%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:02:14 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.70s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 25 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_x] :
( V_x = c_Suc(c_minus(V_x,c_1,tc_nat))
| ~ c_less(c_0,V_x,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0] :
( X0 = c_Suc(c_minus(X0,c_1,tc_nat))
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] :
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
v_x != c_0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0] :
( X0 = c_Suc(c_minus(X0,c_1,tc_nat))
| X0 = c_0 ),
inference(resolution,[status(thm)],[f7,f6]) ).
fof(f12,plain,
! [X0] :
( X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X0,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f11,f8]) ).
fof(f14,plain,
! [X0] :
( X0 = c_0
| X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f15,plain,
! [X0] :
( X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f14]) ).
fof(f16,plain,
v_x = c_0,
inference(resolution,[status(thm)],[f15,f10]) ).
fof(f17,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.66 % Computer : n008.cluster.edu
% 0.19/0.66 % Model : x86_64 x86_64
% 0.19/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.66 % Memory : 8046.5625MB
% 0.19/0.66 % OS : Linux 6.8.0-71-generic
% 0.19/0.66 % CPULimit : 300
% 0.19/0.66 % WCLimit : 300
% 0.19/0.66 % DateTime : Mon Sep 21 13:25:10 UTC 2026
% 0.19/0.66 % CPUTime :
% 0.19/0.68 % Drodi V4.1.1
% 0.23/0.70 % Refutation found
% 0.23/0.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.76 % Elapsed time: 0.089177 seconds
% 0.23/0.76 % CPU time: 0.095802 seconds
% 0.23/0.76 % Total memory used: 2.505 MB
% 0.23/0.76 % Net memory used: 2.503 MB
%------------------------------------------------------------------------------