%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG194+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 09:29:13 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 10 unt; 9 def)
% Number of atoms : 274 ( 154 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 324 ( 122 ~; 134 |; 60 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
( ( op(e0,e0) != e0
& op(e1,e1) != e1
& op(e2,e2) != e2
& op(e3,e3) != e3
& op(e4,e4) != e4
& op(e5,e5) != e5
& op(e6,e6) != e6 )
| ( op(e0,e0) = e0
& op(e1,e1) = e1
& op(e2,e2) = e2
& op(e3,e3) = e3
& op(e4,e4) = e4
& op(e5,e5) = e5
& op(e6,e6) = e6 )
| ( ( op(e0,e0) = e0
| op(e1,e1) = e1
| op(e2,e2) = e2
| op(e3,e3) = e3
| op(e4,e4) = e4
| op(e5,e5) = e5
| op(e6,e6) = e6 )
& ( op(e0,e0) != e0
| op(e1,e1) != e1
| op(e2,e2) != e2
| op(e3,e3) != e3
| op(e4,e4) != e4
| op(e5,e5) != e5
| op(e6,e6) != e6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f7,negated_conjecture,
~ ( ( op(e0,e0) != e0
& op(e1,e1) != e1
& op(e2,e2) != e2
& op(e3,e3) != e3
& op(e4,e4) != e4
& op(e5,e5) != e5
& op(e6,e6) != e6 )
| ( op(e0,e0) = e0
& op(e1,e1) = e1
& op(e2,e2) = e2
& op(e3,e3) = e3
& op(e4,e4) = e4
& op(e5,e5) = e5
& op(e6,e6) = e6 )
| ( ( op(e0,e0) = e0
| op(e1,e1) = e1
| op(e2,e2) = e2
| op(e3,e3) = e3
| op(e4,e4) = e4
| op(e5,e5) = e5
| op(e6,e6) = e6 )
& ( op(e0,e0) != e0
| op(e1,e1) != e1
| op(e2,e2) != e2
| op(e3,e3) != e3
| op(e4,e4) != e4
| op(e5,e5) != e5
| op(e6,e6) != e6 ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
( ( e0 = op(e0,e0)
| e1 = op(e1,e1)
| e2 = op(e2,e2)
| e3 = op(e3,e3)
| e4 = op(e4,e4)
| e5 = op(e5,e5)
| e6 = op(e6,e6) )
& ( e0 != op(e0,e0)
| e1 != op(e1,e1)
| e2 != op(e2,e2)
| e3 != op(e3,e3)
| e4 != op(e4,e4)
| e5 != op(e5,e5)
| e6 != op(e6,e6) )
& ( ( e0 != op(e0,e0)
& e1 != op(e1,e1)
& e2 != op(e2,e2)
& e3 != op(e3,e3)
& e4 != op(e4,e4)
& e5 != op(e5,e5)
& e6 != op(e6,e6) )
| ( e0 = op(e0,e0)
& e1 = op(e1,e1)
& e2 = op(e2,e2)
& e3 = op(e3,e3)
& e4 = op(e4,e4)
& e5 = op(e5,e5)
& e6 = op(e6,e6) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,definition,
( ( e0 = op(e0,e0)
& e1 = op(e1,e1)
& e2 = op(e2,e2)
& e3 = op(e3,e3)
& e4 = op(e4,e4)
& e5 = op(e5,e5)
& e6 = op(e6,e6) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
( ( e0 = op(e0,e0)
| e1 = op(e1,e1)
| e2 = op(e2,e2)
| e3 = op(e3,e3)
| e4 = op(e4,e4)
| e5 = op(e5,e5)
| e6 = op(e6,e6) )
& ( e0 != op(e0,e0)
| e1 != op(e1,e1)
| e2 != op(e2,e2)
| e3 != op(e3,e3)
| e4 != op(e4,e4)
| e5 != op(e5,e5)
| e6 != op(e6,e6) )
& ( ( e0 != op(e0,e0)
& e1 != op(e1,e1)
& e2 != op(e2,e2)
& e3 != op(e3,e3)
& e4 != op(e4,e4)
& e5 != op(e5,e5)
& e6 != op(e6,e6) )
| sP0 ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
( ( e0 = op(e0,e0)
& e1 = op(e1,e1)
& e2 = op(e2,e2)
& e3 = op(e3,e3)
& e4 = op(e4,e4)
& e5 = op(e5,e5)
& e6 = op(e6,e6) )
| ~ sP0 ),
inference(nnf_transformation,[],[f9]) ).
