%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.15s 15.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 85 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 37 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),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_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
v_c != c_0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,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(f18,plain,
! [X0,X1] :
( c_times(c_1,X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,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)],[f7]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f8]) ).
fof(f26,plain,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f32,plain,
! [X0] : c_lessequals(X0,X0,t_a),
inference(resolution,[status(thm)],[f31,f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_1,X0,X1) = X0 ),
inference(resolution,[status(thm)],[f18,f26]) ).
fof(f34,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| c_times(c_1,X0,X1) = X0 ),
inference(resolution,[status(thm)],[f33,f28]) ).
fof(f35,plain,
! [X0] : c_times(c_1,X0,t_a) = X0,
inference(resolution,[status(thm)],[f34,f16]) ).
fof(f37,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)],[f25,f28]) ).
fof(f38,plain,
! [X0] :
( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[f37,f16]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(resolution,[status(thm)],[f20,f27]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(resolution,[status(thm)],[f39,f28]) ).
fof(f41,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)],[f40,f16]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_HOL_Oabs(c_times(X0,X1,X2),X2) = c_times(c_HOL_Oabs(X0,X2),c_HOL_Oabs(X1,X2),X2) ),
inference(resolution,[status(thm)],[f24,f29]) ).
fof(f44,plain,
! [X0,X1] :
( X1 = c_0
| c_times(c_1,X0,t_a) = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f38,f41]) ).
fof(f49,plain,
! [X0,X1] :
( X1 = c_0
| X0 = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f35,f44]) ).
fof(f50,plain,
! [X0] : X0 = c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,X0,t_a),t_a),
inference(resolution,[status(thm)],[f49,f14]) ).
fof(f99,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)],[f42,f16]) ).
fof(f100,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(backward_demodulation,[status(thm)],[f99,f15]) ).
fof(f111,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),c_HOL_Oabs(c_times(X0,c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),t_a),t_a),t_a),
inference(paramodulation,[status(thm)],[f99,f100]) ).
fof(f132,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),
inference(paramodulation,[status(thm)],[f50,f111]) ).
fof(f141,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f132,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.38 % Computer : n008.cluster.edu
% 0.11/15.38 % Model : x86_64 x86_64
% 0.11/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.38 % Memory : 8046.5625MB
% 0.11/15.38 % OS : Linux 6.8.0-71-generic
% 0.11/15.38 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 13:24:58 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.15/15.40 % Drodi V4.1.1
% 0.15/15.45 % Refutation found
% 0.15/15.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/15.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/15.48 % Elapsed time: 0.069980 seconds
% 0.15/15.48 % CPU time: 0.137060 seconds
% 0.15/15.48 % Total memory used: 25.995 MB
% 0.15/15.48 % Net memory used: 25.967 MB
%------------------------------------------------------------------------------