%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL265-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 11:51:49 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.60s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 24 unt; 3 def)
% Number of atoms : 107 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 100 ( 52 ~; 45 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f7,axiom,
! [X0] :
( theorem(X0)
| ~ axiom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( theorem(X0)
| ~ theorem(implies(X1,X0))
| ~ theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f9,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,negated_conjecture,
~ theorem(equivalent(p,not(not(p)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f12,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f13,plain,
~ theorem(not(or(not(or(not(p),not(not(p)))),not(or(not(not(not(p))),p))))),
inference(definition_unfolding,[],[f11,f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ theorem(or(not(X1),X0))
| theorem(X0)
| ~ theorem(X1) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f15,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f16,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f17,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f18,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f19,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f21,plain,
! [X0,X1] :
( ~ axiom(or(not(X1),X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[],[f14,f7]) ).
fof(f23,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[],[f21,f19]) ).
fof(f24,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f21,f17]) ).
fof(f25,plain,
! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f21,f16]) ).
fof(f26,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(resolution,[],[f15,f21]) ).
fof(f30,plain,
! [X0,X1] :
( ~ theorem(or(X0,not(X1)))
| theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f24,f14]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,X2))
| ~ theorem(X1) ),
inference(resolution,[],[f25,f14]) ).
fof(f43,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(or(X0,X1),X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f25,f23]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ),
inference(resolution,[],[f26,f14]) ).
fof(f54,plain,
! [X0,X1] :
( ~ axiom(or(X0,or(or(X0,X1),X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f43,f7]) ).
fof(f58,plain,
! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),X2))
| ~ theorem(X0)
| ~ theorem(or(not(X1),X2)) ),
inference(resolution,[],[f42,f26]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ theorem(or(X1,not(X2)))
| ~ theorem(or(X0,X2))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f49,f24]) ).
fof(f94,plain,
! [X0] : theorem(or(not(X0),X0)),
inference(resolution,[],[f54,f18]) ).
fof(f120,plain,
! [X0,X1] :
( theorem(or(X0,not(not(X1))))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f62,f94]) ).
fof(f139,plain,
! [X2,X0,X1] :
( theorem(not(or(not(X0),X1)))
| ~ theorem(or(not(X1),not(X2)))
| ~ theorem(X0)
| ~ theorem(X2) ),
inference(resolution,[],[f58,f30]) ).
fof(f699,plain,
! [X0] :
( ~ theorem(or(not(not(or(not(not(not(p))),p))),not(X0)))
| ~ theorem(or(not(p),not(not(p))))
| ~ theorem(X0) ),
inference(resolution,[],[f139,f13]) ).
fof(f705,definition,
( spl0_27
<=> theorem(or(not(p),not(not(p)))) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f706,plain,
( ~ theorem(or(not(p),not(not(p))))
| spl0_27 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f708,definition,
( spl0_28
<=> ! [X0] :
( ~ theorem(or(not(not(or(not(not(not(p))),p))),not(X0)))
| ~ theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f709,plain,
( ! [X0] :
( ~ theorem(or(not(not(or(not(not(not(p))),p))),not(X0)))
| ~ theorem(X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f710,plain,
( ~ spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f699,f708,f705]) ).
fof(f716,plain,
( ~ theorem(or(not(not(p)),not(p)))
| spl0_27 ),
inference(resolution,[],[f706,f24]) ).
fof(f719,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f716,f94]) ).
fof(f720,plain,
spl0_27,
inference(avatar_contradiction_clause,[],[f719]) ).
fof(f769,plain,
( ~ theorem(or(not(not(not(p))),p))
| ~ spl0_28 ),
inference(resolution,[],[f709,f94]) ).
fof(f792,definition,
( spl0_37
<=> theorem(or(not(not(not(p))),p)) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f793,plain,
( ~ theorem(or(not(not(not(p))),p))
| spl0_37 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f795,plain,
( ~ spl0_37
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f769,f708,f792]) ).
fof(f810,plain,
( ~ theorem(or(p,not(not(not(p)))))
| spl0_37 ),
inference(resolution,[],[f793,f24]) ).
fof(f1396,plain,
( ~ theorem(or(p,not(p)))
| spl0_37 ),
inference(resolution,[],[f120,f810]) ).
fof(f1404,plain,
( ~ theorem(or(not(p),p))
| spl0_37 ),
inference(resolution,[],[f1396,f24]) ).
fof(f1407,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f1404,f94]) ).
fof(f1408,plain,
spl0_37,
inference(avatar_contradiction_clause,[],[f1407]) ).
cnf(s47,plain,
( ~ spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f710]) ).
cnf(s48,plain,
spl0_27,
inference(sat_conversion,[],[f720]) ).
cnf(s59,plain,
( ~ spl0_28
| ~ spl0_37 ),
inference(sat_conversion,[],[f795]) ).
cnf(s96,plain,
spl0_37,
inference(sat_conversion,[],[f1408]) ).
cnf(s97,plain,
~ spl0_28,
inference(rat,[],[s59,s96]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s47,s97,s48]) ).
fof(f1409,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL265-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:29:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.11/1.40 % (1592093)Input is clausal, will run a generic CNF schedule.
