%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV690-1 : 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 : n009.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 09:08:57 AM UTC 2026
% Result : Unsatisfiable 8.92s 1.69s
% Output : CNFRefutation 8.92s
% 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 : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 7 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_less__imp__diff__less_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(VAR_0,VAR_2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(VAR_0,VAR_1,tc_nat),VAR_2,tc_nat) ),
file('theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(c_682,plain,
( ~ c_HOL_Oord__class_Oless(A,C,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat) ),
inference(clausify,[status(thm)],[cls_less__imp__diff__less_0]) ).
fof(cls_conjecture_0,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_687,plain,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),v_n,tc_nat),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_688,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),v_n,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_6125,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,A,tc_nat),v_n,tc_nat),
inference(resolve,[status(thm)],[c_687,c_682]) ).
cnf(c_6126,plain,
$false,
inference(resolve,[status(thm)],[c_6125,c_688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV690-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 14:47:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 421145 was started by sandbox on n009,
% 0.17/0.44 % Sat Sep 26 14:47:14 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.49
% 0.17/0.49 % From the command line: assign(max_seconds, 300).
% 8.92/1.69
% 8.92/1.69 % SZS status Unsatisfiable for theBenchmark
% 8.92/1.69
% 8.92/1.69 % Proof 1 at 1.06 (+ 0.13) seconds.
% 8.92/1.69 % Length of proof is 5.
% 8.92/1.69 % Level of proof is 2.
% 8.92/1.69 % Maximum clause weight is 21.000.
% 8.92/1.69 % Given clauses 334.
% 8.92/1.69
% 8.92/1.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------