%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA021-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 5.12s 1.31s
% Output : CNFRefutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 29 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f910,axiom,
c_1 = c_Suc(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f918,axiom,
! [V_y] :
( c_Suc(c_minus(V_y,c_Suc(c_0),tc_nat)) = V_y
| ~ c_less(c_0,V_y,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f983,axiom,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2788,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(f2789,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2790,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(f4015,plain,
c_1 = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f910]) ).
fof(f4023,plain,
! [X0] :
( c_Suc(c_minus(X0,c_Suc(c_0),tc_nat)) = X0
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f918]) ).
fof(f4117,plain,
! [X0] :
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f983]) ).
fof(f6233,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)],[f2788]) ).
fof(f6234,plain,
v_x != c_0,
inference(cnf_transformation,[status(thm)],[f2789]) ).
fof(f6235,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)],[f2790]) ).
fof(f6276,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| ~ c_less(c_0,X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f4015,f4023]) ).
fof(f6477,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| X0 = c_0 ),
inference(resolution,[status(thm)],[f4117,f6276]) ).
fof(f6661,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)],[f6477,f6233]) ).
fof(f6694,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)],[f6477,f6661]) ).
fof(f6696,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)],[f6694]) ).
fof(f6697,plain,
v_x = c_0,
inference(resolution,[status(thm)],[f6696,f6235]) ).
fof(f6699,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6697,f6234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n007.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 13:22:06 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.36/0.61 % Drodi V4.1.1
% 5.12/1.31 % Refutation found
% 5.12/1.31 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.12/1.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.12/1.35 % Elapsed time: 0.905654 seconds
% 5.12/1.35 % CPU time: 5.556002 seconds
% 5.12/1.35 % Total memory used: 282.679 MB
% 5.12/1.35 % Net memory used: 279.746 MB
%------------------------------------------------------------------------------