%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD061-4 : 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 : n005.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 07:11:40 AM UTC 2026
% Result : Unsatisfiable 49.47s 6.87s
% Output : CNFRefutation 49.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 22 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(totality_of_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| sum(VAR_0,VAR_1,add(VAR_0,VAR_1)) ),
file('theBenchmark.p',totality_of_addition) ).
cnf(c_19,plain,
( ~ defined(B)
| ~ defined(A)
| sum(A,B,add(A,B)) ),
inference(clausify,[status(thm)],[totality_of_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_22,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(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ sum(VAR_3,VAR_4,VAR_1)
| ~ sum(VAR_2,VAR_4,VAR_0)
| ~ less_or_equal(VAR_2,VAR_3)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_24,plain,
( ~ sum(D,E,B)
| ~ sum(C,E,A)
| ~ less_or_equal(C,D)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_30,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(less_or_equal_7,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_7) ).
cnf(c_33,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_7]) ).
fof(less_or_equal_8,axiom,
less_or_equal(c,d),
file('theBenchmark.p',less_or_equal_8) ).
cnf(c_34,plain,
less_or_equal(c,d),
inference(clausify,[status(thm)],[less_or_equal_8]) ).
fof(sum_9,axiom,
sum(a,c,u),
file('theBenchmark.p',sum_9) ).
cnf(c_35,plain,
sum(a,c,u),
inference(clausify,[status(thm)],[sum_9]) ).
fof(sum_10,axiom,
sum(d,b,v),
file('theBenchmark.p',sum_10) ).
cnf(c_36,plain,
sum(d,b,v),
inference(clausify,[status(thm)],[sum_10]) ).
fof(not_less_or_equal_11,axiom,
~ less_or_equal(u,v),
file('theBenchmark.p',not_less_or_equal_11) ).
cnf(c_37,plain,
~ less_or_equal(u,v),
inference(clausify,[status(thm)],[not_less_or_equal_11]) ).
cnf(c_95,plain,
( ~ defined(A)
| sum(A,a,add(A,a)) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_188,plain,
( ~ sum(b,C,B)
| ~ sum(a,C,A)
| less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_193,plain,
( ~ sum(d,C,B)
| ~ sum(c,C,A)
| less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_34,c_24]) ).
cnf(c_203,plain,
sum(c,a,u),
inference(resolve,[status(thm)],[c_35,c_5]) ).
cnf(c_215,plain,
sum(b,d,v),
inference(resolve,[status(thm)],[c_36,c_5]) ).
cnf(c_1986,plain,
sum(d,a,add(d,a)),
inference(resolve,[status(thm)],[c_95,c_30]) ).
cnf(c_12379,plain,
( ~ sum(a,d,A)
| less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_188,c_215]) ).
cnf(c_12381,plain,
( ~ sum(d,a,A)
| less_or_equal(u,A) ),
inference(resolve,[status(thm)],[c_193,c_203]) ).
cnf(c_16442,plain,
less_or_equal(u,add(d,a)),
inference(resolve,[status(thm)],[c_1986,c_12381]) ).
cnf(c_16447,plain,
sum(a,d,add(d,a)),
inference(resolve,[status(thm)],[c_1986,c_5]) ).
cnf(c_16554,plain,
( ~ less_or_equal(A,v)
| ~ less_or_equal(u,A) ),
inference(resolve,[status(thm)],[c_22,c_37]) ).
cnf(c_16488,plain,
~ less_or_equal(add(d,a),v),
inference(resolve,[status(thm)],[c_16554,c_16442]) ).
cnf(c_16555,plain,
~ sum(a,d,add(d,a)),
inference(resolve,[status(thm)],[c_12379,c_16488]) ).
cnf(c_16553,plain,
$false,
inference(resolve,[status(thm)],[c_16447,c_16555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD061-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 02:32:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3606048 was started by sandbox2 on n005,
% 0.08/0.35 % Sun Sep 27 02:32:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 49.47/6.87
% 49.47/6.87 % given #500 (A,wt=13): 167 product(multiplicative_inverse(u),u,multiplicative_identity) | sum(additive_identity,u,additive_identity). [resolve(31,a,9,c)].
% 49.47/6.87
% 49.47/6.87 % given #1000 (T,wt=9): 13395 less_or_equal(v,A) | -sum(v,additive_identity,A). [resolve(337,b,731,a)].
% 49.47/6.87
% 49.47/6.87 % SZS status Unsatisfiable for theBenchmark
% 49.47/6.87
% 49.47/6.87 % Proof 1 at 5.55 (+ 0.75) seconds.
% 49.47/6.87 % Length of proof is 23.
% 49.47/6.87 % Level of proof is 5.
% 49.47/6.87 % Maximum clause weight is 16.000.
% 49.47/6.87 % Given clauses 1447.
% 49.47/6.87
% 49.47/6.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------