%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:51:17 AM UTC 2026
% Result : Unsatisfiable 3.95s 1.68s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 9 unt; 2 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 32 ~; 25 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_3) ).
fof(f3,axiom,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_4) ).
fof(f4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q_2) ).
fof(f5,plain,
! [X2,X0,X1] :
( is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2,f1]) ).
fof(f7,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(equivalent(X2,X1)) ),
inference(resolution,[],[f5,f1]) ).
fof(f9,plain,
! [X2,X0,X1] :
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X0,equivalent(X2,X1))))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f7,f2]) ).
fof(f17,plain,
! [X2,X0,X1] :
( is_a_theorem(equivalent(equivalent(X2,X1),X0))
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f9,f7]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(equivalent(X1,X0))
| is_a_theorem(equivalent(X3,X2)) ),
inference(resolution,[],[f17,f7]) ).
fof(f28,definition,
( spl0_1
<=> ! [X2,X3] :
( ~ is_a_theorem(equivalent(X2,X3))
| is_a_theorem(equivalent(X3,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( ! [X2,X3] :
( ~ is_a_theorem(equivalent(X2,X3))
| is_a_theorem(equivalent(X3,X2)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,definition,
( spl0_2
<=> ! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(equivalent(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,X1)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f26,f31,f28]) ).
fof(f48,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))
| ~ is_a_theorem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f32,f9]) ).
fof(f51,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f48,f5]) ).
fof(f65,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f51,f2]) ).
fof(f75,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f124,plain,
( ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2)))
| ~ spl0_1 ),
inference(resolution,[],[f29,f3]) ).
fof(f155,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f124,f4]) ).
fof(f164,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f155]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f75]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f164]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f165,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n020.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 15:24:04 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 3.95/1.68 % (3528093)Input is clausal, will run a generic CNF schedule.
% 3.95/1.68 % (3528109)lrs+10_1_sil=8000:sp=occurrence:random_seed=3717986095:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.95/1.68 % (3528109)First to succeed.
% 3.95/1.68 % (3528109)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3528093"
% 3.95/1.68 % (3528107)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1078282626:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.95/1.68 % (3528106)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=1778297374:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.95/1.68 % (3528108)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=391753407:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.95/1.68 % (3528111)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2834429417:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.95/1.68 % (3528110)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3037058149:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.95/1.68 % (3528110)Also succeeded, but the first one will report.
% 3.95/1.68 % (3528111)Also succeeded, but the first one will report.
% 3.95/1.68 % (3528112)dis-21_1_sil=8000:lcm=predicate:random_seed=3436588979: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)
% 3.95/1.68 % (3528112)Also succeeded, but the first one will report.
% 3.95/1.68 % (3528109)Refutation found. Thanks to Tanya!
% 3.95/1.68 % SZS status Unsatisfiable for theBenchmark
% 3.95/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.68 % (3528109)------------------------------
% 3.95/1.68 % (3528109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.68 % (3528109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.68 % (3528109)CaDiCaL version: 2.1.3
% 3.95/1.68 % (3528109)Termination reason: Refutation
% 3.95/1.68 % (3528109)Time elapsed: 0.005 s
% 3.95/1.68 % (3528109)Peak memory usage: 89 MB
% 3.95/1.68 % (3528109)Instructions burned: 7 (million)
% 3.95/1.68 % (3528109)------------------------------
% 3.95/1.68 % (3528109)------------------------------
% 3.95/1.68 % (3528093)Success in time 0.475 s
% 3.95/1.68 % Vampire exiting
%------------------------------------------------------------------------------