.49 % (969273)Refutation not found, incomplete strategy
% 3.77/1.49 % (969273)------------------------------
% 3.77/1.49 % (969273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.49 % (969273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.49 % (969273)CaDiCaL version: 2.1.3
% 3.77/1.49 % (969272)Refutation not found, incomplete strategy
% 3.77/1.49 % (969272)------------------------------
% 3.77/1.49 % (969272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.49 % (969273)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.49 % (969273)Time elapsed: 0.001 s
% 3.77/1.49 % (969273)Peak memory usage: 86 MB
% 3.77/1.49 % (969272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.49 % (969272)CaDiCaL version: 2.1.3
% 3.77/1.49 % (969272)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.49 % (969272)Time elapsed: 0.001 s
% 3.77/1.49 % (969272)Peak memory usage: 86 MB
% 3.77/1.49 % (969275)Refutation not found, incomplete strategy
% 3.77/1.49 % (969275)------------------------------
% 3.77/1.49 % (969275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.49 % (969275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.49 % (969275)CaDiCaL version: 2.1.3
% 3.77/1.49 % (969275)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.49 % (969275)Time elapsed: 0.002 s
% 3.77/1.49 % (969275)Peak memory usage: 88 MB
% 3.77/1.49 % (969275)Instructions burned: 1 (million)
% 3.77/1.49 % (969274)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2004579456:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.77/1.49 % (969274)First to succeed.
% 3.77/1.49 % (969274)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-969264"
% 3.77/1.49 % (969275)------------------------------
% 3.77/1.49 % (969275)------------------------------
% 3.77/1.49 % (969273)------------------------------
% 3.77/1.49 % (969273)------------------------------
% 3.77/1.49 % (969272)------------------------------
% 3.77/1.49 % (969272)------------------------------
% 3.77/1.49 % (969274)Refutation found. Thanks to Tanya!
% 3.77/1.49 % SZS status Theorem for theBenchmark
% 3.77/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.49 % (969274)------------------------------
% 3.77/1.49 % (969274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.49 % (969274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.49 % (969274)CaDiCaL version: 2.1.3
% 3.77/1.49 % (969274)Termination reason: Refutation
% 3.77/1.49 % (969274)Time elapsed: 0.006 s
% 3.77/1.49 % (969274)Peak memory usage: 90 MB
% 3.77/1.49 % (969274)Instructions burned: 7 (million)
% 3.77/1.49 % (969274)------------------------------
% 3.77/1.49 % (969274)------------------------------
% 3.77/1.49 % (969264)Success in time 0.453 s
% 3.77/1.49 % Vampire exiting
%------------------------------------------------------------------------------