%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA022-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:02:15 PM UTC 2026
% Result : Unsatisfiable 103.62s 13.64s
% Output : CNFRefutation 103.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 28
% Syntax : Number of formulae : 164 ( 38 unt; 3 def)
% Number of atoms : 330 ( 87 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 320 ( 154 ~; 163 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 298 ( 298 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),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_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a] :
( c_HOL_Oabs(c_uminus(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a] :
( c_HOL_Oabs(V_a,T_a) = c_uminus(V_a,T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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(f9,axiom,
! [T_a,V_a,V_b,V_c] :
( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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(f11,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(f12,axiom,
! [T_a,V_a,V_b] :
( c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,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(f14,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(f15,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(f16,axiom,
! [T_a,V_y,V_x] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [T_b,V_y,V_z,V_x] :
( c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [T] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0] : c_lessequals(v_k(X0),v_f(X0),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f29,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oabs(c_uminus(V_a,T_a),T_a) = c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = c_uminus(X1,X0)
| ~ c_lessequals(X1,c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,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)],[f8]) ).
fof(f39,plain,
! [X0,X1] :
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( c_plus(X1,c_minus(X2,X3,X0),X0) = c_minus(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,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)],[f10]) ).
fof(f43,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)],[f42]) ).
fof(f44,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)],[f11]) ).
fof(f45,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(X1,X2,X0),c_0,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f46,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)],[f13]) ).
fof(f47,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)],[f46]) ).
fof(f48,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)],[f14]) ).
fof(f49,plain,
! [X0,X1] :
( c_minus(X1,X1,X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,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)],[f15]) ).
fof(f51,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)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
! [T_a,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ! [V_y] :
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f60,plain,
! [X0] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f65,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_HOL_Oabs(X0,X1),X1) ),
inference(resolution,[status(thm)],[f32,f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_minus(X0,X0,X1) = c_0 ),
inference(resolution,[status(thm)],[f49,f63]) ).
fof(f67,plain,
! [X0] : c_minus(X0,X0,t_b) = c_0,
inference(resolution,[status(thm)],[f66,f30]) ).
fof(f68,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[status(thm)],[f65,f30]) ).
fof(f69,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_uminus(X0,X1),X1) = c_HOL_Oabs(X0,X1) ),
inference(resolution,[status(thm)],[f34,f64]) ).
fof(f70,plain,
! [X0] : c_HOL_Oabs(c_uminus(X0,t_b),t_b) = c_HOL_Oabs(X0,t_b),
inference(resolution,[status(thm)],[f69,f30]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f61,f53]) ).
fof(f72,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f62,f57]) ).
fof(f73,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_plus(c_0,X0,X1) = X0 ),
inference(resolution,[status(thm)],[f39,f60]) ).
fof(f74,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(resolution,[status(thm)],[f73,f30]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X1,X0,X2)
| c_less(X0,X1,X2) ),
inference(resolution,[status(thm)],[f52,f61]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X0,X1,X2)
| ~ c_less(X0,X1,X2) ),
inference(resolution,[status(thm)],[f56,f72]) ).
fof(f77,plain,
! [X0,X1] :
( c_lessequals(X1,X0,t_b)
| c_less(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f75,f30]) ).
fof(f78,plain,
! [X0,X1] :
( c_lessequals(X0,X1,t_b)
| ~ c_less(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f76,f30]) ).
fof(f79,plain,
! [X0,X1] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f78,f77]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_minus(X0,c_uminus(X1,X2),X2) = c_plus(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f63]) ).
fof(f83,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(X0,X1) = c_uminus(X0,X1)
| ~ c_lessequals(X0,c_0,X1) ),
inference(resolution,[status(thm)],[f35,f64]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_plus(X0,c_minus(X1,X2,X3),X3) = c_minus(c_plus(X0,X1,X3),X2,X3) ),
inference(resolution,[status(thm)],[f41,f63]) ).
fof(f86,plain,
! [X0,X1] : c_minus(X0,c_uminus(X1,t_b),t_b) = c_plus(X0,X1,t_b),
inference(resolution,[status(thm)],[f82,f30]) ).
fof(f87,plain,
! [X0] : c_0 = c_plus(c_uminus(X0,t_b),X0,t_b),
inference(paramodulation,[status(thm)],[f67,f86]) ).
fof(f89,plain,
! [X0] :
( c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b)
| ~ c_lessequals(X0,c_0,t_b) ),
inference(resolution,[status(thm)],[f83,f30]) ).
fof(f90,plain,
! [X0] :
( c_lessequals(c_0,X0,t_b)
| c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) ),
inference(resolution,[status(thm)],[f89,f79]) ).
