%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:16:03 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adding_zero,axiom,
! [VAR_0] : equalish(add(VAR_0,n0),VAR_0),
file('theBenchmark.p',adding_zero) ).
cnf(c_1,plain,
equalish(add(A,n0),A),
inference(clausify,[status(thm)],[adding_zero]) ).
fof(less_lemma,axiom,
! [VAR_0,VAR_1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(VAR_1,VAR_0)),VAR_0),VAR_1)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',less_lemma) ).
cnf(c_9,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_lemma]) ).
fof(symmetry,axiom,
! [VAR_0,VAR_1] :
( equalish(VAR_1,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry) ).
cnf(c_11,plain,
( equalish(B,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry]) ).
fof(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_2)
| ~ equalish(VAR_1,VAR_2)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity) ).
cnf(c_12,plain,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(plus_substitution,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_2)
| ~ equalish(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',plus_substitution) ).
cnf(c_13,plain,
( equalish(A,C)
| ~ equalish(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[plus_substitution]) ).
fof(commutativity_of_plus,axiom,
! [VAR_0,VAR_1] : equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)),
file('theBenchmark.p',commutativity_of_plus) ).
cnf(c_14,plain,
equalish(add(A,B),add(B,A)),
inference(clausify,[status(thm)],[commutativity_of_plus]) ).
fof(impossible_a_is_less_than_itself,axiom,
less(a,a),
file('theBenchmark.p',impossible_a_is_less_than_itself) ).
cnf(c_15,plain,
less(a,a),
inference(clausify,[status(thm)],[impossible_a_is_less_than_itself]) ).
fof(prove_a_contradiction,axiom,
! [VAR_0] : ~ equalish(successor(VAR_0),n0),
file('theBenchmark.p',prove_a_contradiction) ).
cnf(c_16,plain,
~ equalish(successor(A),n0),
inference(clausify,[status(thm)],[prove_a_contradiction]) ).
cnf(c_27,plain,
equalish(A,add(A,n0)),
inference(resolve,[status(thm)],[c_11,c_1]) ).
cnf(c_40,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
inference(resolve,[status(thm)],[c_9,c_15]) ).
cnf(c_41,plain,
~ equalish(add(successor(A),B),add(n0,B)),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_573,plain,
( equalish(A,B)
| ~ equalish(add(A,n0),B) ),
inference(resolve,[status(thm)],[c_12,c_27]) ).
cnf(c_80,plain,
equalish(A,add(n0,A)),
inference(resolve,[status(thm)],[c_573,c_14]) ).
cnf(c_574,plain,
( equalish(A,add(n0,B))
| ~ equalish(A,B) ),
inference(resolve,[status(thm)],[c_12,c_80]) ).
cnf(c_571,plain,
~ equalish(add(successor(A),B),B),
inference(resolve,[status(thm)],[c_574,c_41]) ).
cnf(c_572,plain,
$false,
inference(resolve,[status(thm)],[c_571,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n001.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 01:59:41 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 641926 was started by sandbox on n001,
% 0.19/0.46 % Sat Sep 26 01:59:41 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.57
% 0.19/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.57
% 0.19/0.57 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.19/0.57 % Length of proof is 14.
% 0.19/0.57 % Level of proof is 4.
% 0.19/0.57 % Maximum clause weight is 11.000.
% 0.19/0.57 % Given clauses 74.
% 0.19/0.57
% 0.19/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------