%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA016-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:02:13 PM UTC 2026
% Result : Unsatisfiable 197.61s 25.52s
% Output : CNFRefutation 198.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 16 unt; 2 def)
% Number of atoms : 76 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1111,axiom,
! [T_a,V_y] :
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1394,axiom,
! [T_a,V_a] :
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2356,axiom,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2395,axiom,
! [T] :
( class_Ring__and__Field_Opordered__ring(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2413,axiom,
! [T] :
( class_Ring__and__Field_Oordered__semidom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2548,axiom,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Oordered__semidom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2675,axiom,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Opordered__ring(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2781,axiom,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2786,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2788,negated_conjecture,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2789,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4291,plain,
! [T_a] :
( ! [V_y] : c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(miniscoping,[status(thm)],[f1111]) ).
fof(f4292,plain,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X0,X1) = X0 ),
inference(cnf_transformation,[status(thm)],[f4291]) ).
fof(f4717,plain,
! [X0,X1] :
( X0 = c_0
| ~ class_Ring__and__Field_Ofield(X1)
| c_times(X0,c_HOL_Oinverse(X0,X1),X1) = c_1 ),
inference(cnf_transformation,[status(thm)],[f1394]) ).
fof(f5797,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f2356]) ).
fof(f5836,plain,
! [X0] :
( class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f2395]) ).
fof(f5854,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f2413]) ).
fof(f5989,plain,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f2548]) ).
fof(f6116,plain,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) ),
inference(cnf_transformation,[status(thm)],[f2675]) ).
fof(f6222,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(miniscoping,[status(thm)],[f2781]) ).
fof(f6223,plain,
! [X0,X1,X2,X3] :
( ~ class_OrderedGroup_Osemigroup__mult(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f6222]) ).
fof(f6231,plain,
v_c != c_0,
inference(cnf_transformation,[status(thm)],[f2786]) ).
fof(f6233,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f2788]) ).
fof(f6234,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(thm)],[f2789]) ).
fof(f15229,plain,
class_Ring__and__Field_Opordered__ring(t_a),
inference(resolution,[status(thm)],[f5836,f6234]) ).
fof(f15246,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[f15229,f6116]) ).
fof(f15313,plain,
! [X0,X1,X2] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(resolution,[status(thm)],[f15246,f6223]) ).
fof(f15805,plain,
class_Ring__and__Field_Oordered__semidom(t_a),
inference(resolution,[status(thm)],[f5854,f6234]) ).
fof(f15831,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolution,[status(thm)],[f15805,f5989]) ).
fof(f17436,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[f5797,f6234]) ).
fof(f17437,plain,
! [X0] :
( c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) = c_1
| c_0 = X0 ),
inference(resolution,[status(thm)],[f17436,f4717]) ).
fof(f17568,plain,
! [X0,X1] :
( c_0 = X0
| c_times(X0,c_times(c_HOL_Oinverse(X0,t_a),X1,t_a),t_a) = c_times(c_1,X1,t_a) ),
inference(paramodulation,[status(thm)],[f17437,f15313]) ).
fof(f17744,plain,
( c_0 = v_c
| v_g(v_x) != c_times(c_1,v_g(v_x),t_a) ),
inference(paramodulation,[status(thm)],[f17568,f6233]) ).
fof(f17749,definition,
( sQ656_spl
<=> v_g(v_x) = c_times(c_1,v_g(v_x),t_a) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f17751,plain,
( sQ656_spl
| c_times(c_1,v_g(v_x),t_a) != v_g(v_x) ),
inference(component_clause,[status(thm)],[f17749]) ).
fof(f17752,definition,
( sQ657_spl
<=> c_0 = v_c ),
introduced(definition,[new_symbols(definition,[sQ657_spl])],[split_symbol_definition]) ).
fof(f17753,plain,
( ~ sQ657_spl
| c_0 = v_c ),
inference(component_clause,[status(thm)],[f17752]) ).
fof(f17755,plain,
( sQ657_spl
| ~ sQ656_spl ),
inference(split_clause,[status(thm)],[f17744,f17749,f17752]) ).
fof(f39268,plain,
! [X0] : c_times(c_1,X0,t_a) = X0,
inference(resolution,[status(thm)],[f4292,f15831]) ).
fof(f39273,plain,
( sQ656_spl
| v_g(v_x) != v_g(v_x) ),
inference(backward_demodulation,[status(thm)],[f39268,f17751]) ).
fof(f39284,plain,
( sQ656_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f39273]) ).
fof(f39285,plain,
sQ656_spl,
inference(contradiction_clause,[status(thm)],[f39284]) ).
fof(f39287,plain,
( ~ sQ657_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17753,f6231]) ).
fof(f39288,plain,
~ sQ657_spl,
inference(contradiction_clause,[status(thm)],[f39287]) ).
fof(f39289,plain,
$false,
inference(sat_refutation,[status(thm)],[f17755,f39285,f39288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA016-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:27:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.25/0.51 % Drodi V4.1.1
% 197.61/25.52 % Refutation found
% 197.61/25.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 197.61/25.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 45.20/26.77 % Elapsed time: 26.173358 seconds
% 45.20/26.77 % CPU time: 193.961653 seconds
% 45.20/26.77 % Total memory used: 822.995 MB
% 45.20/26.77 % Net memory used: 751.449 MB
%------------------------------------------------------------------------------