%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:11:39 AM UTC 2026
% Result : Unsatisfiable 2.89s 0.83s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 19 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 37 ~; 30 |; 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 : 33 ( 0 sgn 14 !; 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(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(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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_29,plain,
defined(u),
inference(clausify,[status(thm)],[u_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(add_equals_u_4,axiom,
equalish(add(a,a),u),
file('theBenchmark.p',add_equals_u_4) ).
cnf(c_31,plain,
equalish(add(a,a),u),
inference(clausify,[status(thm)],[add_equals_u_4]) ).
fof(not_less_or_equal_5,axiom,
~ less_or_equal(additive_identity,u),
file('theBenchmark.p',not_less_or_equal_5) ).
cnf(c_32,plain,
~ less_or_equal(additive_identity,u),
inference(clausify,[status(thm)],[not_less_or_equal_5]) ).
cnf(c_155,plain,
equalish(add(additive_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_173,plain,
( ~ defined(A)
| less_or_equal(u,A)
| less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_29,c_18]) ).
cnf(c_4911,plain,
( ~ defined(u)
| less_or_equal(u,u) ),
inference(factor,[status(thm)],[c_173]) ).
cnf(c_197,plain,
less_or_equal(u,u),
inference(resolve,[status(thm)],[c_29,c_4911]) ).
cnf(c_220,plain,
equalish(u,add(a,a)),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_4912,plain,
( ~ less_or_equal(A,u)
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_17,c_32]) ).
cnf(c_221,plain,
~ less_or_equal(a,u),
inference(resolve,[status(thm)],[c_4912,c_30]) ).
cnf(c_322,plain,
( ~ equalish(u,A)
| less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_197,c_26]) ).
cnf(c_4913,plain,
( ~ equalish(A,a)
| ~ less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_26,c_221]) ).
cnf(c_1585,plain,
~ less_or_equal(add(additive_identity,a),u),
inference(resolve,[status(thm)],[c_4913,c_155]) ).
cnf(c_1610,plain,
less_or_equal(add(a,a),u),
inference(resolve,[status(thm)],[c_220,c_322]) ).
cnf(c_4914,plain,
( ~ less_or_equal(A,u)
| ~ less_or_equal(add(additive_identity,a),A) ),
inference(resolve,[status(thm)],[c_17,c_1585]) ).
cnf(c_2555,plain,
~ less_or_equal(add(additive_identity,a),add(a,a)),
inference(resolve,[status(thm)],[c_4914,c_1610]) ).
cnf(c_4915,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_19,c_2555]) ).
cnf(c_4916,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_4915,c_30]) ).
cnf(c_4910,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_4916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:35:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1252002 was started by sandbox2 on n015,
% 0.10/0.37 % Sun Sep 27 02:35:59 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 2.89/0.83
% 2.89/0.83 % SZS status Unsatisfiable for theBenchmark
% 2.89/0.83
% 2.89/0.83 % Proof 1 at 0.30 (+ 0.12) seconds.
% 2.89/0.83 % Length of proof is 21.
% 2.89/0.83 % Level of proof is 6.
% 2.89/0.83 % Maximum clause weight is 16.000.
% 2.89/0.83 % Given clauses 377.
% 2.89/0.83
% 2.89/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------