%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD018-1 : 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 : n020.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 17.57s 2.91s
% Output : CNFRefutation 17.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 26 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(VAR_0,additive_inverse(VAR_0)),additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| equalish(add(A,additive_inverse(A)),additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(well_definedness_of_additive_inverse,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| defined(additive_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_additive_inverse) ).
cnf(c_12,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
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(a_equals_additive_identity_2,axiom,
equalish(a,additive_identity),
file('theBenchmark.p',a_equals_additive_identity_2) ).
cnf(c_29,plain,
equalish(a,additive_identity),
inference(clausify,[status(thm)],[a_equals_additive_identity_2]) ).
fof(additive_inverse_not_equal_to_additive_identity_3,axiom,
~ equalish(additive_inverse(a),additive_identity),
file('theBenchmark.p',additive_inverse_not_equal_to_additive_identity_3) ).
cnf(c_30,plain,
~ equalish(additive_inverse(a),additive_identity),
inference(clausify,[status(thm)],[additive_inverse_not_equal_to_additive_identity_3]) ).
cnf(c_136,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_28,c_12]) ).
cnf(c_150,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_167,plain,
( ~ defined(A)
| equalish(add(a,A),add(additive_identity,A)) ),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_548,plain,
equalish(add(additive_identity,additive_inverse(a)),additive_inverse(a)),
inference(resolve,[status(thm)],[c_136,c_2]) ).
cnf(c_29211,plain,
( ~ equalish(A,additive_identity)
| ~ equalish(additive_inverse(a),A) ),
inference(resolve,[status(thm)],[c_23,c_30]) ).
cnf(c_6382,plain,
~ equalish(additive_inverse(a),add(a,additive_inverse(a))),
inference(resolve,[status(thm)],[c_29211,c_150]) ).
cnf(c_6389,plain,
~ equalish(add(a,additive_inverse(a)),additive_inverse(a)),
inference(resolve,[status(thm)],[c_22,c_6382]) ).
cnf(c_7050,plain,
equalish(add(a,additive_inverse(a)),add(additive_identity,additive_inverse(a))),
inference(resolve,[status(thm)],[c_167,c_136]) ).
cnf(c_29212,plain,
( ~ equalish(A,additive_inverse(a))
| ~ equalish(add(a,additive_inverse(a)),A) ),
inference(resolve,[status(thm)],[c_23,c_6389]) ).
cnf(c_29213,plain,
~ equalish(add(a,additive_inverse(a)),add(additive_identity,additive_inverse(a))),
inference(resolve,[status(thm)],[c_29212,c_548]) ).
cnf(c_29210,plain,
$false,
inference(resolve,[status(thm)],[c_7050,c_29213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD018-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:24:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3016136 was started by sandbox2 on n020,
% 0.08/0.37 % Sun Sep 27 02:24:05 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 17.57/2.91
% 17.57/2.91 % given #500 (F,wt=15): 4468 -equalish(additive_identity,add(a,multiplicative_identity)). [ur(22,a,4463,a)].
% 17.57/2.91
% 17.57/2.91 % given #1000 (T,wt=18): 4752 less_or_equal(A,add(a,additive_identity)) | -equalish(a,A). [resolve(4739,a,26,b)].
% 17.57/2.91
% 17.57/2.91 % given #1500 (T,wt=20): 4226 less_or_equal(A,multiply(additive_identity,additive_identity)) | -less_or_equal(A,multiply(multiplicative_identity,additive_identity)). [resolve(4163,a,17,c)].
% 17.57/2.91
% 17.57/2.91 % given #2000 (T,wt=20): 7702 less_or_equal(A,multiply(a,multiplicative_identity)) | -equalish(multiply(multiplicative_identity,additive_identity),A). [resolve(7663,a,26,b)].
% 17.57/2.91
% 17.57/2.91 % given #2500 (F,wt=23): 25559 -equalish(add(additive_identity,multiplicative_inverse(multiplicative_identity)),multiply(multiplicative_identity,additive_identity)). [ur(1447,a,25551,a)].
% 17.57/2.91
% 17.57/2.91 % SZS status Unsatisfiable for theBenchmark
% 17.57/2.91
% 17.57/2.91 % Proof 1 at 1.77 (+ 0.71) seconds.
% 17.57/2.91 % Length of proof is 17.
% 17.57/2.91 % Level of proof is 4.
% 17.57/2.91 % Maximum clause weight is 24.000.
% 17.57/2.91 % Given clauses 2958.
% 17.57/2.91
% 17.57/2.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------