%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 12:54:04 PM UTC 2026
% Result : Unsatisfiable 7.58s 1.99s
% Output : CNFRefutation 7.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f520,axiom,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_lessequals(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),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f521,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f522,negated_conjecture,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f523,negated_conjecture,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(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),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tcf(c_1047,plain,
! [X0: $i] :
( c_lessequals(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),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_1048,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f521]) ).
tcf(c_1049,negated_conjecture,
! [X0: $i] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_1050,negated_conjecture,
! [X0: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(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),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f523]) ).
tcf(c_1586,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_1047,c_1050]) ).
tcf(c_4317,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(global_subsumption_just,[status(thm)],[c_1586,c_1048,c_1586]) ).
tcf(c_4322,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_1049,c_4317]) ).
tcf(c_4324,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1048,c_4322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n011.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 05:25:28 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.51
% 0.26/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.51
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 7.58/1.99 % SZS status Started for theBenchmark.p
% 7.58/1.99 % SZS status Unsatisfiable for theBenchmark.p
% 7.58/1.99
% 7.58/1.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.58/1.99
% 7.58/1.99 % ------ iProver source info
% 7.58/1.99
% 7.58/1.99 % git: date: 2026-07-19 20:42:38 +0200
% 7.58/1.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.58/1.99 % git: non_committed_changes: false
% 7.58/1.99
% 7.58/1.99 % ------ Parsing...% successful
% 7.58/1.99
% 7.58/1.99
% 7.58/1.99 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.58/1.99 % ------ Proving...
% 7.58/1.99 % ------ Problem Properties
% 7.58/1.99
% 7.58/1.99 %
% 7.58/1.99 % clauses 563
% 7.58/1.99 % conjectures 2
% 7.58/1.99 % EPR 134
% 7.58/1.99 % Horn 457
% 7.58/1.99 % unary 92
% 7.58/1.99 % binary 142
% 7.58/1.99 % lits 1730
% 7.58/1.99 % lits eq 207
% 7.58/1.99 % fd_pure 0
% 7.58/1.99 % fd_pseudo 0
% 7.58/1.99 % fd_cond 1
% 7.58/1.99 % fd_pseudo_cond 61
% 7.58/1.99 % AC symbols 0
% 7.58/1.99
% 7.58/1.99 % ------ Input Options Time Limit: Unbounded
% 7.58/1.99
% 7.58/1.99
% 7.58/1.99 % ------
% 7.58/1.99 % Current options:
% 7.58/1.99 % ------
% 7.58/1.99
% 7.58/1.99
% 7.58/1.99 %
% 7.58/1.99
% 7.58/1.99 % ------ Proving...
% 7.58/1.99 %
% 7.58/1.99
% 7.58/1.99 % SZS status Unsatisfiable for theBenchmark.p
% 7.58/1.99
% 7.58/1.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.58/1.99
% 7.58/1.99
%------------------------------------------------------------------------------