%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD065-1 : 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 : n009.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 07:11:41 AM UTC 2026
% Result : Unsatisfiable 276.17s 37.58s
% Output : CNFRefutation 276.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 24 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 20 !; 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(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(VAR_0,additive_inverse(VAR_0)),additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| equalish(add(A,additive_inverse(A)),additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
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(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(well_definedness_of_additive_inverse,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| defined(additive_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_additive_inverse) ).
cnf(c_12,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
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_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(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(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(less_or_equal_2,axiom,
less_or_equal(additive_inverse(a),additive_identity),
file('theBenchmark.p',less_or_equal_2) ).
cnf(c_29,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(clausify,[status(thm)],[less_or_equal_2]) ).
fof(not_less_or_equal_3,axiom,
~ less_or_equal(additive_identity,a),
file('theBenchmark.p',not_less_or_equal_3) ).
cnf(c_30,plain,
~ less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_178,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_28,c_12]) ).
cnf(c_193,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_194,plain,
equalish(add(additive_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_27001,plain,
( ~ defined(A)
| less_or_equal(A,a)
| less_or_equal(a,A) ),
inference(resolve,[status(thm)],[c_18,c_28]) ).
cnf(c_27002,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolve,[status(thm)],[c_27001,c_28]) ).
cnf(c_198,plain,
less_or_equal(a,a),
inference(copy,[status(thm)],[c_27002]) ).
cnf(c_27003,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_27004,plain,
( less_or_equal(a,additive_identity)
| less_or_equal(additive_identity,a) ),
inference(resolve,[status(thm)],[c_27003,c_28]) ).
cnf(c_200,plain,
less_or_equal(a,additive_identity),
inference(resolve,[status(thm)],[c_30,c_27004]) ).
cnf(c_27005,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,a),add(B,a)) ),
inference(resolve,[status(thm)],[c_19,c_28]) ).
cnf(c_293,plain,
less_or_equal(add(additive_inverse(a),a),add(additive_identity,a)),
inference(resolve,[status(thm)],[c_27005,c_29]) ).
cnf(c_27006,plain,
( ~ equalish(A,additive_identity)
| ~ less_or_equal(A,a) ),
inference(resolve,[status(thm)],[c_26,c_30]) ).
cnf(c_371,plain,
~ equalish(a,additive_identity),
inference(resolve,[status(thm)],[c_27006,c_198]) ).
cnf(c_374,plain,
( ~ equalish(a,A)
| less_or_equal(A,additive_identity) ),
inference(resolve,[status(thm)],[c_200,c_26]) ).
cnf(c_395,plain,
~ equalish(additive_identity,a),
inference(resolve,[status(thm)],[c_22,c_371]) ).
cnf(c_27007,plain,
( ~ defined(A)
| equalish(add(additive_inverse(a),A),add(A,additive_inverse(a))) ),
inference(resolve,[status(thm)],[c_4,c_178]) ).
cnf(c_1802,plain,
equalish(add(additive_inverse(a),a),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_27007,c_28]) ).
cnf(c_20920,plain,
equalish(a,add(additive_identity,a)),
inference(resolve,[status(thm)],[c_194,c_22]) ).
cnf(c_27008,plain,
( ~ equalish(A,a)
| ~ equalish(additive_identity,A) ),
inference(resolve,[status(thm)],[c_23,c_395]) ).
cnf(c_20976,plain,
~ equalish(additive_identity,add(additive_identity,a)),
inference(resolve,[status(thm)],[c_27008,c_194]) ).
cnf(c_21846,plain,
less_or_equal(add(additive_identity,a),additive_identity),
inference(resolve,[status(thm)],[c_20920,c_374]) ).
cnf(c_27009,plain,
( ~ less_or_equal(additive_identity,add(additive_identity,a))
| equalish(additive_identity,add(additive_identity,a)) ),
inference(resolve,[status(thm)],[c_21846,c_16]) ).
cnf(c_22100,plain,
~ less_or_equal(additive_identity,add(additive_identity,a)),
inference(resolve,[status(thm)],[c_20976,c_27009]) ).
cnf(c_27010,plain,
( ~ equalish(A,additive_identity)
| ~ less_or_equal(A,add(additive_identity,a)) ),
inference(resolve,[status(thm)],[c_26,c_22100]) ).
cnf(c_24760,plain,
~ less_or_equal(add(a,additive_inverse(a)),add(additive_identity,a)),
inference(resolve,[status(thm)],[c_27010,c_193]) ).
cnf(c_27011,plain,
( ~ equalish(A,add(a,additive_inverse(a)))
| ~ less_or_equal(A,add(additive_identity,a)) ),
inference(resolve,[status(thm)],[c_26,c_24760]) ).
cnf(c_27012,plain,
~ equalish(add(additive_inverse(a),a),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_27011,c_293]) ).
cnf(c_27000,plain,
$false,
inference(resolve,[status(thm)],[c_1802,c_27012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.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 02:33:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 1645127 was started by sandbox on n009,
% 0.14/0.37 % Sun Sep 27 02:33:59 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 276.17/37.58
% 276.17/37.58 % given #500 (F,wt=23): 20837 -equalish(add(additive_identity,additive_inverse(additive_identity)),add(additive_identity,multiplicative_identity)). [ur(23,a,3395,a,c,106,a)].
% 276.17/37.58
% 276.17/37.58 % SZS status Unsatisfiable for theBenchmark
% 276.17/37.58
% 276.17/37.58 % Proof 1 at 3.41 (+ 1.47) seconds.
% 276.17/37.58 % Length of proof is 30.
% 276.17/37.58 % Level of proof is 7.
% 276.17/37.58 % Maximum clause weight is 24.000.
% 276.17/37.58 % Given clauses 713.
% 276.17/37.58
% 276.17/37.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------