fof(f91,plain,
( c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b)
| c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b) ),
inference(resolution,[status(thm)],[f90,f89]) ).
fof(f92,definition,
( sQ0_spl
<=> c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ0_spl
| c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f91,f92]) ).
fof(f96,plain,
( ~ sQ0_spl
| c_0 = c_plus(c_HOL_Oabs(c_0,t_b),c_0,t_b) ),
inference(paramodulation,[status(thm)],[f93,f87]) ).
fof(f97,plain,
! [X0] :
( ~ sQ0_spl
| c_minus(X0,c_HOL_Oabs(c_0,t_b),t_b) = c_plus(X0,c_0,t_b) ),
inference(paramodulation,[status(thm)],[f93,f86]) ).
fof(f102,plain,
! [X0,X1,X2] : c_plus(X0,c_minus(X1,X2,t_b),t_b) = c_minus(c_plus(X0,X1,t_b),X2,t_b),
inference(resolution,[status(thm)],[f85,f30]) ).
fof(f103,plain,
! [X0,X1,X2] :
( c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f71,f30]) ).
fof(f107,plain,
! [X0,X1,X2] : c_plus(X0,c_plus(X1,X2,t_b),t_b) = c_minus(c_plus(X0,X1,t_b),c_uminus(X2,t_b),t_b),
inference(paramodulation,[status(thm)],[f86,f102]) ).
fof(f108,plain,
! [X0,X1] : c_plus(X0,c_0,t_b) = c_minus(c_plus(X0,X1,t_b),X1,t_b),
inference(paramodulation,[status(thm)],[f67,f102]) ).
fof(f113,plain,
! [X0,X1,X2] : c_plus(X0,c_plus(X1,X2,t_b),t_b) = c_plus(c_plus(X0,X1,t_b),X2,t_b),
inference(forward_demodulation,[status(thm)],[f86,f107]) ).
fof(f117,plain,
! [X0] : c_plus(c_uminus(X0,t_b),c_0,t_b) = c_minus(c_0,X0,t_b),
inference(paramodulation,[status(thm)],[f87,f108]) ).
fof(f135,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(resolution,[status(thm)],[f103,f29]) ).
fof(f137,definition,
( sQ1_spl
<=> c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ1_spl
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,definition,
( sQ2_spl
<=> c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ2_spl
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f135,f137,f140]) ).
fof(f144,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f68]) ).
fof(f145,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f148,plain,
! [X0] :
( ~ sQ0_spl
| c_plus(c_HOL_Oabs(c_0,t_b),c_plus(c_0,X0,t_b),t_b) = c_plus(c_0,X0,t_b) ),
inference(paramodulation,[status(thm)],[f96,f113]) ).
fof(f150,plain,
! [X0,X1] : c_plus(c_uminus(X0,t_b),c_plus(X0,X1,t_b),t_b) = c_plus(c_0,X1,t_b),
inference(paramodulation,[status(thm)],[f87,f113]) ).
fof(f159,plain,
! [X0] :
( ~ sQ0_spl
| c_plus(c_HOL_Oabs(c_0,t_b),X0,t_b) = c_plus(c_0,X0,t_b) ),
inference(forward_demodulation,[status(thm)],[f74,f148]) ).
fof(f161,plain,
! [X0] :
( ~ sQ0_spl
| c_plus(c_HOL_Oabs(c_0,t_b),X0,t_b) = X0 ),
inference(forward_demodulation,[status(thm)],[f74,f159]) ).
fof(f163,plain,
! [X0,X1] : c_plus(c_uminus(X0,t_b),c_plus(X0,X1,t_b),t_b) = X1,
inference(forward_demodulation,[status(thm)],[f74,f150]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_uminus(c_minus(X0,X1,X2),X2) = c_minus(X1,X0,X2) ),
inference(resolution,[status(thm)],[f51,f63]) ).
fof(f174,plain,
! [X0] :
( ~ sQ0_spl
| c_plus(c_uminus(c_HOL_Oabs(c_0,t_b),t_b),X0,t_b) = X0 ),
inference(paramodulation,[status(thm)],[f161,f163]) ).
fof(f182,plain,
! [X0,X1] : c_plus(c_uminus(X0,t_b),c_0,t_b) = c_minus(X1,c_plus(X0,X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f163,f108]) ).
fof(f193,plain,
! [X0,X1] : c_minus(c_0,X0,t_b) = c_minus(X1,c_plus(X0,X1,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f117,f182]) ).
fof(f194,plain,
! [X0,X1] : c_uminus(c_minus(X0,X1,t_b),t_b) = c_minus(X1,X0,t_b),
inference(resolution,[status(thm)],[f172,f30]) ).