% 3.11/1.40 % (1592192)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2533656210:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.11/1.40 % (1592191)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2574146638:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.11/1.40 % (1592189)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1304241686:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.11/1.40 % (1592190)lrs+10_1_sil=8000:sp=occurrence:random_seed=3649664151:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.11/1.40 % (1592187)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=1235943202:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.11/1.40 % (1592188)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1828574655:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.70/1.40 % (1592192)Instruction limit reached!
% 3.70/1.40 % (1592192)------------------------------
% 3.70/1.40 % (1592192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.40 % (1592192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.40 % (1592192)CaDiCaL version: 2.1.3
% 3.70/1.40 % (1592192)Termination reason: Instruction limit
% 3.70/1.40 % (1592192)Termination phase: Saturation
% 3.70/1.40 % (1592192)Time elapsed: 0.099 s
% 3.70/1.40 % (1592192)Peak memory usage: 89 MB
% 3.70/1.40 % (1592192)Instructions burned: 181 (million)
% 3.70/1.40 % (1592193)dis-21_1_sil=8000:lcm=predicate:random_seed=3316386626: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)
% 3.70/1.40 % (1592191)First to succeed.
% 3.70/1.40 % (1592191)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1592093"
% 3.70/1.40 % (1592190)Instruction limit reached!
% 3.70/1.40 % (1592190)------------------------------
% 3.70/1.40 % (1592190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.40 % (1592190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.40 % (1592190)CaDiCaL version: 2.1.3
% 3.70/1.40 % (1592190)Termination reason: Instruction limit
% 3.70/1.40 % (1592190)Termination phase: Saturation
% 3.70/1.40 % (1592190)Time elapsed: 0.106 s
% 3.70/1.40 % (1592190)Peak memory usage: 89 MB
% 3.70/1.40 % (1592190)Instructions burned: 108 (million)
% 3.70/1.40 % (1592193)Instruction limit reached!
% 3.70/1.40 % (1592193)------------------------------
% 3.70/1.40 % (1592193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.40 % (1592193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.40 % (1592193)CaDiCaL version: 2.1.3
% 3.70/1.40 % (1592193)Termination reason: Instruction limit
% 3.70/1.40 % (1592193)Termination phase: Saturation
% 3.70/1.40 % (1592193)Time elapsed: 0.099 s
% 3.70/1.40 % (1592193)Peak memory usage: 87 MB
% 3.70/1.40 % (1592193)Instructions burned: 118 (million)
% 3.70/1.40 % (1592228)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=2489862242:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.70/1.40 % (1592228)Refutation not found, incomplete strategy
% 3.70/1.40 % (1592228)------------------------------
% 3.70/1.40 % (1592228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.40 % (1592228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.40 % (1592228)CaDiCaL version: 2.1.3
% 3.70/1.40 % (1592228)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.40 % (1592228)Time elapsed: 0.001 s
% 3.70/1.40 % (1592228)Peak memory usage: 88 MB
% 3.70/1.40 % (1592238)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1935536281:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 3.70/1.40 % (1592236)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1176451536:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 3.70/1.40 % (1592236)Refutation not found, incomplete strategy
% 3.70/1.40 % (1592236)------------------------------
% 0.17/1.60 % (1592236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.60 % (1592236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.60 % (1592236)CaDiCaL version: 2.1.3
% 0.17/1.60 % (1592236)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.60 % (1592236)Time elapsed: 0.001 s
% 0.17/1.60 % (1592236)Peak memory usage: 87 MB
% 0.17/1.60 % (1592238)Refutation not found, incomplete strategy
% 0.17/1.60 % (1592238)------------------------------
% 0.17/1.60 % (1592238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.60 % (1592238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.60 % (1592238)CaDiCaL version: 2.1.3
% 0.17/1.60 % (1592238)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.60 % (1592238)Time elapsed: 0.001 s
% 0.17/1.60 % (1592238)Peak memory usage: 88 MB
% 0.17/1.60 % (1592191)Refutation found. Thanks to Tanya!
% 0.17/1.60 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.60 % (1592191)------------------------------
% 0.17/1.60 % (1592191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.60 % (1592191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.60 % (1592191)CaDiCaL version: 2.1.3
% 0.17/1.60 % (1592191)Termination reason: Refutation
% 0.17/1.60 % (1592191)Time elapsed: 0.052 s
% 0.17/1.60 % (1592191)Peak memory usage: 89 MB
% 0.17/1.60 % (1592191)Instructions burned: 50 (million)
% 0.17/1.60 % (1592191)------------------------------
% 0.17/1.60 % (1592191)------------------------------
% 0.17/1.60 % (1592093)Success in time 0.525 s
% 0.17/1.60 % Vampire exiting
%------------------------------------------------------------------------------