%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG368-1 : 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 : n002.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 09:19:52 AM UTC 2026
% Result : Unsatisfiable 0.66s 0.98s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 13 unt; 2 def)
% Number of atoms : 76 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 42 ~; 32 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f297,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f991,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f992,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(reorient_equations,[],[f991]) ).
fof(f993,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f994,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(reorient_equations,[],[f993]) ).
fof(f995,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_1) ).
fof(f996,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0)
| ~ class_Ring__and__Field_Oidom(X0) ),
inference(reorient_equations,[],[f995]) ).
fof(f997,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ep_0) ).
fof(f1011,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1012,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f1011]) ).
fof(f1038,negated_conjecture,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X0),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1101,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1153,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1156,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1164,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1178,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1262,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X0),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1038,f1012]) ).
fof(f1263,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X0),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[],[f1262,f1164]) ).
fof(f1695,definition,
( spl0_3
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1696,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1695]) ).
fof(f1702,definition,
( spl0_5
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f1703,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| spl0_5 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f1705,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| spl0_5 ),
inference(superposition,[],[f1703,f994]) ).
fof(f1706,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1705,f1153]) ).
fof(f1707,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1263,f996]) ).
fof(f1717,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| spl0_5 ),
inference(superposition,[],[f1706,f1012]) ).
fof(f1718,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1717,f1164]) ).
fof(f1719,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_5 ),
inference(superposition,[],[f1718,f992]) ).
fof(f1720,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1719,f997]) ).
fof(f1721,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1720,f1156]) ).
fof(f1722,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f1721]) ).
fof(f1723,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[],[f1707,f1178]) ).
fof(f1724,plain,
( spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1723,f1702,f1695]) ).
fof(f1731,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(resolution,[],[f1696,f297]) ).
fof(f1738,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1731,f1101]) ).
fof(f1739,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1738]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f1722]) ).
cnf(s7,plain,
( spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f1724]) ).
cnf(s12,plain,
~ spl0_3,
inference(sat_conversion,[],[f1739]) ).
cnf(s13,plain,
~ spl0_5,
inference(rat,[],[s7,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s13]) ).
fof(f1740,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG368-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 20:16:22 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 0.66/0.98 % (701337)Input is clausal, will run a generic CNF schedule.
% 0.66/0.98 % (701347)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3137870616:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.66/0.98 % (701347)First to succeed.
% 0.66/0.98 % (701347)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-701337"
% 0.66/0.98 % (701346)lrs+10_1_sil=8000:sp=occurrence:random_seed=4272877934:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.66/0.98 % (701344)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2634944114:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.66/0.98 % (701349)dis-21_1_sil=8000:lcm=predicate:random_seed=316023814: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)
% 0.66/0.98 % (701348)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3715628109:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.66/0.98 % (701343)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=2038650425:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.66/0.98 % (701345)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2598930226:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.66/0.98 % (701348)Also succeeded, but the first one will report.
% 0.66/0.98 % (701349)Instruction limit reached!
% 0.66/0.98 % (701349)------------------------------
% 0.66/0.98 % (701349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.98 % (701349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.98 % (701349)CaDiCaL version: 2.1.3
% 0.66/0.98 % (701349)Termination reason: Instruction limit
% 0.66/0.98 % (701349)Termination phase: Saturation
% 0.66/0.98 % (701349)Time elapsed: 0.068 s
% 0.66/0.98 % (701349)Peak memory usage: 89 MB
% 0.66/0.98 % (701349)Instructions burned: 117 (million)
% 0.66/0.98 % (701346)Instruction limit reached!
% 0.66/0.98 % (701346)------------------------------
% 0.66/0.98 % (701346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.98 % (701346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.98 % (701346)CaDiCaL version: 2.1.3
% 0.66/0.98 % (701346)Termination reason: Instruction limit
% 0.66/0.98 % (701346)Termination phase: Saturation
% 0.66/0.98 % (701346)Time elapsed: 0.071 s
% 0.66/0.98 % (701346)Peak memory usage: 89 MB
% 0.66/0.98 % (701346)Instructions burned: 108 (million)
% 0.66/0.98 % (701347)Refutation found. Thanks to Tanya!
% 0.66/0.98 % SZS status Unsatisfiable for theBenchmark
% 0.66/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.18 % (701347)------------------------------
% 2.77/1.18 % (701347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.18 % (701347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.18 % (701347)CaDiCaL version: 2.1.3
% 2.77/1.18 % (701347)Termination reason: Refutation
% 2.77/1.18 % (701347)Time elapsed: 0.014 s
% 2.77/1.18 % (701347)Peak memory usage: 90 MB
% 2.77/1.18 % (701347)Instructions burned: 36 (million)
% 2.77/1.18 % (701347)------------------------------
% 2.77/1.18 % (701347)------------------------------
% 2.77/1.18 % (701337)Success in time 0.333 s
% 2.77/1.18 % Vampire exiting
%------------------------------------------------------------------------------