%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA012-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 136.47s 17.77s
% Output : CNFRefutation 30.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 15 unt; 3 def)
% Number of atoms : 88 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 35 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1288,axiom,
! [T_a] :
( c_HOL_Oabs(c_1,T_a) = c_1
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1322,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(f1689,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(f2356,axiom,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2384,axiom,
! [T] :
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2413,axiom,
! [T] :
( class_Ring__and__Field_Oordered__semidom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2544,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2781,axiom,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2784,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2785,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(f2786,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4549,plain,
! [X0] :
( c_HOL_Oabs(c_1,X0) = c_1
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f1288]) ).
fof(f4601,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)],[f1322]) ).
fof(f5108,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f1689]) ).
fof(f5109,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5108]) ).
fof(f5794,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f2356]) ).
fof(f5822,plain,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f2384]) ).
fof(f5851,plain,
! [X0] :
( class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f2413]) ).
fof(f5982,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f2544]) ).
fof(f6219,plain,
! [T_a] :
( ! [V_a,V_b] : c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(miniscoping,[status(thm)],[f2781]) ).
fof(f6220,plain,
! [X0,X1,X2] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6219]) ).
fof(f6225,plain,
v_c != c_0,
inference(cnf_transformation,[status(thm)],[f2784]) ).
fof(f6226,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)],[f2785]) ).
fof(f6227,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(thm)],[f2786]) ).
fof(f22569,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[f5794,f6227]) ).
fof(f23802,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[f5822,f6227]) ).
fof(f23819,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_a),t_a) = c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a),
inference(resolution,[status(thm)],[f23802,f6220]) ).
fof(f23820,plain,
c_HOL_Oabs(c_1,t_a) = c_1,
inference(resolution,[status(thm)],[f23802,f4549]) ).
fof(f24639,plain,
class_Ring__and__Field_Oordered__semidom(t_a),
inference(resolution,[status(thm)],[f5851,f6227]) ).
fof(f24703,plain,
! [X0] : ~ c_lessequals(c_1,c_HOL_Oabs(c_times(X0,v_c,t_a),t_a),t_a),
inference(paramodulation,[status(thm)],[f23819,f6226]) ).
fof(f40373,definition,
( sQ1209_spl
<=> class_Orderings_Oorder(t_a) ),
introduced(definition,[new_symbols(definition,[sQ1209_spl])],[split_symbol_definition]) ).
fof(f40374,plain,
( ~ sQ1209_spl
| class_Orderings_Oorder(t_a) ),
inference(component_clause,[status(thm)],[f40373]) ).
fof(f40375,plain,
( sQ1209_spl
| ~ class_Orderings_Oorder(t_a) ),
inference(component_clause,[status(thm)],[f40373]) ).
fof(f40422,plain,
( sQ1209_spl
| ~ class_Ring__and__Field_Oordered__semidom(t_a) ),
inference(resolution,[status(thm)],[f40375,f5982]) ).
fof(f40441,plain,
( sQ1209_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40422,f24639]) ).
fof(f40442,plain,
sQ1209_spl,
inference(contradiction_clause,[status(thm)],[f40441]) ).
fof(f45474,plain,
! [X0] :
( ~ sQ1209_spl
| c_lessequals(X0,X0,t_a) ),
inference(resolution,[status(thm)],[f5109,f40374]) ).
fof(f46303,plain,
! [X0] :
( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[f4601,f22569]) ).
fof(f46316,plain,
( v_c = c_0
| ~ c_lessequals(c_1,c_HOL_Oabs(c_1,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f46303,f24703]) ).
fof(f46322,definition,
( sQ1379_spl
<=> c_lessequals(c_1,c_HOL_Oabs(c_1,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ1379_spl])],[split_symbol_definition]) ).
fof(f46324,plain,
( sQ1379_spl
| ~ c_lessequals(c_1,c_HOL_Oabs(c_1,t_a),t_a) ),
inference(component_clause,[status(thm)],[f46322]) ).
fof(f46325,definition,
( sQ1380_spl
<=> v_c = c_0 ),
introduced(definition,[new_symbols(definition,[sQ1380_spl])],[split_symbol_definition]) ).
fof(f46326,plain,
( ~ sQ1380_spl
| v_c = c_0 ),
inference(component_clause,[status(thm)],[f46325]) ).
fof(f46328,plain,
( sQ1380_spl
| ~ sQ1379_spl ),
inference(split_clause,[status(thm)],[f46316,f46322,f46325]) ).
fof(f46342,plain,
( sQ1379_spl
| ~ c_lessequals(c_1,c_1,t_a) ),
inference(forward_demodulation,[status(thm)],[f23820,f46324]) ).
fof(f46343,plain,
( sQ1379_spl
| ~ sQ1209_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f46342,f45474]) ).
fof(f46344,plain,
( sQ1379_spl
| ~ sQ1209_spl ),
inference(contradiction_clause,[status(thm)],[f46343]) ).
fof(f46345,plain,
( ~ sQ1380_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f46326,f6225]) ).
fof(f46346,plain,
~ sQ1380_spl,
inference(contradiction_clause,[status(thm)],[f46345]) ).
fof(f46347,plain,
$false,
inference(sat_refutation,[status(thm)],[f40442,f46328,f46344,f46346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA012-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 13:22:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.47 % Drodi V4.1.1
% 136.47/17.77 % Refutation found
% 136.47/17.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 136.47/17.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.82/18.37 % Elapsed time: 18.006892 seconds
% 7.82/18.37 % CPU time: 138.637765 seconds
% 7.82/18.37 % Total memory used: 707.314 MB
% 7.82/18.37 % Net memory used: 643.933 MB
%------------------------------------------------------------------------------