%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 09:06:38 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.32s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 76 ( 38 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( less(VAR_1,VAR_0)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( less(B,A)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_3,axiom,
less_or_equal(m,p),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
less_or_equal(m,p),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
less_or_equal(p,q),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
less_or_equal(p,q),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_5,axiom,
less_or_equal(q,n),
file('theBenchmark.p',clause_5) ).
cnf(c_5,plain,
less_or_equal(q,n),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0,VAR_1] :
( less_or_equal(a(VAR_0),a(VAR_1))
| ~ less_or_equal(VAR_1,n)
| ~ less(j,VAR_1)
| ~ less(VAR_0,i)
| ~ less_or_equal(m,VAR_0) ),
file('theBenchmark.p',clause_6) ).
cnf(c_6,plain,
( less_or_equal(a(A),a(B))
| ~ less_or_equal(B,n)
| ~ less(j,B)
| ~ less(A,i)
| ~ less_or_equal(m,A) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_7,axiom,
! [VAR_0,VAR_1] :
( less_or_equal(a(VAR_0),a(VAR_1))
| ~ less_or_equal(VAR_1,j)
| ~ less_or_equal(VAR_0,VAR_1)
| ~ less_or_equal(m,VAR_0) ),
file('theBenchmark.p',clause_7) ).
cnf(c_7,plain,
( less_or_equal(a(A),a(B))
| ~ less_or_equal(B,j)
| ~ less_or_equal(A,B)
| ~ less_or_equal(m,A) ),
inference(clausify,[status(thm)],[clause_7]) ).
fof(clause_8,axiom,
! [VAR_0,VAR_1] :
( less_or_equal(a(VAR_0),a(VAR_1))
| ~ less_or_equal(VAR_1,n)
| ~ less_or_equal(VAR_0,VAR_1)
| ~ less_or_equal(i,VAR_0) ),
file('theBenchmark.p',clause_8) ).
cnf(c_8,plain,
( less_or_equal(a(A),a(B))
| ~ less_or_equal(B,n)
| ~ less_or_equal(A,B)
| ~ less_or_equal(i,A) ),
inference(clausify,[status(thm)],[clause_8]) ).
fof(clause_9,axiom,
~ less_or_equal(a(p),a(q)),
file('theBenchmark.p',clause_9) ).
cnf(c_9,plain,
~ less_or_equal(a(p),a(q)),
inference(clausify,[status(thm)],[clause_9]) ).
cnf(c_19,plain,
( less_or_equal(i,A)
| less_or_equal(a(A),a(B))
| ~ less_or_equal(B,n)
| ~ less(j,B)
| ~ less_or_equal(m,A) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_38,plain,
( less_or_equal(a(p),a(q))
| ~ less_or_equal(q,j)
| ~ less_or_equal(m,p) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_39,plain,
( less_or_equal(a(p),a(q))
| ~ less_or_equal(q,j) ),
inference(resolve,[status(thm)],[c_3,c_38]) ).
cnf(c_26,plain,
~ less_or_equal(q,j),
inference(resolve,[status(thm)],[c_9,c_39]) ).
cnf(c_40,plain,
( less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less_or_equal(i,p) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_41,plain,
( less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p) ),
inference(resolve,[status(thm)],[c_5,c_40]) ).
cnf(c_29,plain,
~ less_or_equal(i,p),
inference(resolve,[status(thm)],[c_9,c_41]) ).
cnf(c_42,plain,
( less_or_equal(i,p)
| less_or_equal(a(p),a(A))
| ~ less_or_equal(A,n)
| ~ less(j,A) ),
inference(resolve,[status(thm)],[c_19,c_3]) ).
cnf(c_43,plain,
( less_or_equal(i,p)
| less_or_equal(a(p),a(q))
| ~ less(j,q) ),
inference(resolve,[status(thm)],[c_42,c_5]) ).
cnf(c_44,plain,
( less_or_equal(i,p)
| ~ less(j,q) ),
inference(resolve,[status(thm)],[c_43,c_9]) ).
cnf(c_35,plain,
~ less(j,q),
inference(resolve,[status(thm)],[c_44,c_29]) ).
cnf(c_45,plain,
less_or_equal(q,j),
inference(resolve,[status(thm)],[c_35,c_1]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 26 13:04:24 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 670318 was started by sandbox2 on n012,
% 0.03/0.31 % Sat Sep 26 13:04:24 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.07/0.32
% 0.07/0.32 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.32
% 0.07/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.32 % Length of proof is 13.
% 0.07/0.32 % Level of proof is 3.
% 0.07/0.32 % Maximum clause weight is 17.000.
% 0.07/0.32 % Given clauses 26.
% 0.07/0.32
% 0.07/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------