%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 06:51:08 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 30 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 12 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_NatBin_OSuc__pred_H_0,axiom,
! [VAR_0] :
( VAR_0 = c_Suc(c_minus(VAR_0,c_1,tc_nat))
| ~ c_less(c_0,VAR_0,tc_nat) ),
file('theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
cnf(c_1,plain,
( A = c_Suc(c_minus(A,c_1,tc_nat))
| ~ c_less(c_0,A,tc_nat) ),
inference(clausify,[status(thm)],[cls_NatBin_OSuc__pred_H_0]) ).
cnf(c_2,plain,
( c_Suc(c_minus(A,c_1,tc_nat)) = A
| ~ c_less(c_0,A,tc_nat) ),
inference(copy,[status(thm)],[c_1]) ).
fof(cls_Nat_Onot__gr0_0,axiom,
! [VAR_0] :
( VAR_0 = c_0
| c_less(c_0,VAR_0,tc_nat) ),
file('theBenchmark.p',cls_Nat_Onot__gr0_0) ).
cnf(c_3,plain,
( A = c_0
| c_less(c_0,A,tc_nat) ),
inference(clausify,[status(thm)],[cls_Nat_Onot__gr0_0]) ).
cnf(c_4,plain,
( c_0 = A
| c_less(c_0,A,tc_nat) ),
inference(copy,[status(thm)],[c_3]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(VAR_0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(VAR_0)),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_5,plain,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(A)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(A)),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
v_x != c_0,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_6,plain,
v_x != c_0,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ 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('theBenchmark.p',cls_conjecture_4) ).
cnf(c_7,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(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_8,plain,
( c_Suc(c_minus(A,c_1,tc_nat)) = A
| c_0 = A ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_9,plain,
( c_lessequals(c_HOL_Oabs(v_f(A),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(A,c_1,tc_nat))),t_a),t_a),t_a)
| c_0 = A ),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_13,plain,
( c_lessequals(c_HOL_Oabs(v_f(A),t_a),c_times(v_c,c_HOL_Oabs(v_h(A),t_a),t_a),t_a)
| c_0 = A
| c_0 = A ),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_11,plain,
( c_lessequals(c_HOL_Oabs(v_f(A),t_a),c_times(v_c,c_HOL_Oabs(v_h(A),t_a),t_a),t_a)
| c_0 = A ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_14,plain,
c_0 = v_x,
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_15,plain,
v_x = c_0,
inference(copy,[status(thm)],[c_14]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:05:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 5608 was started by sandbox2 on n014,
% 0.08/0.35 % Sat Sep 26 22:05:46 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 11.
% 0.13/0.37 % Level of proof is 5.
% 0.13/0.37 % Maximum clause weight is 20.000.
% 0.13/0.37 % Given clauses 8.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------