%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG198+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:19:06 AM UTC 2026
% Result : Theorem 2.59s 1.09s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 64 ( 25 ~; 0 |; 39 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f8,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 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( 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(flattening,[],[f8]) ).
fof(f10,plain,
e6 = op(e6,e6),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
e6 != op(e6,e6),
inference(cnf_transformation,[],[f9]) ).
fof(f541,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG198+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 19:44:28 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.59/1.09 % (4177921)Detected formulas, will run a generic FOF schedule.
% 2.59/1.09 % (4177930)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3060771729:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.09 % (4177930)First to succeed.
% 2.59/1.09 % (4177930)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4177921"
% 2.59/1.09 % (4177928)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3998688136:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.09 % (4177926)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=1071018940:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.09 % (4177927)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1602006011:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.09 % (4177929)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3902158177:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.09 % (4177932)dis-21_1_sil=8000:lcm=predicate:random_seed=2995235305:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.59/1.09 % (4177931)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1948147381:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.09 % (4177929)Also succeeded, but the first one will report.
% 2.59/1.09 % (4177932)Also succeeded, but the first one will report.
% 2.59/1.09 % (4177931)Also succeeded, but the first one will report.
% 2.59/1.09 % (4177930)Refutation found. Thanks to Tanya!
% 2.59/1.09 % SZS status Theorem for theBenchmark
% 2.59/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.09 % (4177930)------------------------------
% 2.59/1.09 % (4177930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.09 % (4177930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.09 % (4177930)CaDiCaL version: 2.1.3
% 2.59/1.09 % (4177930)Termination reason: Refutation
% 2.59/1.09 % (4177930)Time elapsed: 0.005 s
% 2.59/1.09 % (4177930)Peak memory usage: 88 MB
% 2.59/1.09 % (4177930)Instructions burned: 18 (million)
% 2.59/1.09 % (4177930)------------------------------
% 2.59/1.09 % (4177930)------------------------------
% 2.59/1.09 % (4177921)Success in time 0.299 s
% 2.59/1.09 % Vampire exiting
%------------------------------------------------------------------------------