%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV675-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 09:08:55 AM UTC 2026
% Result : Unsatisfiable 18.99s 3.21s
% Output : CNFRefutation 18.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_415,plain,
c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_not__less__eq__eq_1,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(c_Suc(VAR_1),VAR_0,tc_nat)
| ~ c_lessequals(VAR_0,VAR_1,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(c_418,plain,
( ~ c_lessequals(c_Suc(B),A,tc_nat)
| ~ c_lessequals(A,B,tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq__eq_1]) ).
fof(cls_le0_0,axiom,
! [VAR_0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0,tc_nat),
file('theBenchmark.p',cls_le0_0) ).
cnf(c_420,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),
inference(clausify,[status(thm)],[cls_le0_0]) ).
cnf(c_1917,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_y,tc_nat),
inference(resolve,[status(thm)],[c_418,c_415]) ).
cnf(c_1916,plain,
$false,
inference(resolve,[status(thm)],[c_420,c_1917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV675-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:40:03 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 968673 was started by sandbox on n017,
% 0.13/0.36 % Sat Sep 26 14:40:03 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 18.99/3.21
% 18.99/3.21 % SZS status Unsatisfiable for theBenchmark
% 18.99/3.21
% 18.99/3.21 % Proof 1 at 2.62 (+ 0.05) seconds.
% 18.99/3.21 % Length of proof is 4.
% 18.99/3.21 % Level of proof is 1.
% 18.99/3.21 % Maximum clause weight is 9.000.
% 18.99/3.21 % Given clauses 30.
% 18.99/3.21
% 18.99/3.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------