%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.38s 0.69s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 34 unt; 0 def)
% Number of atoms : 97 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 131 ( 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [T_a,V_y] :
( c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_a,V_b,V_c] :
( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_a,V_b,V_c] :
( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_c,V_b] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a] :
( c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [V_U] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [T_a] :
( ! [V_y] : c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( c_plus(c_minus(X1,X2,X0),X3,X0) = c_minus(c_plus(X1,X3,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( c_minus(X1,c_minus(X2,X3,X0),X0) = c_minus(c_plus(X1,X3,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_minus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_plus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [T_a] :
( ! [V_a] : c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] :
( c_minus(X1,X1,X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0] : c_lessequals(v_g(X0),v_k(X0),t_b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_plus(c_0,X0,X1) = X0 ),
inference(resolution,[status(thm)],[f15,f28]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_plus(c_minus(X0,X1,X2),X3,X2) = c_minus(c_plus(X0,X3,X2),X1,X2) ),
inference(resolution,[status(thm)],[f19,f29]) ).
fof(f34,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_minus(X0,X0,X1) = c_0 ),
inference(resolution,[status(thm)],[f25,f29]) ).
fof(f35,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(resolution,[status(thm)],[f32,f31]) ).
fof(f37,plain,
! [X0] : c_minus(X0,X0,t_b) = c_0,
inference(resolution,[status(thm)],[f34,f31]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_minus(X0,c_minus(X1,X2,X3),X3) = c_minus(c_plus(X0,X2,X3),X1,X3) ),
inference(resolution,[status(thm)],[f21,f29]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_minus(X0,X2,X3),X1,X3)
| ~ c_lessequals(X0,c_plus(X1,X2,X3),X3) ),
inference(resolution,[status(thm)],[f22,f30]) ).
fof(f42,plain,
! [X0,X1,X2] : c_plus(c_minus(X0,X1,t_b),X2,t_b) = c_minus(c_plus(X0,X2,t_b),X1,t_b),
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f50,plain,
! [X0,X1] : c_plus(c_0,X0,t_b) = c_minus(c_plus(X1,X0,t_b),X1,t_b),
inference(paramodulation,[status(thm)],[f37,f42]) ).
fof(f53,plain,
! [X0,X1] : X0 = c_minus(c_plus(X1,X0,t_b),X1,t_b),
inference(forward_demodulation,[status(thm)],[f35,f50]) ).
fof(f58,plain,
! [X0] : X0 = c_minus(X0,c_0,t_b),
inference(paramodulation,[status(thm)],[f35,f53]) ).
fof(f74,plain,
! [X0,X1,X2] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_minus(c_plus(X0,X2,t_b),X1,t_b),
inference(resolution,[status(thm)],[f39,f31]) ).
fof(f75,plain,
! [X0,X1] : X0 = c_minus(X1,c_minus(X1,X0,t_b),t_b),
inference(backward_demodulation,[status(thm)],[f74,f53]) ).
fof(f76,plain,
! [X0,X1,X2] : c_plus(c_minus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_minus(X1,X2,t_b),t_b),
inference(backward_demodulation,[status(thm)],[f74,f42]) ).
fof(f77,plain,
! [X0,X1] : c_minus(X0,c_minus(c_0,X1,t_b),t_b) = c_plus(X0,X1,t_b),
inference(paramodulation,[status(thm)],[f58,f74]) ).
fof(f106,plain,
! [X0] : c_0 = c_plus(c_minus(c_0,X0,t_b),X0,t_b),
inference(paramodulation,[status(thm)],[f37,f77]) ).
fof(f121,plain,
! [X0] : c_0 = c_plus(c_plus(c_0,X0,t_b),c_minus(c_0,X0,t_b),t_b),
inference(paramodulation,[status(thm)],[f77,f106]) ).
fof(f128,plain,
! [X0] : c_0 = c_plus(X0,c_minus(c_0,X0,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f35,f121]) ).
fof(f137,plain,
! [X0,X1] : c_minus(X0,c_minus(X1,c_minus(c_0,X0,t_b),t_b),t_b) = c_minus(c_0,X1,t_b),
inference(paramodulation,[status(thm)],[f128,f74]) ).
fof(f140,plain,
! [X0,X1] : c_minus(X0,c_plus(X1,X0,t_b),t_b) = c_minus(c_0,X1,t_b),
inference(forward_demodulation,[status(thm)],[f77,f137]) ).
