%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 11:49:23 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 26 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f708,axiom,
! [T_a,V_p,V_q,V_x] :
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f710,axiom,
! [T_a,V_p,V_n,V_x] :
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f713,axiom,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f732,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f771,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f772,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2019,plain,
! [T_a] :
( ! [V_p,V_q,V_x] : c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f708]) ).
fof(f2020,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X3,X0) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X1,X3,X0),c_Polynomial_Opoly(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f2019]) ).
fof(f2023,plain,
! [T_a] :
( ! [V_p,V_n,V_x] : c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f710]) ).
fof(f2024,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X0)),X3,X0) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X1,X3,X0),X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f2023]) ).
fof(f2028,plain,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f713]) ).
fof(f2063,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f732]) ).
fof(f2102,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f771]) ).
fof(f2103,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f772]) ).
fof(f2179,plain,
! [X0] :
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,X0,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2028,f2024]) ).
fof(f2180,plain,
! [X0] : c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,X0,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[status(thm)],[f2179,f2102]) ).
fof(f2181,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f2180,f2063]) ).
fof(f2182,plain,
~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f2181,f2020]) ).
fof(f2186,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2103,f2182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 : Mon Sep 21 13:19:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 % Drodi V4.1.1
% 0.10/0.45 % Refutation found
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.49 % Elapsed time: 0.122045 seconds
% 0.22/0.49 % CPU time: 0.277726 seconds
% 0.22/0.49 % Total memory used: 144.476 MB
% 0.22/0.49 % Net memory used: 143.917 MB
%------------------------------------------------------------------------------