%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:02:18 PM UTC 2026
% Result : Unsatisfiable 16.47s 2.60s
% Output : CNFRefutation 15.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 84 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f186,axiom,
! [T_a,V_i,V_k] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,axiom,
! [T_a,V_k,V_i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,axiom,
! [T_a,V_y,V_x] :
( c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f359,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f597,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f705,axiom,
! [T] :
( class_Orderings_Oord(T)
| ~ class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f942,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f954,axiom,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Olordered__ring(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1090,axiom,
! [T] :
( class_Ring__and__Field_Olordered__ring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1411,axiom,
! [T_a,V_a] :
( c_lessequals(V_a,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(f1412,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(f1414,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1415,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1417,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1418,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1693,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| ~ c_in(X1,c_SetInterval_OatLeast(X2,X0),X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f1694,plain,
! [X0,X1,X2] :
( c_in(X2,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f1696,plain,
! [X0,X1,X2] :
( c_lessequals(c_SetInterval_OatLeast(X2,X0),c_SetInterval_OatLeast(X1,X0),tc_set(X0))
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f1922,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f359]) ).
fof(f1923,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1922]) ).
fof(f2171,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f597]) ).
fof(f2279,plain,
! [X0] :
( class_Orderings_Oord(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f705]) ).
fof(f2516,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Olordered__ring(X0) ),
inference(cnf_transformation,[status(thm)],[f942]) ).
fof(f2528,plain,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Olordered__ring(X0) ),
inference(cnf_transformation,[status(thm)],[f954]) ).
fof(f2664,plain,
! [X0] :
( class_Ring__and__Field_Olordered__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f1090]) ).
fof(f2985,plain,
! [T_a] :
( ! [V_a] : c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1411]) ).
fof(f2986,plain,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f2985]) ).
fof(f2987,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)],[f1412]) ).
fof(f2988,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)],[f2987]) ).
fof(f2991,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f1414]) ).
fof(f2992,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f1415]) ).
fof(f2994,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f1417]) ).
fof(f2995,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(thm)],[f1418]) ).
fof(f6163,plain,
! [X0,X1,X2,X3] :
( c_in(X3,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_in(X3,c_SetInterval_OatLeast(X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(resolution,[status(thm)],[f1696,f1923]) ).
fof(f6200,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X2,X3,X0)
| ~ class_Orderings_Oord(X0)
| c_in(X3,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(resolution,[status(thm)],[f6163,f1694]) ).
fof(f6201,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X2,X3,X0)
| c_in(X3,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6200,f2279]) ).
fof(f6230,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,X0)
| ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(resolution,[status(thm)],[f6201,f1693]) ).
fof(f6258,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6230,f2279]) ).
fof(f6340,plain,
! [X0] :
( ~ c_lessequals(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),X0,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[f6258,f2994]) ).
fof(f6613,plain,
! [X0] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[f6340,f2991]) ).
fof(f6620,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[f6613,f2992]) ).
fof(f6904,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[f6620,f2988]) ).
fof(f6908,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f6904,f2171]) ).
fof(f6912,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f6908,f2986]) ).
fof(f7786,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Olordered__ring(t_a) ),
inference(resolution,[status(thm)],[f2516,f6912]) ).
fof(f8040,plain,
~ class_Ring__and__Field_Olordered__ring(t_a),
inference(backward_subsumption_resolution,[status(thm)],[f7786,f2528]) ).
fof(f10893,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[f2664,f8040]) ).
fof(f10908,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10893,f2995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 13:26:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.40 % Drodi V4.1.1
% 16.47/2.60 % Refutation found
% 16.47/2.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.47/2.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.58/2.68 % Elapsed time: 2.317833 seconds
% 15.58/2.68 % CPU time: 17.675044 seconds
% 15.58/2.68 % Total memory used: 351.101 MB
% 15.58/2.68 % Net memory used: 336.342 MB
%------------------------------------------------------------------------------