%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 12:54:11 PM UTC 2026
% Result : Unsatisfiable 26.34s 4.32s
% Output : CNFRefutation 26.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 47 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f430,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f596,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0)
| ~ class_Ring__and__Field_Omult__mono(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f627,axiom,
! [X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f634,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I2_J_0) ).
fof(f682,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f690,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f764,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f790,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f430]) ).
tcf(c_1198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0)
| ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(cnf_transformation,[],[f596]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f627]) ).
tcf(c_1232,plain,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f634]) ).
tcf(c_1274,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(cnf_transformation,[],[f682]) ).
tcf(c_1281,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f690]) ).
tcf(c_1355,plain,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f764]) ).
tcf(c_1381,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f790]) ).
tcf(c_1959,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_1227]) ).
tcf(c_6571,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_1281,c_1274]) ).
tcf(c_8579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1198,c_1355]) ).
tcf(c_8580,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_8579]) ).
tcf(c_9544,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1959,c_1381]) ).
tcf(c_9545,plain,
! [X0: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_9544]) ).
tcf(c_18342,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_1274,c_8580]) ).
tcf(c_20440,plain,
( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_18342,c_6571]) ).
tcf(c_20445,plain,
~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_20440,c_9545]) ).
tcf(c_26062,plain,
c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_1232,c_1058]) ).
tcf(c_26072,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_26062,c_20445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 05:34:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 26.34/4.32 % SZS status Started for theBenchmark.p
% 26.34/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 26.34/4.32
% 26.34/4.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.34/4.32
% 26.34/4.32 % ------ iProver source info
% 26.34/4.32
% 26.34/4.32 % git: date: 2026-07-19 20:42:38 +0200
% 26.34/4.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.34/4.32 % git: non_committed_changes: false
% 26.34/4.32
% 26.34/4.32 % ------ Parsing...% successful
% 26.34/4.32
% 26.34/4.32
% 26.34/4.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.34/4.32
% 26.34/4.32 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e %
% 26.34/4.32
% 26.34/4.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.34/4.32
% 26.34/4.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e
% 26.34/4.32 % ------ Proving...
% 26.34/4.32 % ------ Problem Properties
% 26.34/4.32
% 26.34/4.32 %
% 26.34/4.32 % clauses 591
% 26.34/4.32 % conjectures 0
% 26.34/4.32 % EPR 34
% 26.34/4.32 % Horn 539
% 26.34/4.32 % unary 240
% 26.34/4.32 % binary 176
% 26.34/4.32 % lits 1155
% 26.34/4.32 % lits eq 356
% 26.34/4.32 % fd_pure 0
% 26.34/4.32 % fd_pseudo 0
% 26.34/4.32 % fd_cond 56
% 26.34/4.32 % fd_pseudo_cond 38
% 26.34/4.32 % AC symbols 0
% 26.34/4.32
% 26.34/4.32 % ------ Input Options Time Limit: Unbounded
% 26.34/4.32
% 26.34/4.32
% 26.34/4.32 % ------
% 26.34/4.32 % Current options:
% 26.34/4.32 % ------
% 26.34/4.32
% 26.34/4.32
% 26.34/4.32 %
% 26.34/4.32
% 26.34/4.32 % ------ Proving...
% 26.34/4.32 %
% 26.34/4.32
% 26.34/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 26.34/4.32
% 26.34/4.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.34/4.32
% 26.34/4.32
%------------------------------------------------------------------------------