%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW216+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 : n026.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 03:07:27 PM UTC 2026
% Result : Theorem 0.17s 11.15s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 13 unt; 3 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 24 ~; 23 |; 2 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1134,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1250,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1251,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(negated_conjecture,[status(cth)],[f1250]) ).
fof(f1255,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1256,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1373,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f1374,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(NNF_transformation,[status(thm)],[f1373]) ).
fof(f1375,plain,
! [T_a] :
( ! [V_ca_2] :
( ( ! [V_b_2,V_a_2] :
( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) )
& ! [V_b_2,V_a_2] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ~ class_Fields_Olinordered__field(T_a) ),
inference(miniscoping,[status(thm)],[f1374]) ).
fof(f1376,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X0,hAPP(c_Groups_Otimes__class_Otimes(X0,X2),X1),X3)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X3,X1))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Fields_Olinordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f1375]) ).
fof(f4652,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1134]) ).
fof(f4768,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(cnf_transformation,[status(thm)],[f1251]) ).
fof(f6016,definition,
( sQ43_spl
<=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f6018,plain,
( sQ43_spl
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6016]) ).
fof(f6095,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6018,f4652]) ).
fof(f6096,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f6095]) ).
fof(f6488,definition,
( sQ104_spl
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f6490,plain,
( sQ104_spl
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(component_clause,[status(thm)],[f6488]) ).
fof(f6525,plain,
( sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6490,f1255]) ).
fof(f6526,plain,
sQ104_spl,
inference(contradiction_clause,[status(thm)],[f6525]) ).
fof(f6843,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1376,f1256]) ).
fof(f6873,definition,
( sQ168_spl
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f6874,plain,
( ~ sQ168_spl
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
inference(component_clause,[status(thm)],[f6873]) ).
fof(f6876,plain,
( sQ168_spl
| ~ sQ104_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f6843,f6016,f6488,f6873]) ).
fof(f6885,plain,
( ~ sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6874,f4768]) ).
fof(f6886,plain,
~ sQ168_spl,
inference(contradiction_clause,[status(thm)],[f6885]) ).
fof(f6887,plain,
$false,
inference(sat_refutation,[status(thm)],[f6096,f6526,f6876,f6886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW216+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.83 % Computer : n026.cluster.edu
% 0.14/10.83 % Model : x86_64 x86_64
% 0.14/10.83 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.83 % Memory : 8046.5625MB
% 0.14/10.83 % OS : Linux 6.8.0-71-generic
% 0.14/10.83 % CPULimit : 300
% 0.14/10.83 % WCLimit : 300
% 0.14/10.83 % DateTime : Mon Sep 21 09:45:04 UTC 2026
% 0.14/10.83 % CPUTime :
% 0.17/10.93 % Drodi V4.1.1
% 0.17/11.15 % Refutation found
% 0.17/11.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/11.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.57/11.19 % Elapsed time: 0.343039 seconds
% 1.57/11.19 % CPU time: 1.789593 seconds
% 1.57/11.19 % Total memory used: 228.566 MB
% 1.57/11.19 % Net memory used: 226.906 MB
%------------------------------------------------------------------------------