%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG359-1 : 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 : n002.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 12:54:06 PM UTC 2026
% Result : Unsatisfiable 9.03s 3.80s
% Output : CNFRefutation 9.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 30 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f894,axiom,
! [X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_Power_Opower__class_Opower(c_NthRoot_Oroot(X0,X1),X0,tc_RealDef_Oreal) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__real__root__pow_0) ).
fof(f1037,axiom,
! [X0,X1] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__of__real__power_0) ).
fof(f1056,axiom,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o_0) ).
fof(f1079,axiom,
! [X2,X3,X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f1122,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1229,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(f1255,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_1072,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1122]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] : c_RealVector_Oof__real(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1037]) ).
tcf(c_1168,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1255]) ).
tcf(c_1170,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1229]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ( c_Power_Opower__class_Opower(c_NthRoot_Oroot(X0,X1),X0,tc_RealDef_Oreal) = X1 ) ),
inference(cnf_transformation,[],[f894]) ).
tcf(c_1206,plain,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
inference(cnf_transformation,[],[f1056]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X3,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X2,X0) )
| ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0) ),
inference(cnf_transformation,[],[f1079]) ).
tcf(c_8054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X3,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X2,X0) )
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1255,c_1168]) ).
tcf(c_8055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(unflattening,[status(thm)],[c_8054]) ).
tcf(c_8057,plain,
! [X0: $i,X1: $i,X2: $i] : c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(global_subsumption_just,[status(thm)],[c_8055,c_1170,c_8055]) ).
tcf(c_15724,plain,
! [X0: $i] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,X0),v_na____,tc_RealDef_Oreal) = X0,
inference(superposition,[status(thm)],[c_1200,c_1206]) ).
tcf(c_15819,plain,
! [X0: $i] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X0),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_RealVector_Oof__real(X0,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_15724,c_1167]) ).
tcf(c_38165,plain,
! [X0: $i,X1: $i] : c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_15819,c_8057]) ).
tcf(c_38185,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1072,c_38165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG359-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 05:30:34 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 9.03/3.80 % SZS status Started for theBenchmark.p
% 9.03/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 9.03/3.80
% 9.03/3.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.03/3.80
% 9.03/3.80 % ------ iProver source info
% 9.03/3.80
% 9.03/3.80 % git: date: 2026-07-19 20:42:38 +0200
% 9.03/3.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.03/3.80 % git: non_committed_changes: false
% 9.03/3.80
% 9.03/3.80 % ------ Parsing...% successful
% 9.03/3.80
% 9.03/3.80
% 9.03/3.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.03/3.80
% 9.03/3.80 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 9.03/3.80
% 9.03/3.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.03/3.80
% 9.03/3.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.03/3.80 % ------ Proving...
% 9.03/3.80 % ------ Problem Properties
% 9.03/3.80
% 9.03/3.80 %
% 9.03/3.80 % clauses 406
% 9.03/3.80 % conjectures 1
% 9.03/3.80 % EPR 9
% 9.03/3.80 % Horn 314
% 9.03/3.80 % unary 190
% 9.03/3.80 % binary 88
% 9.03/3.80 % lits 800
% 9.03/3.80 % lits eq 302
% 9.03/3.80 % fd_pure 0
% 9.03/3.80 % fd_pseudo 0
% 9.03/3.80 % fd_cond 45
% 9.03/3.80 % fd_pseudo_cond 7
% 9.03/3.80 % AC symbols 0
% 9.03/3.80
% 9.03/3.80 % ------ Schedule dynamic 5 is on
% 9.03/3.80
% 9.03/3.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.03/3.80
% 9.03/3.80
% 9.03/3.80 % ------
% 9.03/3.80 % Current options:
% 9.03/3.80 % ------
% 9.03/3.80
% 9.03/3.80
% 9.03/3.80 %
% 9.03/3.80
% 9.03/3.80 % ------ Proving...
% 9.03/3.80 %
% 9.03/3.80
% 9.03/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 9.03/3.80
% 9.03/3.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.03/3.80
% 9.03/3.80
%------------------------------------------------------------------------------