%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV678-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:49:20 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.50s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 7 unt; 4 def)
% Number of atoms : 57 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 25 ~; 26 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f426,axiom,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f603,axiom,
! [T_a,V_a,V_m,V_n] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f613,axiom,
c_lessequals(v_n,v_m,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f641,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f643,negated_conjecture,
( ~ c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1340,plain,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(cnf_transformation,[status(thm)],[f426]) ).
fof(f1605,plain,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ! [V_m,V_n] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(miniscoping,[status(thm)],[f603]) ).
fof(f1606,plain,
! [X0,X1,X2,X3] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1605]) ).
fof(f1621,plain,
c_lessequals(v_n,v_m,tc_nat),
inference(cnf_transformation,[status(thm)],[f613]) ).
fof(f1667,plain,
class_Ring__and__Field_Ofield(t_a),
inference(cnf_transformation,[status(thm)],[f641]) ).
fof(f1669,plain,
( ~ c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
inference(cnf_transformation,[status(thm)],[f643]) ).
fof(f1714,definition,
( sQ0_spl
<=> class_Ring__and__Field_Ofield(t_a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1716,plain,
( sQ0_spl
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(component_clause,[status(thm)],[f1714]) ).
fof(f1717,definition,
( sQ1_spl
<=> v_a = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1720,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1340,f1714,f1717]) ).
fof(f1725,definition,
( sQ3_spl
<=> c_lessequals(v_n,v_m,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1727,plain,
( sQ3_spl
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(component_clause,[status(thm)],[f1725]) ).
fof(f1729,definition,
( sQ4_spl
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1731,plain,
( sQ4_spl
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
inference(component_clause,[status(thm)],[f1729]) ).
fof(f1732,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1669,f1729,f1725]) ).
fof(f1735,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1716,f1667]) ).
fof(f1736,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1735]) ).
fof(f1765,plain,
( sQ4_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(v_n,v_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(resolution,[status(thm)],[f1606,f1731]) ).
fof(f1766,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1765,f1714,f1725,f1717,f1729]) ).
fof(f1767,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1727,f1621]) ).
fof(f1768,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1767]) ).
fof(f1769,plain,
$false,
inference(sat_refutation,[status(thm)],[f1720,f1732,f1736,f1766,f1768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV678-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n020.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 09:19:17 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.53/0.52 % Elapsed time: 0.158105 seconds
% 0.53/0.52 % CPU time: 0.810343 seconds
% 0.53/0.52 % Total memory used: 145.269 MB
% 0.53/0.52 % Net memory used: 144.564 MB
%------------------------------------------------------------------------------