%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD013-2 : 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 : n011.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 07:11:27 AM UTC 2026
% Result : Unsatisfiable 22.28s 6.45s
% Output : CNFRefutation 22.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 29 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 36 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_0,VAR_2)
| ~ defined(VAR_1)
| equalish(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_equality_and_addition) ).
cnf(c_24,plain,
( ~ equalish(A,C)
| ~ defined(B)
| equalish(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_addition]) ).
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(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_29,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_30,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_31,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(a_equals_b_6,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_6) ).
cnf(c_33,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_6]) ).
fof(c_equals_d_7,axiom,
equalish(c,d),
file('theBenchmark.p',c_equals_d_7) ).
cnf(c_34,plain,
equalish(c,d),
inference(clausify,[status(thm)],[c_equals_d_7]) ).
fof(add_equals_u_8,axiom,
equalish(add(a,c),u),
file('theBenchmark.p',add_equals_u_8) ).
cnf(c_35,plain,
equalish(add(a,c),u),
inference(clausify,[status(thm)],[add_equals_u_8]) ).
fof(add_not_equal_to_u_9,axiom,
~ equalish(add(d,b),u),
file('theBenchmark.p',add_not_equal_to_u_9) ).
cnf(c_36,plain,
~ equalish(add(d,b),u),
inference(clausify,[status(thm)],[add_not_equal_to_u_9]) ).
cnf(c_136,plain,
( ~ equalish(A,B)
| equalish(add(A,a),add(B,a)) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_156,plain,
( ~ defined(A)
| equalish(add(A,a),add(a,A)) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_157,plain,
( ~ defined(A)
| equalish(add(a,A),add(A,a)) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_194,plain,
( ~ defined(A)
| equalish(add(A,b),add(b,A)) ),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_250,plain,
( ~ equalish(A,B)
| equalish(add(A,d),add(B,d)) ),
inference(resolve,[status(thm)],[c_31,c_24]) ).
cnf(c_330,plain,
equalish(b,a),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_336,plain,
equalish(d,c),
inference(resolve,[status(thm)],[c_34,c_22]) ).
cnf(c_21781,plain,
( ~ equalish(A,u)
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_36]) ).
cnf(c_343,plain,
~ equalish(add(d,b),add(a,c)),
inference(resolve,[status(thm)],[c_21781,c_35]) ).
cnf(c_5806,plain,
equalish(add(d,a),add(c,a)),
inference(resolve,[status(thm)],[c_136,c_336]) ).
cnf(c_9184,plain,
equalish(add(c,a),add(a,c)),
inference(resolve,[status(thm)],[c_156,c_30]) ).
cnf(c_9242,plain,
equalish(add(a,d),add(d,a)),
inference(resolve,[status(thm)],[c_157,c_31]) ).
cnf(c_12708,plain,
equalish(add(d,b),add(b,d)),
inference(resolve,[status(thm)],[c_194,c_31]) ).
cnf(c_15764,plain,
equalish(add(b,d),add(a,d)),
inference(resolve,[status(thm)],[c_250,c_330]) ).
cnf(c_21782,plain,
( ~ equalish(A,add(a,c))
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_343]) ).
cnf(c_21586,plain,
~ equalish(add(d,b),add(c,a)),
inference(resolve,[status(thm)],[c_21782,c_9184]) ).
cnf(c_21783,plain,
( ~ equalish(A,add(c,a))
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_21586]) ).
cnf(c_21611,plain,
~ equalish(add(d,b),add(d,a)),
inference(resolve,[status(thm)],[c_21783,c_5806]) ).
cnf(c_21784,plain,
( ~ equalish(A,add(d,a))
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_21611]) ).
cnf(c_21620,plain,
~ equalish(add(d,b),add(a,d)),
inference(resolve,[status(thm)],[c_21784,c_9242]) ).
cnf(c_21785,plain,
( ~ equalish(A,add(a,d))
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_21620]) ).
cnf(c_21786,plain,
~ equalish(add(b,d),add(a,d)),
inference(resolve,[status(thm)],[c_21785,c_12708]) ).
cnf(c_21780,plain,
$false,
inference(resolve,[status(thm)],[c_15764,c_21786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % Computer : n011.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8046.5625MB
% 0.12/0.45 % OS : Linux 6.8.0-71-generic
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Sun Sep 27 02:23:00 UTC 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.46 % Process 1996893 was started by sandbox on n011,
% 0.12/0.46 % Sun Sep 27 02:23:00 2026
% 0.12/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.46
% 0.12/0.46 % From the command line: assign(max_seconds, 300).
% 22.28/6.45
% 22.28/6.45 % given #500 (W,wt=14): 1489 less_or_equal(b,d) | less_or_equal(A,a) | -less_or_equal(A,d). [resolve(1444,b,17,c)].
% 22.28/6.45
% 22.28/6.45 % given #1000 (T,wt=17): 1209 equalish(multiply(c,multiplicative_identity),multiply(multiplicative_identity,c)). [resolve(95,b,30,a)].
% 22.28/6.45
% 22.28/6.45 % SZS status Unsatisfiable for theBenchmark
% 22.28/6.45
% 22.28/6.45 % Proof 1 at 2.07 (+ 0.84) seconds.
% 22.28/6.45 % Length of proof is 29.
% 22.28/6.45 % Level of proof is 6.
% 22.28/6.45 % Maximum clause weight is 22.000.
% 22.28/6.45 % Given clauses 1372.
% 22.28/6.45
% 22.28/6.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------