%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL312-3 : 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 : n015.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 11:51:56 AM UTC 2026
% Result : Unsatisfiable 6.31s 7.06s
% Output : Refutation 6.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 24 unt; 2 def)
% Number of atoms : 99 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 44 ~; 40 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 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(implies(not(p),p),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(or(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p)))))),
inference(definition_unfolding,[],[f11,f12,f6]) ).
fof(f14,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(f15,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f16,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f17,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f18,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f19,plain,
! [X0,X1] :
( ~ theorem(or(not(X1),X0))
| theorem(X0)
| ~ theorem(X1) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f21,plain,
! [X0,X1] :
( ~ axiom(or(not(X1),X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[],[f19,f7]) ).
fof(f23,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[],[f21,f18]) ).
fof(f24,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f21,f16]) ).
fof(f25,plain,
! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f21,f15]) ).
fof(f26,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(resolution,[],[f14,f21]) ).
fof(f30,plain,
! [X0,X1] :
( ~ theorem(or(X0,not(X1)))
| theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f24,f19]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,X2))
| ~ theorem(X1) ),
inference(resolution,[],[f25,f19]) ).
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,f19]) ).
fof(f54,plain,
! [X0,X1] :
( ~ axiom(or(X0,or(or(X0,X1),X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f43,f7]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ axiom(or(X0,or(not(X2),X1)))
| ~ theorem(X2)
| theorem(or(X0,X1)) ),
inference(resolution,[],[f42,f7]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ axiom(or(not(X2),X1))
| ~ theorem(or(X0,X2))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f49,f7]) ).
fof(f94,plain,
! [X0] : theorem(or(not(X0),X0)),
inference(resolution,[],[f54,f17]) ).
fof(f107,plain,
! [X0,X1] :
( theorem(or(not(or(X1,not(X0))),X1))
| ~ theorem(X0) ),
inference(resolution,[],[f59,f16]) ).
fof(f110,plain,
! [X2,X0,X1] :
( theorem(or(not(or(not(X1),X2)),or(X0,X2)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f59,f14]) ).
fof(f122,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X2,X1)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f65,f17]) ).
fof(f123,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f65,f18]) ).
fof(f131,plain,
! [X0,X1] :
( theorem(not(or(not(X1),not(X0))))
| ~ theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f107,f30]) ).
fof(f415,plain,
! [X0,X1] :
( theorem(or(not(or(not(X1),X0)),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f110,f123]) ).
fof(f705,definition,
( spl0_27
<=> theorem(or(not(or(not(not(p)),p)),p)) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f706,plain,
( ~ theorem(or(not(or(not(not(p)),p)),p))
| spl0_27 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f1644,plain,
( ~ theorem(or(not(p),or(not(not(p)),p)))
| ~ theorem(or(not(or(not(not(p)),p)),p)) ),
inference(resolution,[],[f131,f13]) ).
fof(f1967,plain,
( ~ theorem(or(p,not(p)))
| spl0_27 ),
inference(resolution,[],[f415,f706]) ).
fof(f1993,plain,
( ~ theorem(or(not(p),p))
| spl0_27 ),
inference(resolution,[],[f1967,f24]) ).
fof(f2000,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f1993,f94]) ).
fof(f2001,plain,
spl0_27,
inference(avatar_contradiction_clause,[],[f2000]) ).
fof(f2003,definition,
( spl0_67
<=> theorem(or(not(p),or(not(not(p)),p))) ),
introduced(definition,[new_symbols(definition,[spl0_67])],[avatar_definition]) ).
fof(f2004,plain,
( ~ theorem(or(not(p),or(not(not(p)),p)))
| spl0_67 ),
inference(avatar_component_clause,[],[f2003]) ).
fof(f2005,plain,
( ~ spl0_27
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1644,f2003,f705]) ).
fof(f2044,plain,
( ~ theorem(or(not(p),p))
| spl0_67 ),
inference(resolution,[],[f2004,f122]) ).
fof(f2060,plain,
( $false
| spl0_67 ),
inference(forward_subsumption_resolution,[],[f2044,f94]) ).
fof(f2061,plain,
spl0_67,
inference(avatar_contradiction_clause,[],[f2060]) ).
cnf(s138,plain,
spl0_27,
inference(sat_conversion,[],[f2001]) ).
cnf(s139,plain,
( ~ spl0_27
| ~ spl0_67 ),
inference(sat_conversion,[],[f2005]) ).
cnf(s151,plain,
spl0_67,
inference(sat_conversion,[],[f2061]) ).
cnf(s153,plain,
~ spl0_27,
inference(rat,[],[s139,s151]) ).
cnf(s154,plain,
$false,
inference(rat,[],[s138,s153]) ).
fof(f2062,plain,
$false,
inference(avatar_sat_refutation,[],[s154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL312-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n015.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sun Sep 27 15:37:36 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/5.51 Running first-order theorem proving
% 0.23/5.51 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
% 6.31/7.06 % (1796857)Input is clausal, will run a generic CNF schedule.
