%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG370-1 : 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 : 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 12:54:07 PM UTC 2026
% Result : Unsatisfiable 10.86s 12.30s
% Output : CNFRefutation 10.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 18 unt; 0 def)
% Number of atoms : 40 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 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 : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f323,axiom,
! [X2,X0,X1] :
( c_RealVector_Odist__class_Odist(X1,X2,X0) = c_RealVector_Odist__class_Odist(X2,X1,X0)
| ~ class_RealVector_Ometric__space(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__commute_0) ).
fof(f432,axiom,
! [X0,X1] : c_RealVector_Odist__class_Odist(X0,X1,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__complex__def_0) ).
fof(f498,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f499,axiom,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f500,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f608,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f636,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
tcf(c_685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Odist__class_Odist(X1,X2,X0) = c_RealVector_Odist__class_Odist(X2,X1,X0) )
| ~ class_RealVector_Ometric__space(X0) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i] : c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Odist__class_Odist(X0,X1,tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f432]) ).
tcf(c_1082,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f498]) ).
tcf(c_1083,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f499]) ).
tcf(c_1084,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f500]) ).
tcf(c_1192,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f608]) ).
tcf(c_1220,plain,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f636]) ).
tcf(c_4200,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_w____,v_z,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_1084,c_1026]) ).
tcf(c_4201,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_w____,v_z,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_1083,c_1026]) ).
tcf(c_5733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_RealVector_Odist__class_Odist(X1,X2,X0) = c_RealVector_Odist__class_Odist(X2,X1,X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_929,c_1220]) ).
tcf(c_5734,plain,
! [X0: $i,X1: $i] : c_RealVector_Odist__class_Odist(X0,X1,tc_Complex_Ocomplex) = c_RealVector_Odist__class_Odist(X1,X0,tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_5733]) ).
tcf(c_18214,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_4200,c_5734]) ).
tcf(c_18215,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_4201,c_5734]) ).
tcf(c_48477,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,v_e,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_685]) ).
tcf(c_48961,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_48477]) ).
tcf(c_48962,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_48961,c_18215,c_18214,c_1082,c_1192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG370-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.38 % Computer : n010.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Fri Sep 25 05:30:12 UTC 2026
% 0.12/10.38 % CPUTime :
% 0.12/10.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 10.86/12.30 % SZS status Started for theBenchmark.p
% 10.86/12.30 % SZS status Unsatisfiable for theBenchmark.p
% 10.86/12.30
% 10.86/12.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.86/12.30
% 10.86/12.30 % ------ iProver source info
% 10.86/12.30
% 10.86/12.30 % git: date: 2026-07-19 20:42:38 +0200
% 10.86/12.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.86/12.30 % git: non_committed_changes: false
% 10.86/12.30
% 10.86/12.30 % ------ Parsing...% successful
% 10.86/12.30
% 10.86/12.30
% 10.86/12.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.86/12.30
% 10.86/12.30 % ------ 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_e sup_sim: 13 sf_s rm: 12 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 14 0s sf_e pe_s pe_e %
% 10.86/12.30
% 10.86/12.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.86/12.30
% 10.86/12.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.86/12.30 % ------ Proving...
% 10.86/12.30 % ------ Problem Properties
% 10.86/12.30
% 10.86/12.30 %
% 10.86/12.30 % clauses 572
% 10.86/12.30 % conjectures 0
% 10.86/12.30 % EPR 151
% 10.86/12.30 % Horn 529
% 10.86/12.30 % unary 188
% 10.86/12.30 % binary 179
% 10.86/12.30 % lits 1300
% 10.86/12.30 % lits eq 231
% 10.86/12.30 % fd_pure 0
% 10.86/12.30 % fd_pseudo 0
% 10.86/12.30 % fd_cond 13
% 10.86/12.30 % fd_pseudo_cond 45
% 10.86/12.30 % AC symbols 0
% 10.86/12.30
% 10.86/12.30 % ------ Input Options Time Limit: Unbounded
% 10.86/12.30
% 10.86/12.30
% 10.86/12.30 % ------
% 10.86/12.30 % Current options:
% 10.86/12.30 % ------
% 10.86/12.30
% 10.86/12.30
% 10.86/12.30 %
% 10.86/12.30
% 10.86/12.30 % ------ Proving...
% 10.86/12.30 %
% 10.86/12.30
% 10.86/12.30 % SZS status Unsatisfiable for theBenchmark.p
% 10.86/12.30
% 10.86/12.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.86/12.30
% 10.86/12.30
%------------------------------------------------------------------------------