%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL209-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 11:51:34 AM UTC 2026
% Result : Unsatisfiable 0.16s 1.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 27 unt; 1 def)
% Number of atoms : 54 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 29 ~; 14 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f7,axiom,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( theorem(X0)
| ~ theorem(implies(X1,X0))
| ~ theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f9,negated_conjecture,
~ theorem(implies(implies(not(p),q),or(p,q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f10,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[],[f1,f7]) ).
fof(f11,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[],[f2,f7]) ).
fof(f12,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[],[f3,f7]) ).
fof(f15,plain,
! [X0,X1] : theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f11,f6]) ).
fof(f20,plain,
! [X0] :
( ~ theorem(implies(X0,implies(implies(not(p),q),or(p,q))))
| ~ theorem(X0) ),
inference(resolution,[],[f8,f9]) ).
fof(f22,plain,
! [X0,X1] :
( ~ theorem(implies(X1,implies(X0,implies(implies(not(p),q),or(p,q)))))
| ~ theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f20,f8]) ).
fof(f23,plain,
! [X2,X0,X1] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[],[f4,f7]) ).
fof(f34,plain,
! [X2,X0,X1] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[],[f5,f7]) ).
fof(f40,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[],[f12,f6]) ).
fof(f59,plain,
! [X2,X0,X1] : theorem(implies(or(X1,or(not(X0),X2)),implies(X0,or(X1,X2)))),
inference(superposition,[],[f23,f6]) ).
fof(f60,plain,
! [X2,X0,X1] : theorem(implies(or(X1,implies(X0,X2)),implies(X0,or(X1,X2)))),
inference(forward_demodulation,[],[f59,f6]) ).
fof(f141,plain,
! [X2,X0,X1] : theorem(implies(or(not(X0),implies(X2,X1)),implies(X2,implies(X0,X1)))),
inference(superposition,[],[f60,f6]) ).
fof(f142,plain,
! [X2,X0,X1] : theorem(implies(implies(X0,implies(X2,X1)),implies(X2,implies(X0,X1)))),
inference(forward_demodulation,[],[f141,f6]) ).
fof(f196,plain,
! [X0] :
( ~ theorem(implies(implies(not(p),q),implies(X0,or(p,q))))
| ~ theorem(X0) ),
inference(resolution,[],[f142,f22]) ).
fof(f226,plain,
~ theorem(or(p,not(p))),
inference(resolution,[],[f196,f34]) ).
fof(f228,plain,
! [X0] :
( ~ theorem(implies(X0,or(p,not(p))))
| ~ theorem(X0) ),
inference(resolution,[],[f226,f8]) ).
fof(f246,plain,
~ theorem(implies(p,p)),
inference(resolution,[],[f228,f40]) ).
fof(f258,plain,
! [X0] :
( ~ theorem(implies(X0,implies(p,p)))
| ~ theorem(X0) ),
inference(resolution,[],[f246,f8]) ).
fof(f300,plain,
! [X0,X1] :
( ~ theorem(implies(X1,implies(X0,implies(p,p))))
| ~ theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f258,f8]) ).
fof(f604,plain,
! [X0] :
( ~ theorem(X0)
| ~ theorem(implies(p,implies(X0,p))) ),
inference(resolution,[],[f300,f142]) ).
fof(f606,plain,
! [X0] : ~ theorem(X0),
inference(forward_subsumption_resolution,[],[f604,f15]) ).
fof(f618,definition,
( spl0_2
<=> ! [X0] : ~ theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f619,plain,
( ! [X0] : ~ theorem(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f621,plain,
spl0_2,
inference(avatar_split_clause,[],[f606,f618]) ).
fof(f624,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f619,f10]) ).
fof(f652,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f624]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f621]) ).
cnf(s16,plain,
~ spl0_2,
inference(sat_conversion,[],[f652]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s16]) ).
fof(f653,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL209-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:27:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.16/1.41 % (2555214)Input is clausal, will run a generic CNF schedule.
% 0.16/1.41 % (2555251)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2471009420:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.16/1.41 % (2555251)First to succeed.
% 0.16/1.41 % (2555251)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2555214"
% 0.16/1.41 % (2555248)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3851399376:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.16/1.41 % (2555246)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=3638310055:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.16/1.41 % (2555250)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=934796719:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.16/1.41 % (2555247)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4119769488:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.16/1.41 % (2555249)lrs+10_1_sil=8000:sp=occurrence:random_seed=1789952825:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.16/1.41 % (2555249)Also succeeded, but the first one will report.
% 0.16/1.41 % (2555252)dis-21_1_sil=8000:lcm=predicate:random_seed=428162566: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)
% 0.16/1.41 % (2555250)Instruction limit reached!
% 0.16/1.41 % (2555250)------------------------------
% 0.16/1.41 % (2555250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.41 % (2555250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.41 % (2555250)CaDiCaL version: 2.1.3
% 0.16/1.41 % (2555250)Termination reason: Instruction limit
% 0.16/1.41 % (2555250)Termination phase: Saturation
% 0.16/1.41 % (2555250)Time elapsed: 0.105 s
% 0.16/1.41 % (2555250)Peak memory usage: 87 MB
% 0.16/1.41 % (2555250)Instructions burned: 114 (million)
% 0.16/1.41 % (2555252)Instruction limit reached!
% 0.16/1.41 % (2555252)------------------------------
% 0.16/1.41 % (2555252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.41 % (2555252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.41 % (2555252)CaDiCaL version: 2.1.3
% 0.16/1.41 % (2555252)Termination reason: Instruction limit
% 0.16/1.41 % (2555252)Termination phase: Saturation
% 0.16/1.41 % (2555252)Time elapsed: 0.098 s
% 0.16/1.41 % (2555252)Peak memory usage: 88 MB
% 0.16/1.41 % (2555252)Instructions burned: 117 (million)
% 0.16/1.41 % (2555251)Refutation found. Thanks to Tanya!
% 0.16/1.41 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.41 % (2555251)------------------------------
% 0.16/1.41 % (2555251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.41 % (2555251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.41 % (2555251)CaDiCaL version: 2.1.3
% 0.16/1.41 % (2555251)Termination reason: Refutation
% 0.16/1.41 % (2555251)Time elapsed: 0.037 s
% 0.16/1.41 % (2555251)Peak memory usage: 89 MB
% 0.16/1.41 % (2555251)Instructions burned: 46 (million)
% 0.16/1.41 % (2555251)------------------------------
% 0.16/1.41 % (2555251)------------------------------
% 0.16/1.41 % (2555214)Success in time 0.474 s
% 0.16/1.41 % Vampire exiting
%------------------------------------------------------------------------------