%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG402-1 : 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 : n019.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 10.83s 9.25s
% Output : CNFRefutation 10.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 63 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 27 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f98,axiom,
! [X0] :
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f99,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(reorient_equations,[],[f98]) ).
fof(f182,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f356,axiom,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f521,axiom,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f535,axiom,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f536,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(reorient_equations,[],[f535]) ).
fof(f1044,axiom,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
fof(f1045,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(reorient_equations,[],[f1044]) ).
fof(f1139,negated_conjecture,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1228,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1230,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1236,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1242,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1352,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(definition_unfolding,[],[f1139,f182,f182]) ).
tcf(c_1150,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_1301,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
| ~ class_OrderedGroup_Ocomm__monoid__mult(X0) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_1399,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0,
inference(cnf_transformation,[],[f521]) ).
tcf(c_1413,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f536]) ).
tcf(c_1754,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f1045]) ).
tcf(c_1813,negated_conjecture,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1352]) ).
tcf(c_1902,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1228]) ).
tcf(c_1904,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1230]) ).
tcf(c_1910,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1236]) ).
tcf(c_1916,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1242]) ).
tcf(c_2510,plain,
! [X0: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) )
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(prop_impl_just,[status(thm)],[c_1150]) ).
tcf(c_2511,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(renaming,[status(thm)],[c_2510]) ).
tcf(c_2586,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1754]) ).
tcf(c_2598,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(prop_impl_just,[status(thm)],[c_1413]) ).
tcf(c_2606,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
| ~ class_OrderedGroup_Ocomm__monoid__mult(X0) ),
inference(prop_impl_just,[status(thm)],[c_1301]) ).
tcf(c_7315,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_1813,c_1399]) ).
tcf(c_7599,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2606,c_1904]) ).
tcf(c_7600,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0,
inference(unflattening,[status(thm)],[c_7599]) ).
tcf(c_7735,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2586,c_1902]) ).
tcf(c_7736,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_7735]) ).
tcf(c_8983,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2598,c_1916]) ).
tcf(c_8984,plain,
! [X0: $i] : c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_8983]) ).
tcf(c_11304,plain,
! [X0: $i] :
( ( X0 != tc_Complex_Ocomplex )
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_2511,c_1910]) ).
tcf(c_11305,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_11304]) ).
tcf(c_27864,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_7600,c_7315]) ).
tcf(c_28068,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_7736,c_27864]) ).
tcf(c_28776,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_8984,c_28068]) ).
tcf(c_28780,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28776,c_11305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n019.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 05:34:10 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 10.83/9.25 % SZS status Started for theBenchmark.p
% 10.83/9.25 % SZS status Unsatisfiable for theBenchmark.p
% 10.83/9.25
% 10.83/9.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.83/9.25
% 10.83/9.25 % ------ iProver source info
% 10.83/9.25
% 10.83/9.25 % git: date: 2026-07-19 20:42:38 +0200
% 10.83/9.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.83/9.25 % git: non_committed_changes: false
% 10.83/9.25
% 10.83/9.25 % ------ Parsing...% successful
% 10.83/9.25
% 10.83/9.25
% 10.83/9.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.83/9.25
% 10.83/9.25 % ------ Preprocessing... sup_sim: 27 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 %
% 10.83/9.25
% 10.83/9.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.83/9.25
% 10.83/9.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.83/9.25 % ------ Proving...
% 10.83/9.25 % ------ Problem Properties
% 10.83/9.25
% 10.83/9.25 %
% 10.83/9.25 % clauses 633
% 10.83/9.25 % conjectures 0
% 10.83/9.25 % EPR 36
% 10.83/9.25 % Horn 532
% 10.83/9.25 % unary 208
% 10.83/9.25 % binary 214
% 10.83/9.25 % lits 1307
% 10.83/9.25 % lits eq 423
% 10.83/9.25 % fd_pure 0
% 10.83/9.25 % fd_pseudo 0
% 10.83/9.25 % fd_cond 60
% 10.83/9.25 % fd_pseudo_cond 43
% 10.83/9.25 % AC symbols 0
% 10.83/9.25
% 10.83/9.25 % ------ Input Options Time Limit: Unbounded
% 10.83/9.25
% 10.83/9.25
% 10.83/9.25 % ------
% 10.83/9.25 % Current options:
% 10.83/9.25 % ------
% 10.83/9.25
% 10.83/9.25
% 10.83/9.25 %
% 10.83/9.25
% 10.83/9.25 % ------ Proving...
% 10.83/9.25 %
% 10.83/9.25
% 10.83/9.25 % SZS status Unsatisfiable for theBenchmark.p
% 10.83/9.25
% 10.83/9.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.83/9.25
% 10.83/9.25
%------------------------------------------------------------------------------