%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT019-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 06:56:00 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 62 ( 38 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 31 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_and_equality_implies_equivalence1,axiom,
! [VAR_0,VAR_1] :
( equivalent(VAR_0,VAR_1)
| VAR_0 != VAR_1
| ~ there_exists(VAR_0) ),
file('theBenchmark.p',existence_and_equality_implies_equivalence1) ).
cnf(c_1,plain,
( equivalent(A,B)
| A != B
| ~ there_exists(A) ),
inference(clausify,[status(thm)],[existence_and_equality_implies_equivalence1]) ).
fof(equivalence_implies_existence3,axiom,
! [VAR_0,VAR_1] :
( there_exists(VAR_1)
| ~ equivalent(VAR_0,VAR_1) ),
file('theBenchmark.p',equivalence_implies_existence3) ).
cnf(c_4,plain,
( there_exists(B)
| ~ equivalent(A,B) ),
inference(clausify,[status(thm)],[equivalence_implies_existence3]) ).
cnf(c_6,plain,
( B != A
| ~ there_exists(B)
| there_exists(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_a_equals_b,axiom,
a != b,
file('theBenchmark.p',prove_a_equals_b) ).
cnf(c_7,plain,
a != b,
inference(clausify,[status(thm)],[prove_a_equals_b]) ).
cnf(c_8,plain,
b != a,
inference(copy,[status(thm)],[c_7]) ).
fof(equality_of_a_and_b2,axiom,
! [VAR_0] :
( b != VAR_0
| a = VAR_0
| ~ there_exists(VAR_0) ),
file('theBenchmark.p',equality_of_a_and_b2) ).
cnf(c_9,plain,
( b != A
| a = A
| ~ there_exists(A) ),
inference(clausify,[status(thm)],[equality_of_a_and_b2]) ).
fof(equality_of_a_and_b1,axiom,
! [VAR_0] :
( b = VAR_0
| a != VAR_0
| ~ there_exists(VAR_0) ),
file('theBenchmark.p',equality_of_a_and_b1) ).
cnf(c_10,plain,
( b = A
| a != A
| ~ there_exists(A) ),
inference(clausify,[status(thm)],[equality_of_a_and_b1]) ).
fof(indiscernibles2,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| VAR_1 = f1(VAR_0,VAR_1)
| VAR_0 = f1(VAR_0,VAR_1) ),
file('theBenchmark.p',indiscernibles2) ).
cnf(c_13,plain,
( A = B
| B = f1(A,B)
| A = f1(A,B) ),
inference(clausify,[status(thm)],[indiscernibles2]) ).
cnf(c_94,plain,
( A = B
| B = f1(A,B)
| f1(A,B) = A ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_14,plain,
( A = B
| f1(A,B) = B
| f1(A,B) = A ),
inference(copy,[status(thm)],[c_94]) ).
fof(indiscernibles1,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| there_exists(f1(VAR_0,VAR_1)) ),
file('theBenchmark.p',indiscernibles1) ).
cnf(c_15,plain,
( A = B
| there_exists(f1(A,B)) ),
inference(clausify,[status(thm)],[indiscernibles1]) ).
cnf(c_95,plain,
a != b,
inference(copy,[status(thm)],[c_8]) ).
cnf(c_96,plain,
( b != b
| ~ there_exists(b) ),
inference(resolve,[status(thm)],[c_9,c_95]) ).
cnf(c_28,plain,
~ there_exists(b),
inference(xxres,[status(thm)],[c_96]) ).
cnf(c_97,plain,
( b = a
| ~ there_exists(a) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_29,plain,
~ there_exists(a),
inference(resolve,[status(thm)],[c_97,c_8]) ).
cnf(c_32,plain,
( f1(b,a) = a
| f1(b,a) = b ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_41,plain,
there_exists(f1(b,a)),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_98,plain,
( A != a
| ~ there_exists(A) ),
inference(resolve,[status(thm)],[c_6,c_29]) ).
cnf(c_91,plain,
f1(b,a) != a,
inference(resolve,[status(thm)],[c_98,c_41]) ).
cnf(c_99,plain,
( A != b
| ~ there_exists(A) ),
inference(resolve,[status(thm)],[c_6,c_28]) ).
cnf(c_92,plain,
f1(b,a) != b,
inference(resolve,[status(thm)],[c_99,c_41]) ).
cnf(c_100,plain,
f1(b,a) = a,
inference(resolve,[status(thm)],[c_92,c_32]) ).
cnf(c_93,plain,
$false,
inference(resolve,[status(thm)],[c_91,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT019-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n008.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 22:51:13 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.40 % Process 556712 was started by sandbox2 on n008,
% 0.15/0.40 % Sat Sep 26 22:51:13 2026
% 0.15/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.41
% 0.15/0.41 % From the command line: assign(max_seconds, 300).
% 0.15/0.42
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.42
% 0.15/0.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.42 % Length of proof is 17.
% 0.15/0.42 % Level of proof is 4.
% 0.15/0.42 % Maximum clause weight is 23.000.
% 0.15/0.42 % Given clauses 24.
% 0.15/0.42
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------