%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL459+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 : n003.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 11:52:30 AM UTC 2026
% Result : Theorem 0.16s 1.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 24 unt; 8 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 120 ( 52 ~; 48 |; 2 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 13 usr; 13 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f53,conjecture,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f54,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ kn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f71,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f74,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f71]) ).
fof(f75,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f67]) ).
fof(f83,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f63]) ).
fof(f90,plain,
( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f90]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f94]) ).
fof(f117,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f120,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f124,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f135,plain,
~ kn1,
inference(cnf_transformation,[],[f55]) ).
fof(f161,definition,
( spl1_7
<=> is_a_theorem(implies(sK0,and(sK0,sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f163,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| spl1_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl1_8
<=> kn1 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f110,f165,f161]) ).
fof(f218,definition,
( spl1_21
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f222,definition,
( spl1_22
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f223,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl1_21
| spl1_22 ),
inference(avatar_split_clause,[],[f103,f222,f218]) ).
fof(f250,definition,
( spl1_29
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition]) ).
fof(f254,definition,
( spl1_30
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl1_29
| spl1_30 ),
inference(avatar_split_clause,[],[f99,f254,f250]) ).
fof(f282,definition,
( spl1_37
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition]) ).
fof(f286,definition,
( spl1_38
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_38])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( ~ spl1_37
| spl1_38 ),
inference(avatar_split_clause,[],[f95,f286,f282]) ).
fof(f289,plain,
~ spl1_8,
inference(avatar_split_clause,[],[f135,f165]) ).
fof(f303,plain,
spl1_37,
inference(avatar_split_clause,[],[f117,f282]) ).
fof(f312,plain,
spl1_29,
inference(avatar_split_clause,[],[f120,f250]) ).
fof(f324,plain,
spl1_21,
inference(avatar_split_clause,[],[f124,f218]) ).
fof(f346,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,implies(sK0,and(sK0,sK0))))
| ~ is_a_theorem(X0) )
| spl1_7
| ~ spl1_38 ),
inference(resolution,[],[f287,f163]) ).
fof(f404,plain,
( ~ is_a_theorem(implies(sK0,implies(sK0,and(sK0,sK0))))
| spl1_7
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f346,f255]) ).
fof(f409,plain,
( $false
| spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(forward_subsumption_resolution,[],[f404,f223]) ).
fof(f410,plain,
( spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(avatar_contradiction_clause,[],[f409]) ).
cnf(s4,plain,
( ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s11,plain,
( ~ spl1_21
| spl1_22 ),
inference(sat_conversion,[],[f224]) ).
cnf(s15,plain,
( ~ spl1_29
| spl1_30 ),
inference(sat_conversion,[],[f256]) ).
cnf(s19,plain,
( ~ spl1_37
| spl1_38 ),
inference(sat_conversion,[],[f288]) ).
cnf(s20,plain,
~ spl1_8,
inference(sat_conversion,[],[f289]) ).
cnf(s28,plain,
spl1_37,
inference(sat_conversion,[],[f303]) ).
cnf(s34,plain,
spl1_29,
inference(sat_conversion,[],[f312]) ).
cnf(s42,plain,
spl1_21,
inference(sat_conversion,[],[f324]) ).
cnf(s58,plain,
( spl1_7
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(sat_conversion,[],[f410]) ).
cnf(s59,plain,
spl1_38,
inference(rat,[],[s19,s28]) ).
cnf(s63,plain,
spl1_30,
inference(rat,[],[s15,s34]) ).
cnf(s67,plain,
spl1_22,
inference(rat,[],[s11,s42]) ).
cnf(s68,plain,
spl1_7,
inference(rat,[],[s58,s59,s63,s67]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s4,s20,s68]) ).
fof(f411,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:47:11 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.16/1.50 % (734668)Detected formulas, will run a generic FOF schedule.
% 0.16/1.50 % (734676)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1522165140:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.50 % (734676)Refutation not found, incomplete strategy
% 0.16/1.50 % (734676)------------------------------
% 0.16/1.50 % (734676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (734676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (734676)CaDiCaL version: 2.1.3
% 0.16/1.50 % (734676)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.50 % (734676)Time elapsed: 0.0000 s
% 0.16/1.50 % (734676)Peak memory usage: 87 MB
% 0.16/1.50 % (734679)dis-21_1_sil=8000:lcm=predicate:random_seed=2384159985: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)
% 0.16/1.50 % (734673)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=155293012:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.50 % (734677)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2167325458:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.50 % (734675)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=980973786:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.50 % (734678)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1222177356:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.50 % (734674)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=89739866:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.50 % (734677)Refutation not found, incomplete strategy
% 0.16/1.50 % (734677)------------------------------
% 0.16/1.50 % (734677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (734677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (734677)CaDiCaL version: 2.1.3
% 0.16/1.50 % (734677)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.50 % (734677)Time elapsed: 0.001 s
% 0.16/1.50 % (734677)Peak memory usage: 86 MB
% 0.16/1.50 % (734679)Refutation not found, incomplete strategy
% 0.16/1.50 % (734679)------------------------------
% 0.16/1.50 % (734679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (734679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (734679)CaDiCaL version: 2.1.3
% 0.16/1.50 % (734679)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.50 % (734679)Time elapsed: 0.002 s
% 0.16/1.50 % (734679)Peak memory usage: 88 MB
% 0.16/1.50 % (734679)Instructions burned: 1 (million)
% 0.16/1.50 % (734678)First to succeed.
% 0.16/1.50 % (734678)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-734668"
% 0.16/1.50 % (734676)------------------------------
% 0.16/1.50 % (734676)------------------------------
% 0.16/1.50 % (734687)lrs+10_1_sil=8000:sp=occurrence:random_seed=1263661757:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.16/1.50 % (734687)Refutation not found, incomplete strategy
% 0.16/1.50 % (734687)------------------------------
% 0.16/1.50 % (734687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (734687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (734687)CaDiCaL version: 2.1.3
% 0.16/1.50 % (734687)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.50 % (734687)Time elapsed: 0.0000 s
% 0.16/1.50 % (734687)Peak memory usage: 87 MB
% 0.16/1.50 % (734679)------------------------------
% 0.16/1.50 % (734679)------------------------------
% 0.16/1.50 % (734677)------------------------------
% 0.16/1.50 % (734677)------------------------------
% 0.16/1.50 % (734678)Refutation found. Thanks to Tanya!
% 0.16/1.50 % SZS status Theorem for theBenchmark
% 0.16/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (734678)------------------------------
% 0.16/1.50 % (734678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (734678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (734678)CaDiCaL version: 2.1.3
% 0.16/1.50 % (734678)Termination reason: Refutation
% 0.16/1.50 % (734678)Time elapsed: 0.007 s
% 0.16/1.50 % (734678)Peak memory usage: 90 MB
% 0.16/1.50 % (734678)Instructions burned: 8 (million)
% 0.16/1.50 % (734678)------------------------------
% 0.16/1.50 % (734678)------------------------------
% 0.16/1.50 % (734668)Success in time 0.44 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------