%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD058-1 : 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 : n003.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 24 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(transitivity_of_equality,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_1)
| ~ equalish(VAR_0,VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_equality) ).
cnf(c_23,plain,
( ~ equalish(C,B)
| ~ equalish(A,C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity_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(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(a,b),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_31,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(a_not_equal_to_additive_identity_5,axiom,
~ equalish(a,additive_identity),
file('theBenchmark.p',a_not_equal_to_additive_identity_5) ).
cnf(c_32,plain,
~ equalish(a,additive_identity),
inference(clausify,[status(thm)],[a_not_equal_to_additive_identity_5]) ).
fof(b_equals_additive_identity_6,axiom,
equalish(b,additive_identity),
file('theBenchmark.p',b_equals_additive_identity_6) ).
cnf(c_33,plain,
equalish(b,additive_identity),
inference(clausify,[status(thm)],[b_equals_additive_identity_6]) ).
cnf(c_218,plain,
( ~ less_or_equal(b,a)
| equalish(a,b) ),
inference(resolve,[status(thm)],[c_31,c_16]) ).
cnf(c_225,plain,
equalish(additive_identity,b),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_318,plain,
( ~ equalish(A,additive_identity)
| ~ equalish(a,A) ),
inference(resolve,[status(thm)],[c_23,c_32]) ).
cnf(c_226,plain,
~ equalish(a,b),
inference(resolve,[status(thm)],[c_318,c_33]) ).
cnf(c_227,plain,
~ less_or_equal(b,a),
inference(resolve,[status(thm)],[c_226,c_218]) ).
cnf(c_319,plain,
( ~ equalish(A,b)
| ~ less_or_equal(A,a) ),
inference(resolve,[status(thm)],[c_26,c_227]) ).
cnf(c_320,plain,
~ equalish(additive_identity,b),
inference(resolve,[status(thm)],[c_319,c_30]) ).
cnf(c_317,plain,
$false,
inference(resolve,[status(thm)],[c_225,c_320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD058-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 02:33:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 97703 was started by sandbox on n003,
% 0.10/0.36 % Sun Sep 27 02:33:55 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 13.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 14.000.
% 0.10/0.39 % Given clauses 65.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------