%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 50 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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(f5,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(f6,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(f7,axiom,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
v_c != c_0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,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)],[f2]) ).
fof(f12,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,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)],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( c_times(c_1,X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,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)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( c_times(X1,c_HOL_Oinverse(X1,X0),X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[f20,f12]) ).
fof(f22,plain,
! [X0] :
( c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[f17,f21]) ).
fof(f23,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f24,plain,
! [X0] : c_times(c_1,X0,t_a) = X0,
inference(resolution,[status(thm)],[f23,f14]) ).
fof(f25,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[f19,f21]) ).
fof(f26,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)],[f25,f16]) ).
fof(f29,plain,
v_g(v_x) != c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a),
inference(backward_demodulation,[status(thm)],[f26,f11]) ).
fof(f46,plain,
( v_c = c_0
| v_g(v_x) != c_times(c_1,v_g(v_x),t_a) ),
inference(paramodulation,[status(thm)],[f22,f29]) ).
fof(f47,plain,
( v_c = c_0
| v_g(v_x) != v_g(v_x) ),
inference(forward_demodulation,[status(thm)],[f24,f46]) ).
fof(f48,plain,
v_c = c_0,
inference(trivial_equality_resolution,[status(thm)],[f47]) ).
fof(f49,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f48,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA016-2 : 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 : n016.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:28:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.059054 seconds
% 0.11/0.44 % CPU time: 0.167929 seconds
% 0.11/0.44 % Total memory used: 80.018 MB
% 0.11/0.44 % Net memory used: 79.546 MB
%------------------------------------------------------------------------------