%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD064-1 : 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 : n007.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 34.34s 5.42s
% Output : CNFRefutation 34.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 18 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 33 |; 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 : 37 ( 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(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(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(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(less_or_equal_2,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_2) ).
cnf(c_29,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_2]) ).
fof(not_less_or_equal_3,axiom,
~ less_or_equal(additive_inverse(a),additive_identity),
file('theBenchmark.p',not_less_or_equal_3) ).
cnf(c_30,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(clausify,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_115,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_25119,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(factor,[status(thm)],[c_115]) ).
cnf(c_117,plain,
less_or_equal(additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_11,c_25119]) ).
cnf(c_137,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_28,c_12]) ).
cnf(c_152,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_170,plain,
( ~ defined(A)
| less_or_equal(add(additive_identity,A),add(a,A)) ),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_231,plain,
( ~ equalish(additive_identity,A)
| less_or_equal(A,additive_identity) ),
inference(resolve,[status(thm)],[c_117,c_26]) ).
cnf(c_489,plain,
equalish(add(additive_identity,additive_inverse(a)),additive_inverse(a)),
inference(resolve,[status(thm)],[c_137,c_2]) ).
cnf(c_6361,plain,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_152,c_22]) ).
cnf(c_7159,plain,
less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_170,c_137]) ).
cnf(c_17772,plain,
less_or_equal(add(a,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_6361,c_231]) ).
cnf(c_25120,plain,
( ~ less_or_equal(A,additive_identity)
| ~ less_or_equal(additive_inverse(a),A) ),
inference(resolve,[status(thm)],[c_17,c_30]) ).
cnf(c_22773,plain,
~ less_or_equal(additive_inverse(a),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_25120,c_17772]) ).
cnf(c_25121,plain,
( ~ equalish(A,additive_inverse(a))
| ~ less_or_equal(A,add(a,additive_inverse(a))) ),
inference(resolve,[status(thm)],[c_26,c_22773]) ).
cnf(c_25122,plain,
~ less_or_equal(add(additive_identity,additive_inverse(a)),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_25121,c_489]) ).
cnf(c_25118,plain,
$false,
inference(resolve,[status(thm)],[c_7159,c_25122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD064-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 02:31:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1021109 was started by sandbox on n007,
% 0.12/0.38 % Sun Sep 27 02:31:25 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 34.34/5.42
% 34.34/5.42 % given #500 (T,wt=12): 684 defined(add(additive_identity,multiply(multiplicative_identity,multiplicative_identity))). [resolve(212,a,51,b)].
% 34.34/5.42
% 34.34/5.42 % given #1000 (T,wt=12): 9498 less_or_equal(A,add(additive_identity,multiplicative_identity)) | -equalish(multiplicative_identity,A). [resolve(9381,a,26,b)].
% 34.34/5.42
% 34.34/5.42 % SZS status Unsatisfiable for theBenchmark
% 34.34/5.42
% 34.34/5.42 % Proof 1 at 3.05 (+ 1.44) seconds.
% 34.34/5.42 % Length of proof is 24.
% 34.34/5.42 % Level of proof is 6.
% 34.34/5.42 % Maximum clause weight is 16.000.
% 34.34/5.42 % Given clauses 1285.
% 34.34/5.42
% 34.34/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------