%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.09s 0.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 10 unt; 3 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 147 ( 71 ~; 73 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(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(f7,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(f8,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(f9,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(f10,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(f11,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(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(f17,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,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(f19,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)],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,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)],[f8]) ).
fof(f24,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)],[f9]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,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)],[f28,f23]) ).
fof(f32,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f29,f19]) ).
fof(f33,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f35,definition,
( sQ0_spl
<=> class_OrderedGroup_Opordered__ab__group__add(t_b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( sQ0_spl
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f42,plain,
( sQ0_spl
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f43,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f17]) ).
fof(f44,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X0,X1,X2)
| ~ c_less(X0,X1,X2) ),
inference(resolution,[status(thm)],[f26,f27]) ).
fof(f71,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)],[f31,f17]) ).
fof(f72,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(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)],[f71,f16]) ).
fof(f74,definition,
( sQ6_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,[sQ6_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( sQ6_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)],[f74]) ).
fof(f77,definition,
( sQ7_spl
<=> c_lessequals(c_minus(v_f(v_x),v_k(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,[sQ7_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ7_spl
| ~ c_lessequals(c_minus(v_f(v_x),v_k(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)],[f77]) ).
fof(f80,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f72,f74,f77]) ).
fof(f85,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f33]) ).
fof(f86,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f45,f36]) ).
fof(f116,plain,
! [X0] :
( ~ sQ0_spl
| ~ c_lessequals(c_0,X0,t_b)
| ~ c_lessequals(X0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
inference(resolution,[status(thm)],[f111,f15]) ).
fof(f127,plain,
! [X0] :
( ~ sQ0_spl
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
inference(resolution,[status(thm)],[f116,f33]) ).
fof(f146,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X1,X0,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f146,f28]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X1,X0,X2)
| c_lessequals(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f30]) ).
fof(f149,plain,
! [X0,X1] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f148,f17]) ).
fof(f151,plain,
( sQ7_spl
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
inference(resolution,[status(thm)],[f149,f79]) ).
fof(f158,plain,
( sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f127]) ).
fof(f159,plain,
( sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f80,f86,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n010.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 13:25:26 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 0.09/0.56 % Refutation found
% 0.09/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.59 % Elapsed time: 0.056676 seconds
% 0.17/0.59 % CPU time: 0.184090 seconds
% 0.17/0.59 % Total memory used: 18.610 MB
% 0.17/0.59 % Net memory used: 18.041 MB
%------------------------------------------------------------------------------