fof(f141,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,c_plus(X1,X2,t_b),t_b) ),
inference(resolution,[status(thm)],[f40,f31]) ).
fof(f145,plain,
! [X0,X1] : c_0 = c_minus(X0,c_minus(X1,c_minus(c_0,c_minus(X0,X1,t_b),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[f128,f76]) ).
fof(f156,plain,
! [X0,X1] : c_0 = c_minus(X0,c_plus(X1,c_minus(X0,X1,t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f77,f145]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_minus(X0,X3,t_b),c_minus(X1,X2,t_b),t_b)
| ~ c_lessequals(X0,c_minus(X1,c_minus(X2,X3,t_b),t_b),t_b) ),
inference(paramodulation,[status(thm)],[f76,f141]) ).
fof(f189,plain,
! [X0,X1] :
( c_lessequals(c_minus(X0,X1,t_b),c_0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(paramodulation,[status(thm)],[f35,f141]) ).
fof(f191,plain,
! [X0,X1] :
( c_lessequals(c_minus(X0,c_minus(c_0,X1,t_b),t_b),X1,t_b)
| ~ c_lessequals(X0,c_0,t_b) ),
inference(paramodulation,[status(thm)],[f128,f141]) ).
fof(f192,plain,
! [X0,X1] :
( c_lessequals(c_plus(X0,X1,t_b),X1,t_b)
| ~ c_lessequals(X0,c_0,t_b) ),
inference(forward_demodulation,[status(thm)],[f77,f191]) ).
fof(f353,plain,
! [X0,X1] : c_plus(X0,c_minus(X1,X0,t_b),t_b) = c_minus(X1,c_0,t_b),
inference(paramodulation,[status(thm)],[f156,f75]) ).
fof(f393,plain,
! [X0,X1] : c_plus(X0,c_minus(X1,X0,t_b),t_b) = X1,
inference(forward_demodulation,[status(thm)],[f58,f353]) ).
fof(f587,plain,
! [X0] : c_lessequals(c_minus(v_g(X0),v_k(X0),t_b),c_0,t_b),
inference(resolution,[status(thm)],[f189,f26]) ).
fof(f722,plain,
! [X0,X1] : c_lessequals(c_plus(c_minus(v_g(X0),v_k(X0),t_b),X1,t_b),X1,t_b),
inference(resolution,[status(thm)],[f192,f587]) ).
fof(f723,plain,
! [X0,X1] : c_lessequals(c_minus(v_g(X0),c_minus(v_k(X0),X1,t_b),t_b),X1,t_b),
inference(forward_demodulation,[status(thm)],[f76,f722]) ).
fof(f801,plain,
! [X0,X1] : c_lessequals(c_minus(v_g(X0),c_minus(c_0,X1,t_b),t_b),c_plus(X1,v_k(X0),t_b),t_b),
inference(paramodulation,[status(thm)],[f140,f723]) ).
fof(f820,plain,
! [X0,X1] : c_lessequals(c_plus(v_g(X0),X1,t_b),c_plus(X1,v_k(X0),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f77,f801]) ).
fof(f829,plain,
! [X0,X1] : c_lessequals(X0,c_plus(c_minus(X0,v_g(X1),t_b),v_k(X1),t_b),t_b),
inference(paramodulation,[status(thm)],[f393,f820]) ).
fof(f847,plain,
! [X0,X1] : c_lessequals(X0,c_minus(X0,c_minus(v_g(X1),v_k(X1),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f76,f829]) ).
fof(f1048,plain,
! [X0,X1] : c_lessequals(c_minus(X0,v_k(X1),t_b),c_minus(X0,v_g(X1),t_b),t_b),
inference(resolution,[status(thm)],[f847,f188]) ).
fof(f1393,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f27,f1048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.50 % Computer : n017.cluster.edu
% 0.09/0.50 % Model : x86_64 x86_64
% 0.09/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.50 % Memory : 8046.5625MB
% 0.09/0.50 % OS : Linux 6.8.0-71-generic
% 0.09/0.50 % CPULimit : 300
% 0.09/0.50 % WCLimit : 300
% 0.09/0.50 % DateTime : Mon Sep 21 13:20:14 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 0.38/0.69 % Refutation found
% 0.38/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.38/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.47/0.72 % Elapsed time: 0.197834 seconds
% 0.47/0.72 % CPU time: 1.349212 seconds
% 0.47/0.72 % Total memory used: 68.611 MB
% 0.47/0.72 % Net memory used: 67.581 MB
%------------------------------------------------------------------------------