%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:02:12 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 10 unt; 4 def)
% Number of atoms : 87 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 38 ~; 39 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_a] :
( V_a = c_0
| c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a] :
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
v_c != c_0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0] : ~ c_lessequals(c_1,c_times(X0,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [V_a] :
( V_a = c_0
| ! [T_a] :
( c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( X1 = c_0
| c_HOL_Oabs(X1,X0) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
! [X0,X1] :
( X1 = c_0
| c_HOL_Oabs(X1,X0) != c_0
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(resolution,[status(thm)],[f19,f14]) ).
fof(f22,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(resolution,[status(thm)],[f20,f16]) ).
fof(f23,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| c_times(c_HOL_Oinverse(X0,X1),X0,X1) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[f17,f18]) ).
fof(f24,plain,
! [X0] :
( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[f23,f12]) ).
fof(f25,plain,
( c_HOL_Oabs(v_c,t_a) = c_0
| ~ c_lessequals(c_1,c_1,t_a) ),
inference(paramodulation,[status(thm)],[f24,f11]) ).
fof(f26,definition,
( sQ0_spl
<=> c_lessequals(c_1,c_1,t_a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ0_spl
| ~ c_lessequals(c_1,c_1,t_a) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ1_spl
<=> c_HOL_Oabs(v_c,t_a) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ1_spl
| c_HOL_Oabs(v_c,t_a) = c_0 ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f26,f29]) ).
fof(f33,plain,
( sQ0_spl
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(resolution,[status(thm)],[f28,f22]) ).
fof(f34,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f12]) ).
fof(f35,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ1_spl
| v_c = c_0
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(resolution,[status(thm)],[f30,f21]) ).
fof(f39,definition,
( sQ2_spl
<=> class_Ring__and__Field_Oordered__field(t_a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ2_spl
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ3_spl
<=> v_c = c_0 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ3_spl
| v_c = c_0 ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f37,f39,f42,f29]) ).
fof(f50,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f12]) ).
fof(f51,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f10]) ).
fof(f53,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f54,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f35,f45,f51,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 13:23:19 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.48 % Refutation found
% 0.19/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.56 % Elapsed time: 0.106474 seconds
% 0.26/0.56 % CPU time: 0.098221 seconds
% 0.26/0.56 % Total memory used: 5.007 MB
% 0.26/0.56 % Net memory used: 5.006 MB
%------------------------------------------------------------------------------