%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG432-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 11:49:24 AM UTC 2026
% Result : Unsatisfiable 99.46s 13.16s
% Output : CNFRefutation 99.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 27 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f715,axiom,
! [T_a,V_a,V_p,V_x] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f730,axiom,
! [V_x] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),V_x,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f732,axiom,
! [V_c,V_x] : V_c = c_Polynomial_Opoly(c_Polynomial_OpCons(V_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),V_x,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f736,negated_conjecture,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f737,negated_conjecture,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f855,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2160,plain,
! [T_a] :
( ! [V_a,V_p,V_x] : c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f715]) ).
fof(f2161,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X2,X3,X0),X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f2160]) ).
fof(f2183,plain,
! [X0] : c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f730]) ).
fof(f2185,plain,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0,
inference(cnf_transformation,[status(thm)],[f732]) ).
fof(f2191,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f736]) ).
fof(f2192,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f737]) ).
fof(f2310,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f855]) ).
fof(f4324,plain,
! [X0,X1] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2183,f2161]) ).
fof(f4325,plain,
! [X0] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2191,f2161]) ).
fof(f4330,plain,
! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[status(thm)],[f4325,f2310]) ).
fof(f4331,plain,
! [X0,X1] :
( X0 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f2185,f4324]) ).
fof(f4332,plain,
! [X0,X1] : X0 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[status(thm)],[f4331,f2310]) ).
fof(f4463,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f4464,f2192]) ).
fof(f4464,plain,
! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = X0,
inference(forward_demodulation,[status(thm)],[f4332,f4330]) ).
fof(f4466,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG432-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 13:25:59 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.27/0.52 % Drodi V4.1.1
% 99.46/13.16 % Refutation found
% 99.46/13.16 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 99.46/13.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 89.70/13.47 % Elapsed time: 13.018774 seconds
% 89.70/13.47 % CPU time: 100.944125 seconds
% 89.70/13.47 % Total memory used: 764.460 MB
% 89.70/13.47 % Net memory used: 730.684 MB
%------------------------------------------------------------------------------