%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG395-1 : 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 : n018.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 09:19:56 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.20s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 2 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 5 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f900,axiom,
! [X0,X1] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__1(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minimum__modulus_0) ).
fof(f915,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f916,negated_conjecture,
! [X0] :
( v_thesis____
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1067,definition,
( spl0_1
<=> ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1068,plain,
( ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f1070,definition,
( spl0_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1073,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f916,f1070,f1067]) ).
fof(f1074,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f915,f1070]) ).
fof(f1149,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f900,f1068]) ).
fof(f1156,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1149]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f1074]) ).
cnf(s6,plain,
~ spl0_1,
inference(sat_conversion,[],[f1156]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
fof(f1159,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG395-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:18:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.18/1.20 % (3725698)Input is clausal, will run a generic CNF schedule.
% 0.18/1.20 % (3725703)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=2273815629:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.18/1.20 % (3725708)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3741680162:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.18/1.20 % (3725704)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4024770202:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.18/1.20 % (3725706)lrs+10_1_sil=8000:sp=occurrence:random_seed=3745629955:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.18/1.20 % (3725705)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=346194064:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.18/1.20 % (3725707)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4029946351:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.18/1.20 % (3725708)First to succeed.
% 0.18/1.20 % (3725708)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3725698"
% 0.18/1.20 % (3725709)dis-21_1_sil=8000:lcm=predicate:random_seed=4176444800: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)
% 0.18/1.20 % (3725706)Instruction limit reached!
% 0.18/1.20 % (3725706)------------------------------
% 0.18/1.20 % (3725706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (3725706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (3725706)CaDiCaL version: 2.1.3
% 0.18/1.20 % (3725706)Termination reason: Instruction limit
% 0.18/1.20 % (3725706)Termination phase: Saturation
% 0.18/1.20 % (3725706)Time elapsed: 0.067 s
% 0.18/1.20 % (3725706)Peak memory usage: 90 MB
% 0.18/1.20 % (3725706)Instructions burned: 107 (million)
% 0.18/1.20 % (3725707)Instruction limit reached!
% 0.18/1.20 % (3725707)------------------------------
% 0.18/1.20 % (3725707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (3725707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (3725707)CaDiCaL version: 2.1.3
% 0.18/1.20 % (3725707)Termination reason: Instruction limit
% 0.18/1.20 % (3725707)Termination phase: Saturation
% 0.18/1.20 % (3725707)Time elapsed: 0.076 s
% 0.18/1.20 % (3725707)Peak memory usage: 89 MB
% 0.18/1.20 % (3725707)Instructions burned: 114 (million)
% 0.18/1.20 % (3725709)Instruction limit reached!
% 0.18/1.20 % (3725709)------------------------------
% 0.18/1.20 % (3725709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (3725709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (3725709)CaDiCaL version: 2.1.3
% 0.18/1.20 % (3725709)Termination reason: Instruction limit
% 0.18/1.20 % (3725709)Termination phase: Saturation
% 0.18/1.20 % (3725709)Time elapsed: 0.068 s
% 0.18/1.20 % (3725709)Peak memory usage: 89 MB
% 0.18/1.20 % (3725709)Instructions burned: 118 (million)
% 0.18/1.20 % (3725717)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=2482915172:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.18/1.20 % (3725717)Also succeeded, but the first one will report.
% 0.18/1.20 % (3725719)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2792635209:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.18/1.20 % (3725718)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=608349425:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.18/1.20 % (3725718)Also succeeded, but the first one will report.
% 0.18/1.20 % (3725708)Refutation found. Thanks to Tanya!
% 0.18/1.20 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.20 % (3725708)------------------------------
% 0.18/1.20 % (3725708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (3725708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (3725708)CaDiCaL version: 2.1.3
% 0.18/1.20 % (3725708)Termination reason: Refutation
% 0.18/1.20 % (3725708)Time elapsed: 0.019 s
% 0.18/1.20 % (3725708)Peak memory usage: 90 MB
% 0.18/1.20 % (3725708)Instructions burned: 32 (million)
% 0.18/1.20 % (3725708)------------------------------
% 0.18/1.20 % (3725708)------------------------------
% 0.18/1.20 % (3725698)Success in time 0.446 s
% 0.18/1.20 % Vampire exiting
%------------------------------------------------------------------------------