%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW229+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 : Fri Sep 25 03:29:18 PM UTC 2026
% Result : Theorem 6.77s 1.63s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 22 ( 1 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(f1169,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1254,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1255,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(negated_conjecture,[status(cth)],[f1254]) ).
fof(f1260,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(flattening,[],[f1255]) ).
fof(f1262,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f2643,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f4215,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1169]) ).
fof(f4300,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(cnf_transformation,[],[f1260]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2643]) ).
tcf(c_1583,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4215]) ).
tcf(c_1668,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(cnf_transformation,[],[f4300]) ).
tcf(c_2693,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_11759,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2693,c_1583]) ).
tcf(c_11760,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
inference(unflattening,[status(thm)],[c_11759]) ).
tcf(c_11890,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1668,c_11760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW229+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 21:48:43 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 6.77/1.63 % SZS status Started for theBenchmark.p
% 6.77/1.63 % SZS status Theorem for theBenchmark.p
% 6.77/1.63
% 6.77/1.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.77/1.63
% 6.77/1.63 % ------ iProver source info
% 6.77/1.63
% 6.77/1.63 % git: date: 2026-07-19 20:42:38 +0200
% 6.77/1.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.77/1.63 % git: non_committed_changes: false
% 6.77/1.63
% 6.77/1.63 % ------ Parsing...
% 6.77/1.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.77/1.63
% 6.77/1.63 % ------ Preprocessing... sup_sim: 7 pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s%
% 6.77/1.63
% 6.77/1.63 % SZS status Theorem for theBenchmark.p
% 6.77/1.63
% 6.77/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.77/1.63
% 6.77/1.63
%------------------------------------------------------------------------------