%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:51:06 AM UTC 2026
% Result : Unsatisfiable 3.84s 1.55s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 18 unt; 3 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 41 ~; 33 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_19) ).
fof(f3,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_37) ).
fof(f4,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X2,X1),implies(implies(X0,X2),X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_59) ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_3) ).
fof(f6,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f2,f1]) ).
fof(f7,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(implies(not(X0),X2)) ),
inference(resolution,[],[f3,f1]) ).
fof(f8,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[],[f6,f2]) ).
fof(f11,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[],[f4,f1]) ).
fof(f14,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(resolution,[],[f7,f2]) ).
fof(f16,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(not(X0)),implies(implies(X1,X2),implies(implies(X0,X1),X2)))),
inference(resolution,[],[f7,f4]) ).
fof(f17,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(X0),implies(X1,implies(X0,X2)))),
inference(resolution,[],[f7,f8]) ).
fof(f24,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),X1))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[],[f11,f1]) ).
fof(f42,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(implies(X0,X1),X2)))
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f16,f1]) ).
fof(f49,definition,
( spl0_1
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(not(X2),X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(X1) ),
inference(resolution,[],[f24,f1]) ).
fof(f70,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),implies(implies(X0,X1),X2)))
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f42,f7]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(X3,X1),X0))
| ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f57,f14]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(X2,X3))))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(resolution,[],[f57,f17]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,not(X2))))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(implies(X1,not(X2))) ),
inference(resolution,[],[f57,f8]) ).
fof(f155,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f50,f2]) ).
fof(f195,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f91,f2]) ).
fof(f217,definition,
( spl0_6
<=> ! [X3] : ~ is_a_theorem(not(not(X3))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f218,plain,
( ! [X3] : ~ is_a_theorem(not(not(X3)))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,not(implies(X1,X2))))
| is_a_theorem(implies(X2,not(X0))) ),
inference(resolution,[],[f96,f14]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X0,X3))))
| is_a_theorem(implies(X2,implies(X0,X3))) ),
inference(resolution,[],[f94,f2]) ).
fof(f503,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f196,f2]) ).
fof(f544,plain,
! [X0,X1] : is_a_theorem(implies(X0,not(not(implies(X1,X0))))),
inference(resolution,[],[f231,f503]) ).
fof(f849,plain,
! [X0,X1] :
( is_a_theorem(not(not(implies(X1,X0))))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f544,f1]) ).
fof(f1326,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl0_6 ),
inference(resolution,[],[f218,f849]) ).
fof(f1327,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1326,f217,f49]) ).
fof(f2052,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ is_a_theorem(not(not(X2))) ),
inference(resolution,[],[f274,f70]) ).
fof(f2063,definition,
( spl0_48
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f2064,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f2063]) ).
fof(f2065,plain,
( spl0_6
| spl0_48 ),
inference(avatar_split_clause,[],[f2052,f2063,f217]) ).
fof(f2093,plain,
( $false
| ~ spl0_48 ),
inference(resolution,[],[f2064,f5]) ).
fof(f2094,plain,
~ spl0_48,
inference(avatar_contradiction_clause,[],[f2093]) ).
cnf(s22,plain,
~ spl0_1,
inference(sat_conversion,[],[f195]) ).
cnf(s70,plain,
( spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s94,plain,
( spl0_6
| spl0_48 ),
inference(sat_conversion,[],[f2065]) ).
cnf(s95,plain,
~ spl0_48,
inference(sat_conversion,[],[f2094]) ).
cnf(s96,plain,
spl0_6,
inference(rat,[],[s94,s95]) ).
cnf(s97,plain,
spl0_1,
inference(rat,[],[s70,s96]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s22,s97]) ).
fof(f2095,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n009.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
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 15:20:45 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 Running first-order theorem proving
% 0.17/0.47 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
% 3.84/1.55 % (2159849)Input is clausal, will run a generic CNF schedule.
% 3.84/1.55 % (2159977)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2490484977:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.84/1.55 % (2159976)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=2710272318:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.84/1.55 % (2159986)dis-21_1_sil=8000:lcm=predicate:random_seed=2737021063:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.84/1.55 % (2159980)lrs+10_1_sil=8000:sp=occurrence:random_seed=60116241:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.84/1.55 % (2159984)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=208783432:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.84/1.55 % (2159982)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3651529947:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.84/1.55 % (2159979)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3955299218:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.84/1.55 % (2159980)First to succeed.
% 3.84/1.55 % (2159980)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2159849"
% 3.84/1.55 % (2159986)Also succeeded, but the first one will report.
% 3.84/1.55 % (2159982)Instruction limit reached!
% 3.84/1.55 % (2159982)------------------------------
% 3.84/1.55 % (2159982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.55 % (2159982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.55 % (2159982)CaDiCaL version: 2.1.3
% 3.84/1.55 % (2159982)Termination reason: Instruction limit
% 3.84/1.55 % (2159982)Termination phase: Saturation
% 3.84/1.55 % (2159982)Time elapsed: 0.071 s
% 3.84/1.55 % (2159982)Peak memory usage: 88 MB
% 3.84/1.55 % (2159982)Instructions burned: 115 (million)
% 3.84/1.55 % (2159984)Instruction limit reached!
% 3.84/1.55 % (2159984)------------------------------
% 3.84/1.55 % (2159984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.55 % (2159984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.55 % (2159984)CaDiCaL version: 2.1.3
% 3.84/1.55 % (2159984)Termination reason: Instruction limit
% 3.84/1.55 % (2159984)Termination phase: Saturation
% 3.84/1.55 % (2159984)Time elapsed: 0.111 s
% 3.84/1.55 % (2159984)Peak memory usage: 89 MB
% 3.84/1.55 % (2159984)Instructions burned: 181 (million)
% 3.84/1.55 % (2159994)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=673095099:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.84/1.55 % (2159994)Refutation not found, incomplete strategy
% 3.84/1.55 % (2159994)------------------------------
% 3.84/1.55 % (2159994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.55 % (2159994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.55 % (2159994)CaDiCaL version: 2.1.3
% 3.84/1.55 % (2159994)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.55 % (2159994)Time elapsed: 0.001 s
% 3.84/1.55 % (2159994)Peak memory usage: 87 MB
% 3.84/1.55 % (2159995)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3681711276:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.84/1.55 % (2159980)Refutation found. Thanks to Tanya!
% 3.84/1.55 % SZS status Unsatisfiable for theBenchmark
% 3.84/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.55 % (2159980)------------------------------
% 3.84/1.55 % (2159980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.55 % (2159980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.55 % (2159980)CaDiCaL version: 2.1.3
% 3.84/1.55 % (2159980)Termination reason: Refutation
% 3.84/1.55 % (2159980)Time elapsed: 0.047 s
% 3.84/1.55 % (2159980)Peak memory usage: 90 MB
% 3.84/1.55 % (2159980)Instructions burned: 72 (million)
% 3.84/1.55 % (2159980)------------------------------
% 3.84/1.55 % (2159980)------------------------------
% 3.84/1.55 % (2159849)Success in time 0.443 s
% 3.84/1.55 % Vampire exiting
%------------------------------------------------------------------------------