%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV626-1 : 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 : n004.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 03:23:55 PM UTC 2026
% Result : Unsatisfiable 3.23s 2.09s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 53 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 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 : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f500,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f982,axiom,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
fof(f983,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f982]) ).
fof(f1031,axiom,
! [X2,X3,X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
fof(f1036,axiom,
! [X2,X0,X1] :
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Odivision__ring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f1091,axiom,
! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f1115,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1218,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1225,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f1235,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1243,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tcf(c_1504,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
inference(cnf_transformation,[],[f500]) ).
tcf(c_1892,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) = X1 )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f983]) ).
tcf(c_1927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f1031]) ).
tcf(c_1931,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0) )
| ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0) ),
inference(cnf_transformation,[],[f1036]) ).
tcf(c_1969,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f1091]) ).
tcf(c_1986,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1115]) ).
tcf(c_2089,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1218]) ).
tcf(c_2096,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1225]) ).
tcf(c_2106,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1235]) ).
tcf(c_2114,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1243]) ).
tcf(c_2683,plain,
! [X0: $i,X1: $i] :
( ~ class_Ring__and__Field_Ofield(X0)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1892,c_1969]) ).
tcf(c_2684,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(renaming,[status(thm)],[c_2683]) ).
tcf(c_14141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1927,c_2106]) ).
tcf(c_14142,plain,
! [X0: $i,X1: $i,X2: $i] : c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_14141]) ).
tcf(c_18209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0) )
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1931,c_2096]) ).
tcf(c_18210,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(unflattening,[status(thm)],[c_18209]) ).
tcf(c_18212,plain,
! [X0: $i,X1: $i] : c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(global_subsumption_just,[status(thm)],[c_18210,c_2089,c_18210]) ).
tcf(c_20094,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2684,c_2114]) ).
tcf(c_20095,plain,
! [X0: $i] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_20094]) ).
tcf(c_33434,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_1986,c_1504,c_14142,c_18212,c_20095]) ).
tcf(c_33435,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_33434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV626-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 20:45:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.23/2.09 % SZS status Started for theBenchmark.p
% 3.23/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/2.09
% 3.23/2.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/2.09
% 3.23/2.09 % ------ iProver source info
% 3.23/2.09
% 3.23/2.09 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/2.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/2.09 % git: non_committed_changes: false
% 3.23/2.09
% 3.23/2.09 % ------ Parsing...% successful
% 3.23/2.09
% 3.23/2.09
% 3.23/2.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/2.09
% 3.23/2.09 % ------ Preprocessing... sup_sim: 2 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 %
% 3.23/2.09
% 3.23/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/2.09
% 3.23/2.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/2.09
% 3.23/2.09
%------------------------------------------------------------------------------