%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV616-1 : 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 : n014.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 03:23:54 PM UTC 2026
% Result : Unsatisfiable 14.86s 2.85s
% Output : CNFRefutation 14.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 23 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 16 :)
% 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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1043,axiom,
! [X2,X3,X0,X1] :
( 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_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
fof(f1044,plain,
! [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_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(reorient_equations,[],[f1043]) ).
fof(f1107,axiom,
! [X0] : c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),X0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
fof(f1108,plain,
! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),X0,tc_Complex_Ocomplex),
inference(reorient_equations,[],[f1107]) ).
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_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1219,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tcf(c_1090,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_1217,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_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1044]) ).
tcf(c_1224,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1219]) ).
tcf(c_1226,plain,
! [X0: $i] : c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),X0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1108]) ).
tcf(c_1293,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_6616,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),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_FFT__Mirabelle_Oroot(v_n),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_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_1090,c_1226]) ).
tcf(c_8991,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_1217,c_1224]) ).
tcf(c_8992,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_8991]) ).
tcf(c_19951,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),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_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_6616,c_1293,c_8992]) ).
tcf(c_36429,plain,
! [X0: $i,X1: $i] : c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1226,c_8992]) ).
tcf(c_36442,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(v_n),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_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_19951,c_36429]) ).
tcf(c_36443,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_36442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV616-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n014.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 : Thu Sep 24 20:43:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 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...
% 14.86/2.85 % SZS status Started for theBenchmark.p
% 14.86/2.85 % SZS status Unsatisfiable for theBenchmark.p
% 14.86/2.85
% 14.86/2.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.86/2.85
% 14.86/2.85 % ------ iProver source info
% 14.86/2.85
% 14.86/2.85 % git: date: 2026-07-19 20:42:38 +0200
% 14.86/2.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.86/2.85 % git: non_committed_changes: false
% 14.86/2.85
% 14.86/2.85 % ------ Parsing...% successful
% 14.86/2.85
% 14.86/2.85
% 14.86/2.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.86/2.85
% 14.86/2.85 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e %
% 14.86/2.85
% 14.86/2.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.86/2.85
% 14.86/2.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e
% 14.86/2.85 % ------ Proving...
% 14.86/2.85 % ------ Problem Properties
% 14.86/2.85
% 14.86/2.85 %
% 14.86/2.85 % clauses 435
% 14.86/2.85 % conjectures 0
% 14.86/2.85 % EPR 23
% 14.86/2.85 % Horn 349
% 14.86/2.85 % unary 174
% 14.86/2.85 % binary 110
% 14.86/2.85 % lits 881
% 14.86/2.85 % lits eq 268
% 14.86/2.85 % fd_pure 0
% 14.86/2.85 % fd_pseudo 0
% 14.86/2.85 % fd_cond 40
% 14.86/2.85 % fd_pseudo_cond 9
% 14.86/2.85 % AC symbols 0
% 14.86/2.85
% 14.86/2.85 % ------ Schedule dynamic 5 is on
% 14.86/2.85
% 14.86/2.85 % ------ no conjectures: strip conj schedule
% 14.86/2.85
% 14.86/2.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 14.86/2.85
% 14.86/2.85
% 14.86/2.85 % ------
% 14.86/2.85 % Current options:
% 14.86/2.85 % ------
% 14.86/2.85
% 14.86/2.85
% 14.86/2.85 %
% 14.86/2.85
% 14.86/2.85 % ------ Proving...
% 14.86/2.85 %
% 14.86/2.85
% 14.86/2.85 % SZS status Unsatisfiable for theBenchmark.p
% 14.86/2.85
% 14.86/2.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.86/2.85
% 14.86/2.85
%------------------------------------------------------------------------------