% 6.31/7.06 % (1796864)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2191017137:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.31/7.06 % (1796863)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4159734641:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.31/7.06 % (1796867)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2741539753:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.31/7.06 % (1796866)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1057561691:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.31/7.06 % (1796865)lrs+10_1_sil=8000:sp=occurrence:random_seed=1558345793:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.31/7.06 % (1796862)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=1902761416:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.31/7.06 % (1796866)First to succeed.
% 6.31/7.06 % (1796866)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1796857"
% 6.31/7.06 % (1796865)Instruction limit reached!
% 6.31/7.06 % (1796865)------------------------------
% 6.31/7.06 % (1796865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.31/7.06 % (1796865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/7.06 % (1796865)CaDiCaL version: 2.1.3
% 6.31/7.06 % (1796865)Termination reason: Instruction limit
% 6.31/7.06 % (1796865)Termination phase: Saturation
% 6.31/7.06 % (1796865)Time elapsed: 0.120 s
% 6.31/7.06 % (1796865)Peak memory usage: 89 MB
% 6.31/7.06 % (1796865)Instructions burned: 107 (million)
% 6.31/7.06 % (1796868)dis-21_1_sil=8000:lcm=predicate:random_seed=1604127319: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)
% 6.31/7.06 % (1796867)Instruction limit reached!
% 6.31/7.06 % (1796867)------------------------------
% 6.31/7.06 % (1796867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.31/7.06 % (1796867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/7.06 % (1796867)CaDiCaL version: 2.1.3
% 6.31/7.06 % (1796867)Termination reason: Instruction limit
% 6.31/7.06 % (1796867)Termination phase: Saturation
% 6.31/7.06 % (1796867)Time elapsed: 0.191 s
% 6.31/7.06 % (1796867)Peak memory usage: 89 MB
% 6.31/7.06 % (1796867)Instructions burned: 180 (million)
% 6.31/7.06 % (1796868)Instruction limit reached!
% 6.31/7.06 % (1796868)------------------------------
% 6.31/7.06 % (1796868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.31/7.06 % (1796868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/7.06 % (1796868)CaDiCaL version: 2.1.3
% 6.31/7.06 % (1796868)Termination reason: Instruction limit
% 6.31/7.06 % (1796868)Termination phase: Saturation
% 6.31/7.06 % (1796868)Time elapsed: 0.118 s
% 6.31/7.06 % (1796868)Peak memory usage: 87 MB
% 6.31/7.06 % (1796868)Instructions burned: 117 (million)
% 6.31/7.06 % (1796875)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=1782031527:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.31/7.06 % (1796875)Refutation not found, incomplete strategy
% 6.31/7.06 % (1796875)------------------------------
% 6.31/7.06 % (1796875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.31/7.06 % (1796875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/7.06 % (1796875)CaDiCaL version: 2.1.3
% 6.31/7.06 % (1796875)Termination reason: Refutation not found, incomplete strategy
% 6.31/7.06 % (1796875)Time elapsed: 0.002 s
% 6.31/7.06 % (1796875)Peak memory usage: 88 MB
% 6.31/7.06 % (1796866)Refutation found. Thanks to Tanya!
% 6.31/7.06 % SZS status Unsatisfiable for theBenchmark
% 6.31/7.06 % SZS output start Proof for theBenchmark
% See solution above
% 6.31/7.06 % (1796866)------------------------------
% 6.31/7.06 % (1796866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.31/7.06 % (1796866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/7.06 % (1796866)CaDiCaL version: 2.1.3
% 6.31/7.06 % (1796866)Termination reason: Refutation
% 6.31/7.06 % (1796866)Time elapsed: 0.078 s
% 6.31/7.06 % (1796866)Peak memory usage: 89 MB
% 6.31/7.06 % (1796866)Instructions burned: 71 (million)
% 6.31/7.06 % (1796866)------------------------------
% 6.31/7.06 % (1796866)------------------------------
% 6.31/7.06 % (1796857)Success in time 0.787 s
% 6.31/7.06 % Vampire exiting
%------------------------------------------------------------------------------