fof(f523,plain,
( e6 = op(e6,e6)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f524,plain,
( e5 = op(e5,e5)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f525,plain,
( e4 = op(e4,e4)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f526,plain,
( e3 = op(e3,e3)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f527,plain,
( e2 = op(e2,e2)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f528,plain,
( e1 = op(e1,e1)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f529,plain,
( e0 = op(e0,e0)
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f530,plain,
( e6 != op(e6,e6)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f531,plain,
( e5 != op(e5,e5)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f532,plain,
( e4 != op(e4,e4)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f533,plain,
( e3 != op(e3,e3)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f534,plain,
( e2 != op(e2,e2)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f535,plain,
( e1 != op(e1,e1)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f536,plain,
( e0 != op(e0,e0)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f537,plain,
( e0 != op(e0,e0)
| e1 != op(e1,e1)
| e2 != op(e2,e2)
| e3 != op(e3,e3)
| e4 != op(e4,e4)
| e5 != op(e5,e5)
| e6 != op(e6,e6) ),
inference(cnf_transformation,[],[f10]) ).
fof(f538,plain,
( e0 = op(e0,e0)
| e1 = op(e1,e1)
| e2 = op(e2,e2)
| e3 = op(e3,e3)
| e4 = op(e4,e4)
| e5 = op(e5,e5)
| e6 = op(e6,e6) ),
inference(cnf_transformation,[],[f10]) ).
fof(f540,definition,
( spl1_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f544,definition,
( spl1_2
<=> e6 = op(e6,e6) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f547,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f530,f544,f540]) ).
fof(f549,definition,
( spl1_3
<=> e5 = op(e5,e5) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f552,plain,
( spl1_1
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f531,f549,f540]) ).
fof(f554,definition,
( spl1_4
<=> e4 = op(e4,e4) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f557,plain,
( spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f532,f554,f540]) ).
fof(f559,definition,
( spl1_5
<=> e3 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f562,plain,
( spl1_1
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f533,f559,f540]) ).
fof(f564,definition,
( spl1_6
<=> e2 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f567,plain,
( spl1_1
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f534,f564,f540]) ).
fof(f569,definition,
( spl1_7
<=> e1 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f572,plain,
( spl1_1
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f535,f569,f540]) ).
fof(f574,definition,
( spl1_8
<=> e0 = op(e0,e0) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f577,plain,
( spl1_1
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f536,f574,f540]) ).
fof(f578,plain,
( ~ spl1_2
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5
| ~ spl1_6
| ~ spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f537,f574,f569,f564,f559,f554,f549,f544]) ).
fof(f579,plain,
( spl1_2
| spl1_3
| spl1_4
| spl1_5
| spl1_6
| spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f538,f574,f569,f564,f559,f554,f549,f544]) ).
fof(f580,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f523,f544,f540]) ).
fof(f581,plain,
( ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f524,f549,f540]) ).
fof(f582,plain,
( ~ spl1_1
| spl1_4 ),
inference(avatar_split_clause,[],[f525,f554,f540]) ).
fof(f583,plain,
( ~ spl1_1
| spl1_5 ),
inference(avatar_split_clause,[],[f526,f559,f540]) ).
fof(f584,plain,
( ~ spl1_1
| spl1_6 ),
inference(avatar_split_clause,[],[f527,f564,f540]) ).
