%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD069-1 : 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 : 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 07:11:42 AM UTC 2026
% Result : Unsatisfiable 2.24s 0.65s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 21 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 40 ~; 34 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_11,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(antisymmetry_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ less_or_equal(VAR_1,VAR_0)
| ~ less_or_equal(VAR_0,VAR_1)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',antisymmetry_of_order_relation) ).
cnf(c_16,plain,
( ~ less_or_equal(B,A)
| ~ less_or_equal(A,B)
| equalish(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_of_order_relation]) ).
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(totality_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| less_or_equal(VAR_1,VAR_0)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',totality_of_order_relation) ).
cnf(c_18,plain,
( ~ defined(B)
| ~ defined(A)
| less_or_equal(B,A)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[totality_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(symmetry_of_equality,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_1,VAR_0)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_equality) ).
cnf(c_22,plain,
( ~ equalish(B,A)
| equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_equality]) ).
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(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(additive_identity,a),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_30,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(less_or_equal_4,axiom,
less_or_equal(additive_identity,b),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_31,plain,
less_or_equal(additive_identity,b),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(b_not_equal_to_additive_identity_5,axiom,
~ equalish(b,additive_identity),
file('theBenchmark.p',b_not_equal_to_additive_identity_5) ).
cnf(c_32,plain,
~ equalish(b,additive_identity),
inference(clausify,[status(thm)],[b_not_equal_to_additive_identity_5]) ).
fof(add_equals_additive_identity_6,axiom,
equalish(add(a,b),additive_identity),
file('theBenchmark.p',add_equals_additive_identity_6) ).
cnf(c_33,plain,
equalish(add(a,b),additive_identity),
inference(clausify,[status(thm)],[add_equals_additive_identity_6]) ).
cnf(c_118,plain,
( ~ defined(A)
| less_or_equal(A,additive_identity)
| less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_4958,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(factor,[status(thm)],[c_118]) ).
cnf(c_120,plain,
less_or_equal(additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_11,c_4958]) ).
cnf(c_194,plain,
equalish(add(additive_identity,b),b),
inference(resolve,[status(thm)],[c_29,c_2]) ).
cnf(c_4959,plain,
( ~ less_or_equal(b,additive_identity)
| equalish(b,additive_identity) ),
inference(resolve,[status(thm)],[c_31,c_16]) ).
cnf(c_222,plain,
~ less_or_equal(b,additive_identity),
inference(resolve,[status(thm)],[c_32,c_4959]) ).
cnf(c_229,plain,
equalish(additive_identity,add(a,b)),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_305,plain,
( ~ equalish(additive_identity,A)
| less_or_equal(A,additive_identity) ),
inference(resolve,[status(thm)],[c_120,c_26]) ).
cnf(c_4960,plain,
( ~ equalish(A,b)
| ~ less_or_equal(A,additive_identity) ),
inference(resolve,[status(thm)],[c_26,c_222]) ).
cnf(c_1985,plain,
~ less_or_equal(add(additive_identity,b),additive_identity),
inference(resolve,[status(thm)],[c_4960,c_194]) ).
cnf(c_1990,plain,
less_or_equal(add(a,b),additive_identity),
inference(resolve,[status(thm)],[c_229,c_305]) ).
cnf(c_4961,plain,
( ~ less_or_equal(A,additive_identity)
| ~ less_or_equal(add(additive_identity,b),A) ),
inference(resolve,[status(thm)],[c_17,c_1985]) ).
cnf(c_2297,plain,
~ less_or_equal(add(additive_identity,b),add(a,b)),
inference(resolve,[status(thm)],[c_4961,c_1990]) ).
cnf(c_4962,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(b) ),
inference(resolve,[status(thm)],[c_19,c_2297]) ).
cnf(c_4963,plain,
~ defined(b),
inference(resolve,[status(thm)],[c_4962,c_30]) ).
cnf(c_4957,plain,
$false,
inference(resolve,[status(thm)],[c_29,c_4963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 27 02:34:19 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.31 % Process 1983306 was started by sandbox on n012,
% 0.05/0.31 % Sun Sep 27 02:34:19 2026
% 0.05/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.31
% 0.05/0.31 % From the command line: assign(max_seconds, 300).
% 2.24/0.65
% 2.24/0.65 % SZS status Unsatisfiable for theBenchmark
% 2.24/0.65
% 2.24/0.65 % Proof 1 at 0.19 (+ 0.07) seconds.
% 2.24/0.65 % Length of proof is 23.
% 2.24/0.65 % Level of proof is 6.
% 2.24/0.65 % Maximum clause weight is 22.000.
% 2.24/0.65 % Given clauses 303.
% 2.24/0.65
% 2.24/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------