fof(f198,plain,
( ~ sQ0_spl
| c_0 = c_HOL_Oabs(c_0,t_b) ),
inference(paramodulation,[status(thm)],[f87,f174]) ).
fof(f210,plain,
! [X0] :
( ~ sQ0_spl
| c_minus(X0,c_0,t_b) = c_plus(X0,c_0,t_b) ),
inference(backward_demodulation,[status(thm)],[f198,f97]) ).
fof(f220,plain,
! [X0] :
( ~ sQ0_spl
| c_minus(c_uminus(X0,t_b),c_0,t_b) = c_minus(c_0,X0,t_b) ),
inference(backward_demodulation,[status(thm)],[f210,f117]) ).
fof(f253,plain,
! [X0,X1,X2] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(X0,c_minus(X2,X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f194,f86]) ).
fof(f254,plain,
! [X0,X1] : c_HOL_Oabs(c_minus(X0,X1,t_b),t_b) = c_HOL_Oabs(c_minus(X1,X0,t_b),t_b),
inference(paramodulation,[status(thm)],[f194,f70]) ).
fof(f258,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(backward_demodulation,[status(thm)],[f253,f102]) ).
fof(f265,plain,
! [X0,X1,X2] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| c_lessequals(c_minus(X0,X1,X2),c_0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f58]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f72]) ).
fof(f268,plain,
! [X0,X1] : c_minus(c_0,c_uminus(X0,t_b),t_b) = c_minus(c_plus(X0,X1,t_b),X1,t_b),
inference(paramodulation,[status(thm)],[f163,f193]) ).
fof(f273,plain,
! [X0,X1] : c_plus(c_0,X0,t_b) = c_minus(c_plus(X0,X1,t_b),X1,t_b),
inference(forward_demodulation,[status(thm)],[f86,f268]) ).
fof(f274,plain,
! [X0,X1] : X0 = c_minus(c_plus(X0,X1,t_b),X1,t_b),
inference(forward_demodulation,[status(thm)],[f74,f273]) ).
fof(f275,plain,
! [X0,X1] : X0 = c_minus(X0,c_minus(X1,X1,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f258,f274]) ).
fof(f277,plain,
! [X0] :
( ~ sQ0_spl
| c_uminus(X0,t_b) = c_minus(c_0,X0,t_b) ),
inference(backward_demodulation,[status(thm)],[f281,f220]) ).
fof(f281,plain,
! [X0] : X0 = c_minus(X0,c_0,t_b),
inference(forward_demodulation,[status(thm)],[f67,f275]) ).
fof(f304,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)],[f43,f63]) ).
fof(f305,plain,
! [X0,X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_minus(X0,X2,X3),X1,X3)
| ~ c_lessequals(X0,c_plus(X1,X2,X3),X3) ),
inference(resolution,[status(thm)],[f44,f58]) ).
fof(f308,plain,
! [X0] :
( ~ sQ0_spl
| c_uminus(c_uminus(X0,t_b),t_b) = c_plus(c_0,X0,t_b) ),
inference(paramodulation,[status(thm)],[f86,f277]) ).
fof(f315,plain,
! [X0] :
( ~ sQ0_spl
| c_uminus(c_uminus(X0,t_b),t_b) = X0 ),
inference(forward_demodulation,[status(thm)],[f74,f308]) ).
fof(f323,plain,
! [X0,X1] :
( ~ sQ0_spl
| c_minus(X0,X1,t_b) = c_plus(X0,c_uminus(X1,t_b),t_b) ),
inference(paramodulation,[status(thm)],[f315,f86]) ).
fof(f403,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| c_minus(X0,c_minus(X1,c_uminus(X2,t_b),t_b),t_b) = c_minus(c_minus(X0,X2,t_b),X1,t_b) ),
inference(paramodulation,[status(thm)],[f323,f258]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| c_minus(X0,c_plus(X1,X2,t_b),t_b) = c_minus(c_minus(X0,X2,t_b),X1,t_b) ),
inference(forward_demodulation,[status(thm)],[f86,f403]) ).
fof(f543,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)],[f304,f30]) ).
fof(f551,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(forward_demodulation,[status(thm)],[f258,f543]) ).
fof(f687,plain,
! [X0,X1] : c_plus(c_0,X0,t_b) = c_minus(X1,c_minus(X1,X0,t_b),t_b),
inference(paramodulation,[status(thm)],[f67,f551]) ).
fof(f722,plain,
! [X0,X1] : X0 = c_minus(X1,c_minus(X1,X0,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f74,f687]) ).
