%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:02:16 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 28 unt; 0 def)
% Number of atoms : 101 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 42 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_y] :
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_b] :
( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a,V_b] :
( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T_a,V_a,V_b] :
( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T_a,V_a,V_b] :
( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T_b,V_y,V_x] :
( c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T_b,V_x,V_y,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X0),v_g(X0),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : ~ c_lessequals(v_f(v_x(X0)),c_plus(v_g(v_x(X0)),c_times(X0,c_HOL_Oabs(v_h(v_x(X0)),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = X1
| ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [T_a] :
( ! [V_a,V_b] : c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( c_plus(X1,c_uminus(X2,X0),X0) = c_minus(X1,X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,c_plus(X3,X2,X0),X0)
| ~ c_lessequals(c_minus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [T_a] :
( ! [V_a,V_b] : c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( c_minus(X1,c_uminus(X2,X0),X0) = c_plus(X1,X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [T_a] :
( ! [V_a,V_b] : c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] :
( c_uminus(c_plus(X1,X2,X0),X0) = c_plus(c_uminus(X1,X0),c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [T_a] :
( ! [V_a,V_b] : c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2] :
( c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
! [T_b] :
( ! [V_y,V_x] : c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f33,plain,
! [X0,X1,X2] :
( c_lessequals(X1,c_Orderings_Omax(X2,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [T_b,V_x,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ! [V_y] : ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f40,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[status(thm)],[f38,f19]) ).
fof(f41,plain,
! [X0,X1] : c_plus(X0,c_uminus(X1,t_b),t_b) = c_minus(X0,X1,t_b),
inference(resolution,[status(thm)],[f22,f40]) ).
fof(f42,plain,
! [X0,X1] : c_minus(X0,c_uminus(X1,t_b),t_b) = c_plus(X0,X1,t_b),
inference(resolution,[status(thm)],[f25,f40]) ).
fof(f43,plain,
! [X0,X1] : c_uminus(c_minus(X0,X1,t_b),t_b) = c_minus(X1,X0,t_b),
inference(resolution,[status(thm)],[f29,f40]) ).
fof(f44,plain,
! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_minus(c_uminus(X1,t_b),X0,t_b),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f47,plain,
! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_plus(c_uminus(X0,t_b),c_uminus(X1,t_b),t_b),
inference(resolution,[status(thm)],[f27,f40]) ).
fof(f48,plain,
! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_minus(c_uminus(X0,t_b),X1,t_b),
inference(forward_demodulation,[status(thm)],[f41,f47]) ).
fof(f49,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[f37,f19]) ).
fof(f50,plain,
! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,t_b),t_b),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f51,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[f39,f19]) ).
fof(f52,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[f51,f36]) ).
fof(f59,plain,
! [X0] :
( c_HOL_Oabs(c_Orderings_Omax(X0,c_0,t_b),t_b) = c_Orderings_Omax(X0,c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[status(thm)],[f50,f20]) ).
fof(f61,plain,
! [X0] : c_HOL_Oabs(c_Orderings_Omax(X0,c_0,t_b),t_b) = c_Orderings_Omax(X0,c_0,t_b),
inference(forward_subsumption_resolution,[status(thm)],[f59,f51]) ).
fof(f66,plain,
! [X0] : c_lessequals(c_Orderings_Omax(c_minus(v_f(X0),v_g(X0),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f61,f17]) ).
fof(f80,plain,
! [X0] :
( c_lessequals(c_minus(v_f(X0),v_g(X0),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[status(thm)],[f66,f35]) ).
fof(f81,plain,
! [X0] : c_lessequals(c_minus(v_f(X0),v_g(X0),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f80,f49]) ).
fof(f82,plain,
! [X0] :
( c_lessequals(v_f(X0),c_plus(c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),v_g(X0),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(resolution,[status(thm)],[f81,f23]) ).
fof(f83,plain,
! [X0] : c_lessequals(v_f(X0),c_plus(c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),v_g(X0),t_b),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f82,f52]) ).
fof(f84,plain,
! [X0,X1] : c_minus(c_uminus(X0,t_b),X1,t_b) = c_minus(c_uminus(X1,t_b),X0,t_b),
inference(forward_demodulation,[status(thm)],[f44,f48]) ).
fof(f98,plain,
! [X0,X1] : c_uminus(c_minus(c_uminus(X0,t_b),X1,t_b),t_b) = c_minus(X0,c_uminus(X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f84,f43]) ).
fof(f108,plain,
! [X0,X1] : c_minus(X0,c_uminus(X1,t_b),t_b) = c_minus(X1,c_uminus(X0,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f43,f98]) ).
fof(f109,plain,
! [X0,X1] : c_plus(X0,X1,t_b) = c_minus(X1,c_uminus(X0,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f42,f108]) ).
fof(f110,plain,
! [X0,X1] : c_plus(X0,X1,t_b) = c_plus(X1,X0,t_b),
inference(forward_demodulation,[status(thm)],[f42,f109]) ).
fof(f142,plain,
! [X0] : c_lessequals(v_f(X0),c_plus(v_g(X0),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f110,f83]) ).
fof(f143,plain,
$false,
inference(resolution,[status(thm)],[f142,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n020.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 13:25:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.48 % Elapsed time: 0.047242 seconds
% 0.16/0.48 % CPU time: 0.158342 seconds
% 0.16/0.48 % Total memory used: 26.856 MB
% 0.16/0.48 % Net memory used: 26.694 MB
%------------------------------------------------------------------------------