%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG426-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 182.28s 23.71s
% Output : CNFRefutation 158.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 121 ( 61 unt; 4 def)
% Number of atoms : 187 ( 106 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 128 ( 62 ~; 62 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 207 ( 207 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [T_a,V_a,V_p,V_b,V_q] :
( V_p = V_q
| c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
| ~ class_HOL_Ozero(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [T_a,V_lx,V_ly,V_rx] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [T_a,V_lx,V_rx,V_ry] :
( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [T_a,V_x,V_y,V_z] :
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f137,axiom,
! [T_a,V_a] :
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f312,axiom,
! [T_a,V_a,V_p,V_x] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f361,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f374,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f453,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(f513,axiom,
! [T_a,V_a] :
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f514,axiom,
! [T_a,V_a] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f554,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f558,axiom,
! [V_p] :
( V_p = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(V_p),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(V_p),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f560,axiom,
v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f570,axiom,
! [T_a,V_x] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f572,negated_conjecture,
! [V_x] : c_Polynomial_Opoly(v_q,V_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f573,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f658,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f659,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f675,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f678,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f690,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f700,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f749,plain,
! [V_p,V_q] :
( V_p = V_q
| ! [T_a] :
( ! [V_a,V_b] : c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
| ~ class_HOL_Ozero(T_a) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f750,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X4
| c_Polynomial_OpCons(X1,X2,X0) != c_Polynomial_OpCons(X3,X4,X0)
| ~ class_HOL_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f749]) ).
fof(f816,plain,
! [T_a] :
( ! [V_lx,V_ly,V_rx] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f817,plain,
! [X0,X1,X2,X3] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f816]) ).
fof(f822,plain,
! [T_a] :
( ! [V_lx,V_rx,V_ry] : c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f823,plain,
! [X0,X1,X2,X3] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f822]) ).
fof(f838,plain,
! [T_a] :
( ! [V_x,V_y,V_z] : c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f839,plain,
! [X0,X1,X2,X3] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f838]) ).
fof(f992,plain,
! [T_a] :
( ! [V_a] : c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(miniscoping,[status(thm)],[f137]) ).
fof(f993,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f992]) ).
fof(f1319,plain,
! [T_a] :
( ! [V_a,V_p,V_x] : c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f312]) ).
fof(f1320,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1319]) ).
fof(f1400,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)],[f361]) ).
fof(f1401,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)],[f1400]) ).
fof(f1425,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)],[f374]) ).
fof(f1426,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)],[f1425]) ).
fof(f1565,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)],[f453]) ).
fof(f1566,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)],[f1565]) ).
fof(f1665,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f513]) ).
fof(f1666,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1
| ~ class_OrderedGroup_Omonoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1665]) ).
fof(f1667,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f514]) ).
fof(f1668,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1667]) ).
fof(f1739,plain,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f554]) ).
fof(f1743,plain,
! [X0] :
( X0 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f558]) ).
fof(f1745,plain,
v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f560]) ).
fof(f1763,plain,
! [T_a] :
( ! [V_x] : c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f570]) ).
fof(f1764,plain,
! [X0,X1] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1763]) ).
fof(f1767,plain,
! [X0] : c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f572]) ).
fof(f1768,plain,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f573]) ).
fof(f1853,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f658]) ).
fof(f1854,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f659]) ).
fof(f1870,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f675]) ).
fof(f1873,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f678]) ).
fof(f1885,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f690]) ).
fof(f1895,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)],[f700]) ).
fof(f4930,plain,
! [X0,X1,X2] : c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X0,X2,tc_Complex_Ocomplex),c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1854,f1426]) ).
fof(f4931,plain,
! [X0,X1,X2] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1854,f1566]) ).
fof(f4932,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(resolution,[status(thm)],[f1854,f1764]) ).
fof(f4933,plain,
! [X0,X1,X2] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1854,f1320]) ).
fof(f4952,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),
inference(paramodulation,[status(thm)],[f4932,f4931]) ).
fof(f4953,plain,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,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),
inference(paramodulation,[status(thm)],[f1767,f4931]) ).
fof(f4981,plain,
! [X0,X1,X2,X3] : c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X3,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X0,X3,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f4933,f4930]) ).
fof(f5057,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_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f4953,f4952]) ).
fof(f5491,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex) != c_Polynomial_OpCons(X2,X3,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1885,f750]) ).
fof(f5820,plain,
! [X0,X1,X2] : c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f1767,f4981]) ).
fof(f5989,plain,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f1745,f5057]) ).
fof(f5990,plain,
! [X0] : c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f1745,f4932]) ).
fof(f5991,plain,
v_q != v_p,
inference(backward_demodulation,[status(thm)],[f1745,f1768]) ).
fof(f6013,plain,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,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),
inference(backward_demodulation,[status(thm)],[f5989,f4953]) ).
fof(f6399,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[status(thm)],[f1895,f1853]) ).
fof(f6439,plain,
! [X0,X1,X2] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f817,f1853]) ).
fof(f6653,plain,
! [X0,X1,X2] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f823,f1853]) ).
