%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG427-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 117.97s 15.54s
% Output : CNFRefutation 101.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 37 unt; 0 def)
% Number of atoms : 108 ( 64 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f225,axiom,
! [T_a,V_x,V_y] :
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f330,axiom,
! [T_a,V_a,V_c] :
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f364,axiom,
! [T_a,V_c,V_p] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) = V_p
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f443,axiom,
! [T_a,V_x] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f483,axiom,
! [T_a,V_p,V_c] :
( c_Polynomial_Osynthetic__div(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Odegree(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f592,axiom,
! [T_a,V_a] :
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f628,axiom,
! [T_a,V_a] :
( c_Polynomial_Omonom(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
| ~ class_HOL_Ozero(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f629,axiom,
! [T_a] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f650,axiom,
! [T_a,V_n] :
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_HOL_Ozero(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f662,axiom,
! [V_k] :
( V_k = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_thesis____
| v_p != c_Polynomial_OpCons(V_k,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f663,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f665,axiom,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f666,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f764,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f765,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f775,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f792,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f808,axiom,
! [T_1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1236,plain,
! [T_a] :
( ! [V_x,V_y] : c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f225]) ).
fof(f1237,plain,
! [X0,X1,X2] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1236]) ).
fof(f1427,plain,
! [T_a] :
( ! [V_a,V_c] : c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f330]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1427]) ).
fof(f1477,plain,
! [T_a] :
( ! [V_c,V_p] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) = V_p
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
inference(miniscoping,[status(thm)],[f364]) ).
fof(f1478,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),c_Polynomial_Osynthetic__div(X2,X1,X0),tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X1,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) = X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1477]) ).
fof(f1612,plain,
! [T_a] :
( ! [V_x] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f443]) ).
fof(f1613,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1612]) ).
fof(f1680,plain,
! [T_a,V_p] :
( ! [V_c] : c_Polynomial_Osynthetic__div(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Odegree(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f483]) ).
fof(f1681,plain,
! [X0,X1,X2] :
( c_Polynomial_Osynthetic__div(X1,X2,X0) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| c_Polynomial_Odegree(X1,X0) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1680]) ).
fof(f1855,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f592]) ).
fof(f1856,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1855]) ).
fof(f1919,plain,
! [T_a] :
( ! [V_a] : c_Polynomial_Omonom(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
| ~ class_HOL_Ozero(T_a) ),
inference(miniscoping,[status(thm)],[f628]) ).
fof(f1920,plain,
! [X0,X1] :
( c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
| ~ class_HOL_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1921,plain,
! [X0] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f629]) ).
fof(f1956,plain,
! [T_a] :
( ! [V_n] : c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_HOL_Ozero(T_a) ),
inference(miniscoping,[status(thm)],[f650]) ).
fof(f1957,plain,
! [X0,X1] :
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f1956]) ).
fof(f1979,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_thesis____
| v_p != c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f662]) ).
fof(f1980,plain,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f663]) ).
fof(f1982,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(thm)],[f665]) ).
fof(f1983,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f666]) ).
fof(f2081,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f764]) ).
fof(f2082,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f765]) ).
fof(f2092,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f775]) ).
fof(f2109,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f792]) ).
fof(f2125,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[status(thm)],[f808]) ).
fof(f2157,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p != c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f1979,f1983]) ).
fof(f2289,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f2125,f2081]) ).
fof(f3053,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(resolution,[status(thm)],[f1856,f2289]) ).
fof(f3485,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f1237,f2289]) ).
fof(f3636,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f1428,f2289]) ).
fof(f3918,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f1613,f2289]) ).
fof(f6006,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Osynthetic__div(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(c_Polynomial_Opoly(X1,X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(resolution,[status(thm)],[f1478,f2092]) ).
fof(f6164,plain,
! [X0] : c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f1957,f2109]) ).
fof(f7279,plain,
! [X0,X1] :
( c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f1681,f2082]) ).
fof(f9233,plain,
! [X0] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1920,f2109]) ).
fof(f9274,plain,
c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1921,f2081]) ).
fof(f39090,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[status(thm)],[f3636,f6006]) ).
fof(f39091,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[status(thm)],[f3485,f39090]) ).
fof(f49971,plain,
! [X0] : c_Polynomial_Osynthetic__div(v_p,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f7279,f1982]) ).
fof(f58556,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(backward_demodulation,[status(thm)],[f9233,f39091]) ).
fof(f58560,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p != c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) ),
inference(backward_demodulation,[status(thm)],[f9233,f2157]) ).
fof(f58587,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[status(thm)],[f9233,f58556]) ).
fof(f58780,plain,
c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f9233,f9274]) ).
fof(f63117,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[status(thm)],[f58780,f58587]) ).
fof(f63130,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(paramodulation,[status(thm)],[f49971,f63117]) ).
fof(f63170,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(forward_demodulation,[status(thm)],[f3918,f63130]) ).
fof(f63171,plain,
! [X0] : c_Polynomial_Omonom(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = v_p,
inference(forward_demodulation,[status(thm)],[f3053,f63170]) ).
fof(f63216,plain,
! [X0] : c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f63171,f58560]) ).
fof(f63246,plain,
c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = v_p,
inference(backward_demodulation,[status(thm)],[f63216,f63171]) ).
fof(f63259,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(forward_demodulation,[status(thm)],[f6164,f63246]) ).
fof(f63260,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f63259,f1980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG427-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:20:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.42 % Drodi V4.1.1
% 117.97/15.54 % Refutation found
% 117.97/15.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 117.97/15.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 101.35/15.64 % Elapsed time: 15.264716 seconds
% 101.35/15.64 % CPU time: 120.395270 seconds
% 101.35/15.64 % Total memory used: 716.747 MB
% 101.35/15.64 % Net memory used: 680.462 MB
%------------------------------------------------------------------------------