%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD060-4 : 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 07:11:40 AM UTC 2026
% Result : Unsatisfiable 17.77s 2.65s
% Output : CNFRefutation 17.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 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(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(less_or_equal_5,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_31,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(sum_6,axiom,
sum(a,a,u),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(a,a,u),
inference(clausify,[status(thm)],[sum_6]) ).
fof(sum_7,axiom,
sum(b,b,v),
file('theBenchmark.p',sum_7) ).
cnf(c_33,plain,
sum(b,b,v),
inference(clausify,[status(thm)],[sum_7]) ).
fof(not_less_or_equal_8,axiom,
~ less_or_equal(u,v),
file('theBenchmark.p',not_less_or_equal_8) ).
cnf(c_34,plain,
~ less_or_equal(u,v),
inference(clausify,[status(thm)],[not_less_or_equal_8]) ).
cnf(c_92,plain,
( ~ defined(A)
| sum(A,a,add(A,a)) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_158,plain,
( ~ sum(B,a,A)
| ~ less_or_equal(a,B)
| less_or_equal(u,A) ),
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_167,plain,
( ~ sum(B,b,A)
| ~ less_or_equal(B,b)
| less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_885,plain,
sum(b,a,add(b,a)),
inference(resolve,[status(thm)],[c_92,c_28]) ).
cnf(c_12971,plain,
( ~ less_or_equal(a,b)
| less_or_equal(u,add(b,a)) ),
inference(resolve,[status(thm)],[c_885,c_158]) ).
cnf(c_12839,plain,
less_or_equal(u,add(b,a)),
inference(resolve,[status(thm)],[c_31,c_12971]) ).
cnf(c_12844,plain,
sum(a,b,add(b,a)),
inference(resolve,[status(thm)],[c_885,c_5]) ).
cnf(c_12972,plain,
( ~ less_or_equal(A,v)
| ~ less_or_equal(u,A) ),
inference(resolve,[status(thm)],[c_22,c_34]) ).
cnf(c_12878,plain,
~ less_or_equal(add(b,a),v),
inference(resolve,[status(thm)],[c_12972,c_12839]) ).
cnf(c_12973,plain,
( ~ sum(A,b,add(b,a))
| ~ less_or_equal(A,b) ),
inference(resolve,[status(thm)],[c_167,c_12878]) ).
cnf(c_12974,plain,
~ sum(a,b,add(b,a)),
inference(resolve,[status(thm)],[c_12973,c_31]) ).
cnf(c_12970,plain,
$false,
inference(resolve,[status(thm)],[c_12844,c_12974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 02:33:00 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1643514 was started by sandbox on n009,
% 0.11/0.36 % Sun Sep 27 02:33:00 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 17.77/2.65
% 17.77/2.65 % given #500 (A,wt=16): 202 product(u,u,multiply(u,u)). [resolve(51,b,29,a)].
% 17.77/2.65
% 17.77/2.65 % given #1000 (F,wt=15): 9317 -product(a,additive_inverse(additive_identity),multiplicative_identity). [ur(10,a,9170,a)].
% 17.77/2.65
% 17.77/2.65 % SZS status Unsatisfiable for theBenchmark
% 17.77/2.65
% 17.77/2.65 % Proof 1 at 2.04 (+ 0.23) seconds.
% 17.77/2.65 % Length of proof is 18.
% 17.77/2.65 % Level of proof is 5.
% 17.77/2.65 % Maximum clause weight is 20.000.
% 17.77/2.65 % Given clauses 1310.
% 17.77/2.65
% 17.77/2.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------