%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD071-2 : 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 : n019.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 07:11:43 AM UTC 2026
% Result : Unsatisfiable 4.51s 1.05s
% Output : CNFRefutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 35 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_multiplication,axiom,
! [VAR_0,VAR_1] :
( ~ less_or_equal(additive_identity,VAR_1)
| ~ less_or_equal(additive_identity,VAR_0)
| less_or_equal(additive_identity,multiply(VAR_0,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
cnf(c_20,plain,
( ~ less_or_equal(additive_identity,B)
| ~ less_or_equal(additive_identity,A)
| less_or_equal(additive_identity,multiply(A,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_multiplication]) ).
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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_30,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(less_or_equal_4,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_31,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(less_or_equal_5,axiom,
less_or_equal(additive_identity,b),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_32,plain,
less_or_equal(additive_identity,b),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(multiply_equals_u_6,axiom,
equalish(multiply(a,b),u),
file('theBenchmark.p',multiply_equals_u_6) ).
cnf(c_33,plain,
equalish(multiply(a,b),u),
inference(clausify,[status(thm)],[multiply_equals_u_6]) ).
fof(not_less_or_equal_7,axiom,
~ less_or_equal(additive_identity,u),
file('theBenchmark.p',not_less_or_equal_7) ).
cnf(c_34,plain,
~ less_or_equal(additive_identity,u),
inference(clausify,[status(thm)],[not_less_or_equal_7]) ).
cnf(c_119,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_213,plain,
( ~ defined(A)
| less_or_equal(u,A)
| less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_3306,plain,
( ~ defined(u)
| less_or_equal(u,u) ),
inference(factor,[status(thm)],[c_213]) ).
cnf(c_237,plain,
less_or_equal(u,u),
inference(resolve,[status(thm)],[c_30,c_3306]) ).
cnf(c_268,plain,
equalish(u,multiply(a,b)),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_3307,plain,
( ~ equalish(A,additive_identity)
| ~ less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_26,c_34]) ).
cnf(c_386,plain,
~ equalish(u,additive_identity),
inference(resolve,[status(thm)],[c_3307,c_237]) ).
cnf(c_399,plain,
~ equalish(additive_identity,u),
inference(resolve,[status(thm)],[c_22,c_386]) ).
cnf(c_3308,plain,
( ~ equalish(A,u)
| ~ equalish(additive_identity,A) ),
inference(resolve,[status(thm)],[c_23,c_399]) ).
cnf(c_402,plain,
~ equalish(additive_identity,multiply(a,b)),
inference(resolve,[status(thm)],[c_3308,c_33]) ).
cnf(c_3309,plain,
( less_or_equal(u,additive_identity)
| less_or_equal(additive_identity,u) ),
inference(resolve,[status(thm)],[c_119,c_30]) ).
cnf(c_592,plain,
less_or_equal(u,additive_identity),
inference(resolve,[status(thm)],[c_34,c_3309]) ).
cnf(c_595,plain,
( ~ equalish(u,A)
| less_or_equal(A,additive_identity) ),
inference(resolve,[status(thm)],[c_592,c_26]) ).
cnf(c_2730,plain,
less_or_equal(multiply(a,b),additive_identity),
inference(resolve,[status(thm)],[c_268,c_595]) ).
cnf(c_3310,plain,
( ~ less_or_equal(additive_identity,multiply(a,b))
| equalish(additive_identity,multiply(a,b)) ),
inference(resolve,[status(thm)],[c_2730,c_16]) ).
cnf(c_3132,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(resolve,[status(thm)],[c_402,c_3310]) ).
cnf(c_3311,plain,
( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(resolve,[status(thm)],[c_20,c_3132]) ).
cnf(c_3312,plain,
~ less_or_equal(additive_identity,a),
inference(resolve,[status(thm)],[c_3311,c_32]) ).
cnf(c_3305,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_3312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD071-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 02:35:04 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2727167 was started by sandbox2 on n019,
% 0.16/0.43 % Sun Sep 27 02:35:04 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 4.51/1.05
% 4.51/1.05 % SZS status Unsatisfiable for theBenchmark
% 4.51/1.05
% 4.51/1.05 % Proof 1 at 0.32 (+ 0.15) seconds.
% 4.51/1.05 % Length of proof is 24.
% 4.51/1.05 % Level of proof is 7.
% 4.51/1.05 % Maximum clause weight is 21.000.
% 4.51/1.05 % Given clauses 307.
% 4.51/1.05
% 4.51/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------