%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG353-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:19:50 AM UTC 2026
% Result : Unsatisfiable 3.57s 1.21s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 21 ( 14 unt; 4 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 9 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f778,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f779,negated_conjecture,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f780,negated_conjecture,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f781,negated_conjecture,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f782,negated_conjecture,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f907,definition,
( spl0_1
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f911,definition,
( spl0_2
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f915,definition,
( spl0_3
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f919,definition,
( spl0_4
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f922,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f778,f919,f915,f911,f907]) ).
fof(f923,plain,
spl0_4,
inference(avatar_split_clause,[],[f782,f919]) ).
fof(f924,plain,
spl0_3,
inference(avatar_split_clause,[],[f781,f915]) ).
fof(f925,plain,
spl0_2,
inference(avatar_split_clause,[],[f780,f911]) ).
fof(f926,plain,
spl0_1,
inference(avatar_split_clause,[],[f779,f907]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f922]) ).
cnf(s2,plain,
spl0_4,
inference(sat_conversion,[],[f923]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f924]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f925]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f926]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s3,s4,s5]) ).
fof(f928,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG353-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:14:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.57/1.21 % (3947954)Input is clausal, will run a generic CNF schedule.
% 3.57/1.21 % (3948007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1070224807:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.57/1.21 % (3948009)lrs+10_1_sil=8000:sp=occurrence:random_seed=1102112696:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.57/1.21 % (3948011)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3055619173:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.57/1.21 % (3948006)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=332588458:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.57/1.21 % (3948008)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2679262775:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.57/1.21 % (3948010)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1370731006:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.57/1.21 % (3948012)dis-21_1_sil=8000:lcm=predicate:random_seed=1953696514: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)
% 3.57/1.21 % (3948009)First to succeed.
% 3.57/1.21 % (3948009)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3947954"
% 3.57/1.21 % (3948012)Also succeeded, but the first one will report.
% 3.57/1.21 % (3948011)Also succeeded, but the first one will report.
% 3.57/1.21 % (3948010)Also succeeded, but the first one will report.
% 3.57/1.21 % (3948009)Refutation found. Thanks to Tanya!
% 3.57/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.57/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.21 % (3948009)------------------------------
% 3.57/1.21 % (3948009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.21 % (3948009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.21 % (3948009)CaDiCaL version: 2.1.3
% 3.57/1.21 % (3948009)Termination reason: Refutation
% 3.57/1.21 % (3948009)Time elapsed: 0.005 s
% 3.57/1.21 % (3948009)Peak memory usage: 89 MB
% 3.57/1.21 % (3948009)Instructions burned: 5 (million)
% 3.57/1.21 % (3948009)------------------------------
% 3.57/1.21 % (3948009)------------------------------
% 3.57/1.21 % (3947954)Success in time 0.438 s
% 3.57/1.21 % Vampire exiting
%------------------------------------------------------------------------------