%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM020-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:26:11 EDT 2023

% Result   : Unsatisfiable 0.20s 0.65s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   20 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    n0: $i ).

tff(decl_23,type,
    add: ( $i * $i ) > $i ).

tff(decl_24,type,
    equalish: ( $i * $i ) > $o ).

tff(decl_25,type,
    successor: $i > $i ).

tff(decl_26,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_27,type,
    n1: $i ).

tff(decl_28,type,
    a: $i ).

cnf(transitivity,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

cnf(successor_substitution,axiom,
    ( equalish(successor(X1),successor(X2))
    | ~ equalish(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).

cnf(addition,axiom,
    equalish(add(X1,successor(X2)),successor(add(X1,X2))),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',addition) ).

cnf(deny_addition_lemma,negated_conjecture,
    ~ equalish(add(a,successor(n0)),successor(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deny_addition_lemma) ).

cnf(adding_zero,axiom,
    equalish(add(X1,n0),X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',adding_zero) ).

cnf(c_0_5,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    transitivity ).

cnf(c_0_6,axiom,
    ( equalish(successor(X1),successor(X2))
    | ~ equalish(X1,X2) ),
    successor_substitution ).

cnf(c_0_7,plain,
    ( equalish(X1,successor(X2))
    | ~ equalish(X1,successor(X3))
    | ~ equalish(X3,X2) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_8,axiom,
    equalish(add(X1,successor(X2)),successor(add(X1,X2))),
    addition ).

cnf(c_0_9,negated_conjecture,
    ~ equalish(add(a,successor(n0)),successor(a)),
    deny_addition_lemma ).

cnf(c_0_10,plain,
    ( equalish(add(X1,successor(X2)),successor(X3))
    | ~ equalish(add(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,axiom,
    equalish(add(X1,n0),X1),
    adding_zero ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM020-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 17:18:54 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.20/0.62  start to proof: theBenchmark
% 0.20/0.65  % Version  : CSE_E---1.5
% 0.20/0.65  % Problem  : theBenchmark.p
% 0.20/0.65  % Proof found
% 0.20/0.65  % SZS status Theorem for theBenchmark.p
% 0.20/0.65  % SZS output start Proof
% See solution above
% 0.20/0.65  % Total time : 0.022000 s
% 0.20/0.65  % SZS output end Proof
% 0.20/0.65  % Total time : 0.024000 s
%------------------------------------------------------------------------------