%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG386-1 : 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 : 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 09:19:55 AM UTC 2026
% Result : Unsatisfiable 3.70s 1.22s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 7 unt; 3 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 14 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f564,axiom,
! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f565,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f566,negated_conjecture,
! [X0] :
( v_thesis____
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f567,negated_conjecture,
! [X0] :
( v_thesis____
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f742,definition,
( spl0_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f751,definition,
( spl0_4
<=> ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f752,plain,
( ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f753,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f567,f742,f751]) ).
fof(f755,definition,
( spl0_5
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f756,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f757,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f566,f742,f755]) ).
fof(f758,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f565,f742]) ).
fof(f928,plain,
( ! [X0] : ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_4 ),
inference(resolution,[],[f564,f752]) ).
fof(f934,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f928,f756]) ).
fof(f949,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f934]) ).
cnf(s3,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f753]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f757]) ).
cnf(s5,plain,
~ spl0_2,
inference(sat_conversion,[],[f758]) ).
cnf(s9,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f949]) ).
cnf(s10,plain,
spl0_5,
inference(rat,[],[s4,s5]) ).
cnf(s11,plain,
~ spl0_4,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s11,s5]) ).
fof(f950,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:15:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.70/1.22 % (492440)Input is clausal, will run a generic CNF schedule.
% 3.70/1.22 % (492451)dis-21_1_sil=8000:lcm=predicate:random_seed=2778463951: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)
% 3.70/1.22 % (492451)Instruction limit reached!
% 3.70/1.22 % (492451)------------------------------
% 3.70/1.22 % (492451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.22 % (492451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.22 % (492451)CaDiCaL version: 2.1.3
% 3.70/1.22 % (492451)Termination reason: Instruction limit
% 3.70/1.22 % (492451)Termination phase: Saturation
% 3.70/1.22 % (492451)Time elapsed: 0.037 s
% 3.70/1.22 % (492451)Peak memory usage: 89 MB
% 3.70/1.22 % (492451)Instructions burned: 119 (million)
% 3.70/1.22 % (492447)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2787159186:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.70/1.22 % (492448)lrs+10_1_sil=8000:sp=occurrence:random_seed=595531356:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.70/1.22 % (492445)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=1443959648:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.70/1.22 % (492449)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2472901376:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.70/1.22 % (492446)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=896689226:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.70/1.22 % (492448)First to succeed.
% 3.70/1.22 % (492448)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-492440"
% 3.70/1.22 % (492450)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=979571860:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.70/1.22 % (492450)Also succeeded, but the first one will report.
% 3.70/1.22 % (492449)Instruction limit reached!
% 3.70/1.22 % (492449)------------------------------
% 3.70/1.22 % (492449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.22 % (492449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.22 % (492449)CaDiCaL version: 2.1.3
% 3.70/1.22 % (492449)Termination reason: Instruction limit
% 3.70/1.22 % (492449)Termination phase: Saturation
% 3.70/1.22 % (492449)Time elapsed: 0.072 s
% 3.70/1.22 % (492449)Peak memory usage: 89 MB
% 3.70/1.22 % (492449)Instructions burned: 115 (million)
% 3.70/1.22 % (492458)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=2795040901:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.70/1.22 % (492458)Also succeeded, but the first one will report.
% 3.70/1.22 % (492460)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1082269589: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)
% 3.70/1.22 % (492460)Also succeeded, but the first one will report.
% 3.70/1.22 % (492448)Refutation found. Thanks to Tanya!
% 3.70/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.70/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.22 % (492448)------------------------------
% 3.70/1.22 % (492448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.22 % (492448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.22 % (492448)CaDiCaL version: 2.1.3
% 3.70/1.22 % (492448)Termination reason: Refutation
% 3.70/1.22 % (492448)Time elapsed: 0.012 s
% 3.70/1.22 % (492448)Peak memory usage: 90 MB
% 3.70/1.22 % (492448)Instructions burned: 15 (million)
% 3.70/1.22 % (492448)------------------------------
% 3.70/1.22 % (492448)------------------------------
% 3.70/1.22 % (492440)Success in time 0.463 s
% 3.70/1.22 % Vampire exiting
%------------------------------------------------------------------------------