%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD017-1 : 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 : n010.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 07:11:28 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 17 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(a_equals_x_5,axiom,
equalish(a,x),
file('theBenchmark.p',a_equals_x_5) ).
cnf(c_32,plain,
equalish(a,x),
inference(clausify,[status(thm)],[a_equals_x_5]) ).
fof(add_equals_c_6,axiom,
equalish(add(a,b),c),
file('theBenchmark.p',add_equals_c_6) ).
cnf(c_33,plain,
equalish(add(a,b),c),
inference(clausify,[status(thm)],[add_equals_c_6]) ).
fof(add_not_equal_to_c_7,axiom,
~ equalish(add(x,b),c),
file('theBenchmark.p',add_not_equal_to_c_7) ).
cnf(c_34,plain,
~ equalish(add(x,b),c),
inference(clausify,[status(thm)],[add_not_equal_to_c_7]) ).
cnf(c_271,plain,
equalish(x,a),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_381,plain,
( ~ equalish(A,c)
| ~ equalish(add(x,b),A) ),
inference(resolve,[status(thm)],[c_23,c_34]) ).
cnf(c_277,plain,
~ equalish(add(x,b),add(a,b)),
inference(resolve,[status(thm)],[c_381,c_33]) ).
cnf(c_382,plain,
( ~ equalish(x,a)
| ~ defined(b) ),
inference(resolve,[status(thm)],[c_24,c_277]) ).
cnf(c_383,plain,
~ equalish(x,a),
inference(resolve,[status(thm)],[c_382,c_29]) ).
cnf(c_380,plain,
$false,
inference(resolve,[status(thm)],[c_271,c_383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD017-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:22:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 528333 was started by sandbox on n010,
% 0.10/0.37 % Sun Sep 27 02:22:45 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 10.
% 0.10/0.41 % Level of proof is 2.
% 0.10/0.41 % Maximum clause weight is 12.000.
% 0.10/0.41 % Given clauses 57.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------