%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:49:14 AM UTC 2026
% Result : Unsatisfiable 92.22s 12.26s
% Output : CNFRefutation 87.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 13 unt; 4 def)
% Number of atoms : 71 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 28 ~; 29 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1017,axiom,
! [T_a,V_p,V_h] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1024,axiom,
! [T_a,V_a,V_p] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
| ~ class_HOL_Ozero(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1026,negated_conjecture,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1027,negated_conjecture,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1028,negated_conjecture,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1029,negated_conjecture,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1038,axiom,
! [T] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2841,plain,
! [T_a,V_p] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ! [V_h] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1017]) ).
fof(f2842,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 ),
inference(cnf_transformation,[status(thm)],[f2841]) ).
fof(f2852,plain,
! [T_a,V_p] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ! [V_a] : c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
| ~ class_HOL_Ozero(T_a) ),
inference(miniscoping,[status(thm)],[f1024]) ).
fof(f2853,plain,
! [X0,X1,X2] :
( c_Suc(c_Polynomial_Odegree(X1,X0)) = c_Polynomial_Odegree(c_Polynomial_OpCons(X2,X1,X0),X0)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f2852]) ).
fof(f2856,plain,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[status(thm)],[f1026]) ).
fof(f2857,plain,
c_Polynomial_Odegree(v_pa,t_a) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),
inference(cnf_transformation,[status(thm)],[f1027]) ).
fof(f2858,plain,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[status(thm)],[f1028]) ).
fof(f2859,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(cnf_transformation,[status(thm)],[f1029]) ).
fof(f2868,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| class_HOL_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f1038]) ).
fof(f3010,definition,
( sQ1_spl
<=> class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f3012,plain,
( sQ1_spl
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(component_clause,[status(thm)],[f3010]) ).
fof(f3019,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3012,f2856]) ).
fof(f3020,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f3019]) ).
fof(f3076,plain,
class_HOL_Ozero(t_a),
inference(resolution,[status(thm)],[f2868,f2856]) ).
fof(f4282,plain,
! [X0,X1] :
( c_Suc(c_Polynomial_Odegree(X0,t_a)) = c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X0,t_a),t_a)
| X0 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(resolution,[status(thm)],[f2853,f3076]) ).
fof(f4306,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ),
inference(paramodulation,[status(thm)],[f4282,f2859]) ).
fof(f4315,definition,
( sQ74_spl
<=> c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f4317,plain,
( sQ74_spl
| c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ),
inference(component_clause,[status(thm)],[f4315]) ).
fof(f4318,definition,
( sQ75_spl
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f4319,plain,
( ~ sQ75_spl
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) ),
inference(component_clause,[status(thm)],[f4318]) ).
fof(f4321,plain,
( sQ75_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f4306,f4315,f4318]) ).
fof(f4326,plain,
( sQ74_spl
| c_Suc(c_Polynomial_Odegree(v_pa,t_a)) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ),
inference(forward_demodulation,[status(thm)],[f2857,f4317]) ).
fof(f4327,plain,
( sQ74_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4326]) ).
fof(f4328,plain,
sQ74_spl,
inference(contradiction_clause,[status(thm)],[f4327]) ).
fof(f4338,plain,
( ~ sQ75_spl
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_pa ),
inference(resolution,[status(thm)],[f4319,f2842]) ).
fof(f4345,definition,
( sQ77_spl
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_pa ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f4346,plain,
( ~ sQ77_spl
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_pa ),
inference(component_clause,[status(thm)],[f4345]) ).
fof(f4353,plain,
( ~ sQ75_spl
| ~ sQ1_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f4338,f4345,f3010,f4318]) ).
fof(f4354,plain,
( ~ sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4346,f2858]) ).
fof(f4355,plain,
~ sQ77_spl,
inference(contradiction_clause,[status(thm)],[f4354]) ).
fof(f4356,plain,
$false,
inference(sat_refutation,[status(thm)],[f3020,f4321,f4328,f4353,f4355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:16:12 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.24/0.49 % Drodi V4.1.1
% 92.22/12.26 % Refutation found
% 92.22/12.26 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 92.22/12.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.55/12.87 % Elapsed time: 12.476110 seconds
% 6.55/12.87 % CPU time: 95.141101 seconds
% 6.55/12.87 % Total memory used: 831.243 MB
% 6.55/12.87 % Net memory used: 772.557 MB
%------------------------------------------------------------------------------