%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG373-1 : 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 : n001.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 12:54:07 PM UTC 2026
% Result : Unsatisfiable 25.07s 4.42s
% Output : CNFRefutation 25.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 25 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f416,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f417,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f416]) ).
fof(f418,negated_conjecture,
! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f419,negated_conjecture,
! [X0] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f420,negated_conjecture,
! [X0] : ~ c_HOL_Oord__class_Oless(v_x(X0),X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_877,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ) ),
inference(cnf_transformation,[],[f417]) ).
tcf(c_878,negated_conjecture,
! [X0: $i] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f418]) ).
tcf(c_879,negated_conjecture,
! [X0: $i] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f419]) ).
tcf(c_880,negated_conjecture,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(v_x(X0),X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f420]) ).
tcf(c_1598,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(v_x(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal) ) ),
inference(instantiation,[status(thm)],[c_877]) ).
tcf(c_3932,plain,
( c_HOL_Oord__class_Oless(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
inference(instantiation,[status(thm)],[c_1598]) ).
tcf(c_3933,plain,
~ c_HOL_Oord__class_Oless(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_880]) ).
tcf(c_14668,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_878]) ).
tcf(c_24546,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_879]) ).
tcf(c_24547,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24546,c_14668,c_3933,c_3932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 05:35:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 25.07/4.42 % SZS status Started for theBenchmark.p
% 25.07/4.42 % SZS status Unsatisfiable for theBenchmark.p
% 25.07/4.42
% 25.07/4.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.07/4.42
% 25.07/4.42 % ------ iProver source info
% 25.07/4.42
% 25.07/4.42 % git: date: 2026-07-19 20:42:38 +0200
% 25.07/4.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.07/4.42 % git: non_committed_changes: false
% 25.07/4.42
% 25.07/4.42 % ------ Parsing...% successful
% 25.07/4.42
% 25.07/4.42
% 25.07/4.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.07/4.42
% 25.07/4.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 25.07/4.42
% 25.07/4.42 % ------ Preprocessing...%
% 25.07/4.42
% 25.07/4.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.07/4.42 % ------ Proving...
% 25.07/4.42 % ------ Problem Properties
% 25.07/4.42
% 25.07/4.42 %
% 25.07/4.42 % clauses 430
% 25.07/4.42 % conjectures 19
% 25.07/4.42 % EPR 137
% 25.07/4.42 % Horn 388
% 25.07/4.42 % unary 117
% 25.07/4.42 % binary 142
% 25.07/4.42 % lits 1023
% 25.07/4.42 % lits eq 139
% 25.07/4.42 % fd_pure 0
% 25.07/4.42 % fd_pseudo 0
% 25.07/4.42 % fd_cond 5
% 25.07/4.42 % fd_pseudo_cond 27
% 25.07/4.42 % AC symbols 0
% 25.07/4.42
% 25.07/4.42 % ------ Input Options Time Limit: Unbounded
% 25.07/4.42
% 25.07/4.42
% 25.07/4.42 % ------
% 25.07/4.42 % Current options:
% 25.07/4.42 % ------
% 25.07/4.42
% 25.07/4.42
% 25.07/4.42 %
% 25.07/4.42
% 25.07/4.42 % ------ Proving...
% 25.07/4.42 %
% 25.07/4.42
% 25.07/4.42 % SZS status Unsatisfiable for theBenchmark.p
% 25.07/4.42
% 25.07/4.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.07/4.42
% 25.07/4.42
%------------------------------------------------------------------------------