%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD060-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:11:40 AM UTC 2026
% Result : Unsatisfiable 7.36s 1.35s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_4,plain,
( ~ defined(B)
| ~ defined(A)
| equalish(add(A,B),add(B,A)) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(transitivity_of_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_2,VAR_1)
| ~ less_or_equal(VAR_0,VAR_2)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_order_relation) ).
cnf(c_17,plain,
( ~ less_or_equal(C,B)
| ~ less_or_equal(A,C)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_order_relation]) ).
fof(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_0,VAR_2)
| ~ defined(VAR_1)
| less_or_equal(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_19,plain,
( ~ less_or_equal(A,C)
| ~ defined(B)
| less_or_equal(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(compatibility_of_equality_and_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_0)
| ~ less_or_equal(VAR_2,VAR_1)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_equality_and_order_relation) ).
cnf(c_26,plain,
( ~ equalish(C,A)
| ~ less_or_equal(C,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_28,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_29,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(less_or_equal_3,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_30,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(not_less_or_equal_4,axiom,
~ less_or_equal(add(a,a),add(b,b)),
file('theBenchmark.p',not_less_or_equal_4) ).
cnf(c_31,plain,
~ less_or_equal(add(a,a),add(b,b)),
inference(clausify,[status(thm)],[not_less_or_equal_4]) ).
cnf(c_143,plain,
( ~ defined(A)
| equalish(add(a,A),add(A,a)) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_195,plain,
( ~ defined(A)
| less_or_equal(add(a,A),add(b,A)) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_8073,plain,
equalish(add(a,b),add(b,a)),
inference(resolve,[status(thm)],[c_143,c_29]) ).
cnf(c_10371,plain,
less_or_equal(add(a,b),add(b,b)),
inference(resolve,[status(thm)],[c_195,c_29]) ).
cnf(c_10372,plain,
less_or_equal(add(a,a),add(b,a)),
inference(resolve,[status(thm)],[c_195,c_28]) ).
cnf(c_10501,plain,
( ~ less_or_equal(A,add(b,b))
| ~ less_or_equal(add(a,a),A) ),
inference(resolve,[status(thm)],[c_17,c_31]) ).
cnf(c_10389,plain,
~ less_or_equal(add(b,a),add(b,b)),
inference(resolve,[status(thm)],[c_10501,c_10372]) ).
cnf(c_10502,plain,
( ~ equalish(A,add(b,a))
| ~ less_or_equal(A,add(b,b)) ),
inference(resolve,[status(thm)],[c_26,c_10389]) ).
cnf(c_10503,plain,
~ less_or_equal(add(a,b),add(b,b)),
inference(resolve,[status(thm)],[c_10502,c_8073]) ).
cnf(c_10500,plain,
$false,
inference(resolve,[status(thm)],[c_10371,c_10503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 27 02:34:52 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 1932462 was started by sandbox on n018,
% 0.10/0.35 % Sun Sep 27 02:34:52 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.35
% 0.10/0.35 % From the command line: assign(max_seconds, 300).
% 7.36/1.35
% 7.36/1.35 % given #500 (A,wt=30): 183 equalish(add(b,add(A,B)),add(add(b,A),B)) | -defined(A) | -defined(B). [resolve(29,a,1,b)].
% 7.36/1.35
% 7.36/1.35 % SZS status Unsatisfiable for theBenchmark
% 7.36/1.35
% 7.36/1.35 % Proof 1 at 0.71 (+ 0.26) seconds.
% 7.36/1.35 % Length of proof is 15.
% 7.36/1.35 % Level of proof is 4.
% 7.36/1.35 % Maximum clause weight is 22.000.
% 7.36/1.35 % Given clauses 555.
% 7.36/1.35
% 7.36/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------