%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD013-1 : 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 : n017.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 22.79s 3.40s
% Output : CNFRefutation 22.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 19 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 26 ~; 19 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 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(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(a_equals_b_5,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_5) ).
cnf(c_32,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_5]) ).
fof(c_equals_d_6,axiom,
equalish(c,d),
file('theBenchmark.p',c_equals_d_6) ).
cnf(c_33,plain,
equalish(c,d),
inference(clausify,[status(thm)],[c_equals_d_6]) ).
fof(add_not_equal_to_add_7,axiom,
~ equalish(add(a,c),add(d,b)),
file('theBenchmark.p',add_not_equal_to_add_7) ).
cnf(c_34,plain,
~ equalish(add(a,c),add(d,b)),
inference(clausify,[status(thm)],[add_not_equal_to_add_7]) ).
cnf(c_172,plain,
( ~ equalish(A,B)
| equalish(add(A,b),add(B,b)) ),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_192,plain,
( ~ defined(A)
| equalish(add(A,b),add(b,A)) ),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_210,plain,
( ~ equalish(A,B)
| equalish(add(A,c),add(B,c)) ),
inference(resolve,[status(thm)],[c_30,c_24]) ).
cnf(c_290,plain,
equalish(b,a),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_296,plain,
equalish(d,c),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_297,plain,
~ equalish(add(d,b),add(a,c)),
inference(resolve,[status(thm)],[c_22,c_34]) ).
cnf(c_15741,plain,
equalish(add(d,b),add(c,b)),
inference(resolve,[status(thm)],[c_172,c_296]) ).
cnf(c_16574,plain,
equalish(add(c,b),add(b,c)),
inference(resolve,[status(thm)],[c_192,c_30]) ).
cnf(c_17752,plain,
equalish(add(b,c),add(a,c)),
inference(resolve,[status(thm)],[c_210,c_290]) ).
cnf(c_19228,plain,
( ~ equalish(A,add(a,c))
| ~ equalish(add(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_297]) ).
cnf(c_19183,plain,
~ equalish(add(c,b),add(a,c)),
inference(resolve,[status(thm)],[c_19228,c_15741]) ).
cnf(c_19229,plain,
( ~ equalish(A,add(a,c))
| ~ equalish(add(c,b),A) ),
inference(resolve,[status(thm)],[c_23,c_19183]) ).
cnf(c_19230,plain,
~ equalish(add(b,c),add(a,c)),
inference(resolve,[status(thm)],[c_19229,c_16574]) ).
cnf(c_19227,plain,
$false,
inference(resolve,[status(thm)],[c_17752,c_19230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 02:17:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2123887 was started by sandbox2 on n017,
% 0.16/0.42 % Sun Sep 27 02:17:04 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 22.79/3.40
% 22.79/3.40 % given #500 (T,wt=16): 138 defined(multiplicative_inverse(a)) | equalish(a,additive_identity). [resolve(28,a,15,b)].
% 22.79/3.40
% 22.79/3.40 % given #1000 (T,wt=17): 11168 equalish(multiply(d,b),multiply(d,b)). [resolve(11057,a,21,b)].
% 22.79/3.40
% 22.79/3.40 % SZS status Unsatisfiable for theBenchmark
% 22.79/3.40
% 22.79/3.40 % Proof 1 at 2.09 (+ 0.82) seconds.
% 22.79/3.40 % Length of proof is 20.
% 22.79/3.40 % Level of proof is 4.
% 22.79/3.40 % Maximum clause weight is 22.000.
% 22.79/3.40 % Given clauses 1095.
% 22.79/3.40
% 22.79/3.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------