%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:30:27 AM UTC 2026
% Result : Unsatisfiable 0.86s 0.39s
% Output : Refutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 8 unt; 3 def)
% Number of atoms : 55 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f273,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cs0_0) ).
fof(f539,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X0,X2),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__infinity_0) ).
fof(f540,plain,
! [X2,X3,X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X0,X2),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 ),
inference(reorient_equations,[],[f539]) ).
fof(f565,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1020,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X0,X2),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 ),
inference(consistent_polarity_flipping,[],[f540]) ).
fof(f1042,plain,
! [X0] :
( v_thesis____
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(consistent_polarity_flipping,[],[f566]) ).
fof(f1043,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f567]) ).
fof(f1151,definition,
( spl0_1
<=> ! [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_1])],[avatar_definition]) ).
fof(f1152,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_1 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f1154,definition,
( spl0_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1157,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1043,f1154,f1151]) ).
fof(f1159,definition,
( spl0_3
<=> ! [X0] : ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1160,plain,
( ! [X0] : ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1161,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f1042,f1154,f1159]) ).
fof(f1162,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f565,f1154]) ).
fof(f3602,plain,
( ! [X0] :
( c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,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),v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ spl0_1 ),
inference(resolution,[],[f1020,f1152]) ).
fof(f3618,plain,
( ! [X0] : c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,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),v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f3602,f273]) ).
fof(f3836,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f3618,f1160]) ).
fof(f3843,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f3836]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1157]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f1161]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f1162]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f3843]) ).
cnf(s55,plain,
spl0_3,
inference(rat,[],[s2,s3]) ).
cnf(s56,plain,
~ spl0_1,
inference(rat,[],[s50,s55]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s1,s3,s56]) ).
fof(f3847,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:14:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.86/0.39 % (3722325)Will run a generic schedule for satisfiability detection.
% 0.86/0.39 % (3722334)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2599252126:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.86/0.39 % (3722331)% WARNING: option uhcvi not known.
% 0.86/0.39 % (3722331)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1905444996:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.86/0.39 % (3722330)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2596230567_2999 on theBenchmark for (2999ds/0Mi)
% 0.86/0.39 % (3722332)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=943915974:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.86/0.39 % (3722333)dis+10_1_sil=32000:sp=arity:random_seed=2893001053:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.86/0.39 % (3722335)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=990003329:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.86/0.39 % (3722336)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2014926916:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.86/0.39 % (3722334)Instruction limit reached!
% 0.86/0.39 % (3722334)------------------------------
% 0.86/0.39 % (3722334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (3722334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (3722334)CaDiCaL version: 2.1.3
% 0.86/0.39 % (3722334)Termination reason: Instruction limit
% 0.86/0.39 % (3722334)Termination phase: Saturation
% 0.86/0.39 % (3722334)Time elapsed: 0.039 s
% 0.86/0.39 % (3722334)Peak memory usage: 13 MB
% 0.86/0.39 % (3722334)Instructions burned: 119 (million)
% 0.86/0.39 % TRYING [1]
% 0.86/0.39 % (3722344)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1097047124:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.86/0.39 % TRYING [2]
% 0.86/0.39 % (3722333)Instruction limit reached!
% 0.86/0.39 % (3722333)------------------------------
% 0.86/0.39 % (3722333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (3722333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (3722333)CaDiCaL version: 2.1.3
% 0.86/0.39 % (3722333)Termination reason: Instruction limit
% 0.86/0.39 % (3722333)Termination phase: Saturation
% 0.86/0.39 % (3722333)Time elapsed: 0.066 s
% 0.86/0.39 % (3722333)Peak memory usage: 13 MB
% 0.86/0.39 % (3722333)Instructions burned: 104 (million)
% 0.86/0.39 % (3722335)Instruction limit reached!
% 0.86/0.39 % (3722335)------------------------------
% 0.86/0.39 % (3722335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (3722335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (3722335)CaDiCaL version: 2.1.3
% 0.86/0.39 % (3722335)Termination reason: Instruction limit
% 0.86/0.39 % (3722335)Termination phase: Saturation
% 0.86/0.39 % (3722335)Time elapsed: 0.076 s
% 0.86/0.39 % (3722335)Peak memory usage: 13 MB
% 0.86/0.39 % (3722335)Instructions burned: 131 (million)
% 0.86/0.39 % TRYING [1]
% 0.86/0.39 % (3722346)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3065287534:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.86/0.39 % TRYING [2]
% 0.86/0.39 % (3722347)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1996704535:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.86/0.39 % (3722331) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3722325-3722331"...
% 0.86/0.39 % TRYING [3]
% 0.86/0.39 % (3722331)...printing done.
% 0.86/0.39 % (3722336)Instruction limit reached!
% 0.86/0.39 % (3722336)------------------------------
% 0.86/0.39 % (3722336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (3722336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (3722336)CaDiCaL version: 2.1.3
% 0.86/0.39 % (3722336)Termination reason: Instruction limit
% 0.86/0.39 % (3722336)Termination phase: Saturation
% 0.86/0.39 % (3722336)Time elapsed: 0.107 s
% 0.86/0.39 % (3722336)Peak memory usage: 15 MB
% 0.86/0.39 % (3722336)Instructions burned: 160 (million)
% 0.86/0.39 % (3722331)Refutation found. Thanks to Tanya!
% 0.86/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.86/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.86/0.39 % (3722331)------------------------------
% 0.86/0.39 % (3722331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (3722331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (3722331)CaDiCaL version: 2.1.3
% 0.86/0.39 % (3722331)Termination reason: Refutation
% 0.86/0.39 % (3722331)Time elapsed: 0.106 s
% 0.86/0.39 % (3722331)Peak memory usage: 14 MB
% 0.86/0.39 % (3722331)Instructions burned: 158 (million)
% 0.86/0.39 % (3722325)Success in time 0.16 s
% 0.86/0.39 % Vampire exiting
%------------------------------------------------------------------------------