%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG359-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 11:49:15 AM UTC 2026
% Result : Unsatisfiable 230.80s 29.72s
% Output : CNFRefutation 230.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 37 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% 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 : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f710,axiom,
! [V_n,V_x] :
( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
| c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f825,axiom,
! [V_x,V_n] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex),V_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f838,axiom,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f855,axiom,
! [T_a,V_a,V_b,V_n] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f885,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') ).
fof(f992,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1018,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2169,plain,
! [V_n] :
( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
| ! [V_x] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x ),
inference(miniscoping,[status(thm)],[f710]) ).
fof(f2170,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_NthRoot_Oroot(X0,X1),X0,tc_RealDef_Oreal) = X1
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2169]) ).
fof(f2343,plain,
! [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),
inference(cnf_transformation,[status(thm)],[f825]) ).
fof(f2366,plain,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
inference(cnf_transformation,[status(thm)],[f838]) ).
fof(f2396,plain,
! [T_a] :
( ! [V_a,V_b,V_n] : c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f855]) ).
fof(f2397,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| 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) ),
inference(cnf_transformation,[status(thm)],[f2396]) ).
fof(f2449,plain,
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) != 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),
inference(cnf_transformation,[status(thm)],[f885]) ).
fof(f2556,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f992]) ).
fof(f2582,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1018]) ).
fof(f13258,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Power_Opower__class_Opower(X2,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2343,f2397]) ).
fof(f13289,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f13258,f2556]) ).
fof(f31704,plain,
! [X0,X1,X2] : c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Power_Opower__class_Opower(X2,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[status(thm)],[f13289,f2582]) ).
fof(f31764,plain,
! [X0,X1,X2] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(c_NthRoot_Oroot(X1,X2),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),c_RealVector_Oof__real(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2170,f31704]) ).
fof(f36934,plain,
( c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat)
| 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) != 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(paramodulation,[status(thm)],[f31764,f2449]) ).
fof(f37005,plain,
c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
inference(trivial_equality_resolution,[status(thm)],[f36934]) ).
fof(f37006,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f37005,f2366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG359-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:17:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.42 % Drodi V4.1.1
% 230.80/29.72 % Refutation found
% 230.80/29.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 230.80/29.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 67.48/30.97 % Elapsed time: 30.399062 seconds
% 67.48/30.97 % CPU time: 225.551428 seconds
% 67.48/30.97 % Total memory used: 1.092 GB
% 67.48/30.97 % Net memory used: 1.060 GB
%------------------------------------------------------------------------------