%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW185+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 03:07:24 PM UTC 2026
% Result : Theorem 5.63s 1.28s
% Output : CNFRefutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 90 ( 26 unt; 6 def)
% Number of atoms : 169 ( 91 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 145 ( 66 ~; 61 |; 0 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 147 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_h,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [V_c,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [V_a,V_p,V_c,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
=> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [V_c,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [V_p,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [V_a,V_p,V_c,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [V_h,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1180,hypothesis,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1181,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1182,conjecture,
c_Polynomial_OpCons(t_a,v_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1183,negated_conjecture,
c_Polynomial_OpCons(t_a,v_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(negated_conjecture,[status(cth)],[f1182]) ).
fof(f1184,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1191,plain,
! [V_h,V_a,T_a] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f1192,plain,
! [T_a] :
( ! [V_h,V_a] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1191]) ).
fof(f1193,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2) = c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1192]) ).
fof(f1286,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f1287,plain,
! [T_a] :
( ! [V_x] : hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1286]) ).
fof(f1288,plain,
! [X0,X1] :
( hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
fof(f1289,plain,
! [V_c,T_a] :
( c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f1290,plain,
! [T_a] :
( ! [V_c] : c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1289]) ).
fof(f1291,plain,
! [X0,X1] :
( c_Polynomial_Osynthetic__div(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1290]) ).
fof(f1296,plain,
! [V_a,V_p,V_c,T_a] :
( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Osmult(T_a,V_c,V_p) != c_Polynomial_OpCons(T_a,V_a,V_p)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f1297,plain,
! [T_a] :
( ! [V_p] :
( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ! [V_a,V_c] : c_Polynomial_Osmult(T_a,V_c,V_p) != c_Polynomial_OpCons(T_a,V_a,V_p) )
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1296]) ).
fof(f1298,plain,
! [X0,X1,X2,X3] :
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| c_Polynomial_Osmult(X0,X1,X2) != c_Polynomial_OpCons(X0,X3,X2)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1297]) ).
fof(f1333,plain,
! [V_a,T_a] :
( c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f1334,plain,
! [T_a] :
( ! [V_a] : c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1333]) ).
fof(f1335,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1334]) ).
fof(f1359,plain,
! [V_c,V_p,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f1360,plain,
! [T_a] :
( ! [V_c,V_p] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1359]) ).
fof(f1361,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,c_Polynomial_Osynthetic__div(X0,X1,X2))) = c_Polynomial_OpCons(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2),c_Polynomial_Osynthetic__div(X0,X1,X2))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1360]) ).
fof(f1394,plain,
! [V_p,V_b,V_a,T_a] :
( c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f1395,plain,
! [T_a] :
( ! [V_p,V_b,V_a] : c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1394]) ).
fof(f1396,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X3),c_Polynomial_Osmult(X0,X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1395]) ).
fof(f1437,plain,
! [V_a,V_p,V_c,T_a] :
( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f1438,plain,
! [T_a] :
( ! [V_p] :
( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ! [V_a,V_c] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1437]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1438]) ).
fof(f1448,plain,
! [V_h,V_p,V_a,T_a] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f1449,plain,
! [T_a] :
( ! [V_h,V_p,V_a] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1448]) ).
fof(f1450,plain,
! [X0,X1,X2,X3] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3)),c_Polynomial_OpCons(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1449]) ).
fof(f4672,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(pre_NNF_transformation,[status(thm)],[f1180]) ).
fof(f4673,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cnf_transformation,[status(thm)],[f4672]) ).
fof(f4674,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[status(thm)],[f1181]) ).
fof(f4675,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[status(thm)],[f1183]) ).
fof(f4676,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[status(thm)],[f1184]) ).
fof(f4723,definition,
( sQ0_spl
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f4726,definition,
( sQ1_spl
<=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f4727,plain,
( ~ sQ1_spl
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(component_clause,[status(thm)],[f4726]) ).
fof(f4729,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4673,f4723,f4726]) ).
fof(f4880,plain,
! [X0,X1] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X1) = c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(resolution,[status(thm)],[f1193,f4676]) ).
fof(f4902,plain,
! [X0] : hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0) = c_Groups_Ozero__class_Ozero(t_a),
inference(resolution,[status(thm)],[f1288,f4676]) ).
fof(f4904,plain,
! [X0] : c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f1291,f4676]) ).
fof(f4941,definition,
( sQ9_spl
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f4945,definition,
( sQ10_spl
<=> class_Rings_Ocomm__semiring__0(t_a) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f4947,plain,
( sQ10_spl
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(component_clause,[status(thm)],[f4945]) ).