fof(f585,plain,
( ~ spl1_1
| spl1_7 ),
inference(avatar_split_clause,[],[f528,f569,f540]) ).
fof(f586,plain,
( ~ spl1_1
| spl1_8 ),
inference(avatar_split_clause,[],[f529,f574,f540]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f547]) ).
cnf(s2,plain,
( spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f552]) ).
cnf(s3,plain,
( spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f557]) ).
cnf(s4,plain,
( spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f562]) ).
cnf(s5,plain,
( spl1_1
| ~ spl1_6 ),
inference(sat_conversion,[],[f567]) ).
cnf(s6,plain,
( spl1_1
| ~ spl1_7 ),
inference(sat_conversion,[],[f572]) ).
cnf(s7,plain,
( spl1_1
| ~ spl1_8 ),
inference(sat_conversion,[],[f577]) ).
cnf(s8,plain,
( ~ spl1_2
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5
| ~ spl1_6
| ~ spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f578]) ).
cnf(s9,plain,
( spl1_2
| spl1_3
| spl1_4
| spl1_5
| spl1_6
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f579]) ).
cnf(s10,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f580]) ).
cnf(s11,plain,
( ~ spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f581]) ).
cnf(s12,plain,
( ~ spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f582]) ).
cnf(s13,plain,
( ~ spl1_1
| spl1_5 ),
inference(sat_conversion,[],[f583]) ).
cnf(s14,plain,
( ~ spl1_1
| spl1_6 ),
inference(sat_conversion,[],[f584]) ).
cnf(s15,plain,
( ~ spl1_1
| spl1_7 ),
inference(sat_conversion,[],[f585]) ).
cnf(s16,plain,
( ~ spl1_1
| spl1_8 ),
inference(sat_conversion,[],[f586]) ).
cnf(s164,plain,
spl1_1,
inference(rat,[],[s9,s1,s2,s3,s4,s5,s6,s7]) ).
cnf(s165,plain,
spl1_8,
inference(rat,[],[s16,s164]) ).
cnf(s166,plain,
spl1_7,
inference(rat,[],[s15,s164]) ).
cnf(s167,plain,
spl1_6,
inference(rat,[],[s14,s164]) ).
cnf(s168,plain,
spl1_5,
inference(rat,[],[s13,s164]) ).
cnf(s169,plain,
spl1_4,
inference(rat,[],[s12,s164]) ).
cnf(s170,plain,
spl1_3,
inference(rat,[],[s11,s164]) ).
cnf(s171,plain,
spl1_2,
inference(rat,[],[s10,s164]) ).
cnf(s172,plain,
$false,
inference(rat,[],[s8,s165,s166,s167,s168,s171,s169,s170]) ).
fof(f2078,plain,
$false,
inference(avatar_sat_refutation,[],[s172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG194+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n026.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 19:44:12 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.26 Running first-order model finding
% 0.08/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.32 % (4176903)Will run a generic schedule for satisfiability detection.
% 0.20/0.32 % (4176911)dis+10_1_sil=32000:sp=arity:random_seed=369883468:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.32 % (4176909)% WARNING: option uhcvi not known.
% 0.20/0.32 % (4176911) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4176903-4176911"...
% 0.20/0.32 % (4176908)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=179859829_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.32 % (4176909)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=855176593:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.32 % (4176910)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1199943824:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.32 % (4176914)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1345286026:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.32 % (4176912)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1039578099:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.32 % (4176911)...printing done.
% 0.20/0.32 % (4176913)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3329550284:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.32 % (4176911)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (4176911)------------------------------
% 0.20/0.32 % (4176911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4176911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4176911)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4176911)Termination reason: Refutation
% 0.20/0.32 % (4176911)Time elapsed: 0.007 s
% 0.20/0.32 % (4176911)Peak memory usage: 13 MB
% 0.20/0.32 % (4176911)Instructions burned: 27 (million)
% 0.20/0.32 % (4176903)Success in time 0.053 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------