%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 8 !; 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(addition,axiom,
! [VAR_0,VAR_1] : equalish(add(VAR_0,successor(VAR_1)),successor(add(VAR_0,VAR_1))),
file('theBenchmark.p',addition) ).
cnf(c_2,plain,
equalish(add(A,successor(B)),successor(add(A,B))),
inference(clausify,[status(thm)],[addition]) ).
fof(successor_substitution,axiom,
! [VAR_0,VAR_1] :
( equalish(successor(VAR_0),successor(VAR_1))
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',successor_substitution) ).
cnf(c_6,plain,
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[successor_substitution]) ).
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_9,plain,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(deny_addition_lemma,axiom,
~ equalish(add(a,successor(n0)),successor(a)),
file('theBenchmark.p',deny_addition_lemma) ).
cnf(c_11,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(clausify,[status(thm)],[deny_addition_lemma]) ).
cnf(c_16,plain,
equalish(successor(add(A,n0)),successor(A)),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_36,plain,
( equalish(add(A,successor(B)),C)
| ~ equalish(successor(add(A,B)),C) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_34,plain,
~ equalish(successor(add(a,n0)),successor(a)),
inference(resolve,[status(thm)],[c_36,c_11]) ).
cnf(c_35,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 01:53:43 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 3514505 was started by sandbox2 on n011,
% 0.13/0.37 % Sat Sep 26 01:53:43 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 8.
% 0.13/0.38 % Level of proof is 2.
% 0.13/0.38 % Maximum clause weight is 9.000.
% 0.13/0.38 % Given clauses 11.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------