fof(f4952,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4947,f4676]) ).
fof(f4953,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f4952]) ).
fof(f5116,plain,
! [X0] : c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f1335,f4676]) ).
fof(f5122,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(paramodulation,[status(thm)],[f5116,f1298]) ).
fof(f5128,definition,
! [X0] :
( sQ18_spl
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f5129,plain,
! [X0] :
( ~ sQ18_spl
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
inference(component_clause,[status(thm)],[f5128]) ).
fof(f5131,plain,
( sQ9_spl
| sQ18_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5122,f4945,f5128,f4941]) ).
fof(f5779,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X0,c_Polynomial_Osmult(t_a,X1,c_Polynomial_Osynthetic__div(t_a,X0,X1))) = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,X0),X1),c_Polynomial_Osynthetic__div(t_a,X0,X1)),
inference(resolution,[status(thm)],[f1361,f4676]) ).
fof(f5791,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0),c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0)),
inference(paramodulation,[status(thm)],[f4904,f5779]) ).
fof(f5794,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0),c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0)),
inference(forward_demodulation,[status(thm)],[f5116,f5791]) ).
fof(f5795,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0)),
inference(forward_demodulation,[status(thm)],[f4902,f5794]) ).
fof(f5796,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(forward_demodulation,[status(thm)],[f4904,f5795]) ).
fof(f6780,plain,
! [X0,X1,X2] : c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X0,X2),c_Polynomial_Osmult(t_a,X1,X2)),
inference(resolution,[status(thm)],[f1396,f4676]) ).
fof(f6787,plain,
! [X0,X1] : c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,X0,X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(paramodulation,[status(thm)],[f5116,f6780]) ).
fof(f6803,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(forward_demodulation,[status(thm)],[f5116,f6787]) ).
fof(f6804,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(forward_demodulation,[status(thm)],[f5116,f6803]) ).
fof(f6805,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(forward_demodulation,[status(thm)],[f5796,f6804]) ).
fof(f7082,plain,
( ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6805,f5129]) ).
fof(f7083,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f7082]) ).
fof(f7957,plain,
! [X0,X1,X2] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2))),
inference(resolution,[status(thm)],[f1450,f4676]) ).
fof(f7967,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,X1),X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(paramodulation,[status(thm)],[f7957,f1439]) ).
fof(f7986,definition,
! [X0,X1,X2] :
( sQ117_spl
<=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,X1),X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f7987,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,X1),X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(component_clause,[status(thm)],[f7986]) ).
fof(f7989,plain,
( sQ117_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f7967,f4945,f7986]) ).
fof(f8037,plain,
( ~ sQ117_spl
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(paramodulation,[status(thm)],[f4674,f7987]) ).
fof(f8045,plain,
( ~ sQ117_spl
| sQ0_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f8037,f4941,f4723,f7986]) ).
fof(f10907,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X1) = c_Polynomial_OpCons(t_a,X0,v_p) ),
inference(backward_demodulation,[status(thm)],[f4727,f4880]) ).
fof(f10909,plain,
( ~ sQ1_spl
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = v_p ),
inference(backward_demodulation,[status(thm)],[f4727,f4674]) ).
fof(f10910,plain,
( ~ sQ1_spl
| c_Polynomial_OpCons(t_a,v_a,v_p) != v_p ),
inference(backward_demodulation,[status(thm)],[f4727,f4675]) ).
fof(f10942,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1) = c_Polynomial_OpCons(t_a,X0,v_p) ),
inference(forward_demodulation,[status(thm)],[f4727,f10907]) ).
fof(f11331,plain,
( ~ sQ1_spl
| c_Polynomial_OpCons(t_a,v_a,v_p) = v_p ),
inference(backward_demodulation,[status(thm)],[f10942,f10909]) ).
fof(f11346,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11331,f10910]) ).
fof(f11347,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f11346]) ).
fof(f11348,plain,
$false,
inference(sat_refutation,[status(thm)],[f4729,f4953,f5131,f7083,f7989,f8045,f11347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW185+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n012.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 09:39:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.44 % Drodi V4.1.1
% 5.63/1.28 % Refutation found
% 5.63/1.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.63/1.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.63/1.33 % Elapsed time: 0.955140 seconds
% 5.63/1.33 % CPU time: 6.517844 seconds
% 5.63/1.33 % Total memory used: 339.685 MB
% 5.63/1.33 % Net memory used: 336.375 MB
%------------------------------------------------------------------------------