fof(f767,plain,
! [X0,X1,X2] : c_plus(X0,X1,t_b) = c_minus(X2,c_minus(c_minus(X2,X0,t_b),X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f722,f551]) ).
fof(f799,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| c_plus(X0,X1,t_b) = c_minus(X2,c_minus(X2,c_plus(X1,X0,t_b),t_b),t_b) ),
inference(forward_demodulation,[status(thm)],[f424,f767]) ).
fof(f800,plain,
! [X0,X1] :
( ~ sQ0_spl
| c_plus(X0,X1,t_b) = c_plus(X1,X0,t_b) ),
inference(forward_demodulation,[status(thm)],[f722,f799]) ).
fof(f814,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(X2,c_minus(X0,X1,t_b),t_b) ),
inference(paramodulation,[status(thm)],[f551,f800]) ).
fof(f970,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(c_minus(X0,X1,X2),c_0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f265,f64]) ).
fof(f971,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f266,f30]) ).
fof(f972,plain,
! [X0,X1] :
( c_lessequals(c_minus(X0,X1,t_b),c_0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f970,f30]) ).
fof(f978,plain,
! [X0,X1] :
( c_lessequals(v_k(X0),X1,t_b)
| ~ c_lessequals(v_f(X0),X1,t_b) ),
inference(resolution,[status(thm)],[f971,f28]) ).
fof(f981,plain,
! [X0] :
( sQ2_spl
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X0,t_b)
| ~ c_lessequals(X0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(resolution,[status(thm)],[f971,f142]) ).
fof(f987,plain,
! [X0,X1] :
( c_lessequals(X1,v_f(X0),t_b)
| c_lessequals(v_k(X0),X1,t_b) ),
inference(resolution,[status(thm)],[f978,f79]) ).
fof(f1008,plain,
! [X0,X1] :
( c_HOL_Oabs(c_minus(X0,X1,t_b),t_b) = c_uminus(c_minus(X0,X1,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f972,f89]) ).
fof(f1020,plain,
! [X0,X1] :
( c_HOL_Oabs(c_minus(X0,X1,t_b),t_b) = c_minus(X1,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_demodulation,[status(thm)],[f194,f1008]) ).
fof(f1053,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)],[f305,f64]) ).
fof(f1054,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)],[f1053,f30]) ).
fof(f1592,plain,
( sQ2_spl
| ~ c_lessequals(v_k(v_x),c_plus(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_g(v_x),t_b),t_b) ),
inference(resolution,[status(thm)],[f1054,f142]) ).
fof(f1610,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ c_lessequals(v_k(v_x),c_plus(v_g(v_x),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(forward_demodulation,[status(thm)],[f800,f1592]) ).
fof(f5625,plain,
( sQ2_spl
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(resolution,[status(thm)],[f981,f68]) ).
fof(f5658,plain,
( sQ2_spl
| ~ c_lessequals(v_k(v_x),v_g(v_x),t_b) ),
inference(resolution,[status(thm)],[f5625,f972]) ).
fof(f5672,plain,
( sQ2_spl
| c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
inference(resolution,[status(thm)],[f5658,f987]) ).
fof(f6622,plain,
( sQ2_spl
| c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b) ),
inference(resolution,[status(thm)],[f1020,f5672]) ).
fof(f6711,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ c_lessequals(v_k(v_x),c_plus(v_g(v_x),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(backward_demodulation,[status(thm)],[f6717,f1610]) ).
fof(f6717,plain,
( sQ2_spl
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b) ),
inference(forward_demodulation,[status(thm)],[f254,f6622]) ).
fof(f6877,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ c_lessequals(v_k(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(forward_demodulation,[status(thm)],[f814,f6711]) ).
fof(f6878,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ c_lessequals(v_k(v_x),c_minus(v_f(v_x),c_0,t_b),t_b) ),
inference(forward_demodulation,[status(thm)],[f67,f6877]) ).
fof(f6879,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
inference(forward_demodulation,[status(thm)],[f281,f6878]) ).
fof(f6880,plain,
( sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6879,f28]) ).
fof(f6881,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f6880]) ).
fof(f6882,plain,
$false,
inference(sat_refutation,[status(thm)],[f95,f143,f145,f6881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA022-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n004.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 13:24:20 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.51 % Drodi V4.1.1
% 103.62/13.64 % Refutation found
% 103.62/13.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 103.62/13.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 84.67/14.87 % Elapsed time: 14.160728 seconds
% 84.67/14.87 % CPU time: 100.090715 seconds
% 84.67/14.87 % Total memory used: 476.624 MB
% 84.67/14.87 % Net memory used: 444.115 MB
%------------------------------------------------------------------------------