fof(f7518,plain,
! [X0,X1,X2] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f839,f1853]) ).
fof(f7726,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f6013,f7518]) ).
fof(f9567,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0,
inference(resolution,[status(thm)],[f993,f1870]) ).
fof(f9603,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f9567,f6653]) ).
fof(f9622,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f9567,f9603]) ).
fof(f10798,definition,
( sQ235_spl
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f10800,plain,
( sQ235_spl
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f10798]) ).
fof(f10807,plain,
( sQ235_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10800,f1854]) ).
fof(f10808,plain,
sQ235_spl,
inference(contradiction_clause,[status(thm)],[f10807]) ).
fof(f11626,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0,
inference(resolution,[status(thm)],[f1666,f1873]) ).
fof(f11641,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f11626,f7726]) ).
fof(f12069,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0,
inference(resolution,[status(thm)],[f1668,f1873]) ).
fof(f12081,plain,
! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f6013,f12069]) ).
fof(f12284,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f9567,f11641]) ).
fof(f12328,plain,
! [X0] : X0 = c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f9567,f12284]) ).
fof(f15050,definition,
! [X0] :
( sQ359_spl
<=> X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f15051,plain,
! [X0] :
( ~ sQ359_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f15050]) ).
fof(f15065,plain,
( ~ sQ359_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1739,f15051]) ).
fof(f15115,plain,
~ sQ359_spl,
inference(contradiction_clause,[status(thm)],[f15065]) ).
fof(f16030,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f12328,f12081]) ).
fof(f17425,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)],[f1401,f6399]) ).
fof(f17431,plain,
! [X0] : c_HOL_Otimes__class_Otimes(v_p,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(forward_demodulation,[status(thm)],[f1745,f17425]) ).
fof(f17432,plain,
! [X0] : c_HOL_Otimes__class_Otimes(v_p,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(forward_demodulation,[status(thm)],[f1745,f17431]) ).
fof(f17444,plain,
! [X0,X1] : c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f17432,f5820]) ).
fof(f17461,plain,
! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f5990,f17444]) ).
fof(f17462,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f5990,f17461]) ).
fof(f17516,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f6653,f17462]) ).
fof(f17581,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f16030,f17516]) ).
fof(f17626,plain,
! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f6439,f17581]) ).
fof(f17704,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f17581,f17626]) ).
fof(f39862,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f17704,f9622]) ).
fof(f41876,plain,
! [X0,X1] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,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)],[f1767,f1566]) ).
fof(f41889,definition,
! [X0,X1] :
( sQ821_spl
<=> c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,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) ),
introduced(definition,[new_symbols(definition,[sQ821_spl])],[split_symbol_definition]) ).
fof(f41890,plain,
! [X0,X1] :
( ~ sQ821_spl
| c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,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) ),
inference(component_clause,[status(thm)],[f41889]) ).
fof(f41892,plain,
( sQ821_spl
| ~ sQ235_spl ),
inference(split_clause,[status(thm)],[f41876,f10798,f41889]) ).
fof(f42150,plain,
! [X0,X1] :
( ~ sQ821_spl
| c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f39862,f41890]) ).
fof(f42151,plain,
! [X0,X1] :
( ~ sQ821_spl
| c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0 ),
inference(forward_demodulation,[status(thm)],[f11626,f42150]) ).
fof(f48952,plain,
! [X0] :
( X0 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),v_p,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1745,f1743]) ).
fof(f48957,plain,
! [X0] :
( ~ sQ821_spl
| c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex)),v_p,tc_Complex_Ocomplex)
| X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f42151,f48952]) ).
fof(f49063,definition,
( sQ1031_spl
<=> v_q = v_p ),
introduced(definition,[new_symbols(definition,[sQ1031_spl])],[split_symbol_definition]) ).
fof(f49064,plain,
( ~ sQ1031_spl
| v_q = v_p ),
inference(component_clause,[status(thm)],[f49063]) ).
fof(f76425,plain,
! [X0] :
( ~ sQ821_spl
| v_q = v_p
| X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f48957,f5491]) ).
fof(f76456,plain,
( ~ sQ821_spl
| sQ1031_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f76425,f15050,f49063,f41889]) ).
fof(f76501,plain,
( ~ sQ1031_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49064,f5991]) ).
fof(f76502,plain,
~ sQ1031_spl,
inference(contradiction_clause,[status(thm)],[f76501]) ).
fof(f76503,plain,
$false,
inference(sat_refutation,[status(thm)],[f10808,f15115,f41892,f76456,f76502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG426-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n013.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 13:20:05 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.21/0.59 % Drodi V4.1.1
% 182.28/23.71 % Refutation found
% 182.28/23.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 182.28/23.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 71.80/24.93 % Elapsed time: 24.230477 seconds
% 71.80/24.93 % CPU time: 174.899842 seconds
% 71.80/24.93 % Total memory used: 765.808 MB
% 71.80/24.93 % Net memory used: 728.210 MB
%------------------------------------------------------------------------------