TSTP Solution File: NUM024-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM024-1 : 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 : n018.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 10:26:12 EDT 2023

% Result   : Unsatisfiable 0.19s 0.73s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :   35 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  14   ~;  12   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   34 (   2 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,
    less: ( $i * $i ) > $o ).

tff(decl_28,type,
    predecessor_of_1st_minus_2nd: ( $i * $i ) > $i ).

tff(decl_29,type,
    a: $i ).

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

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

cnf(commutativity_of_plus,axiom,
    equalish(add(X1,X2),add(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).

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

cnf(less_lemma,axiom,
    ( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
    | ~ less(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',less_lemma) ).

cnf(impossible_a_is_less_than_itself,hypothesis,
    less(a,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).

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

cnf(prove_a_contradiction,negated_conjecture,
    ~ equalish(successor(X1),n0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).

cnf(c_0_8,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    transitivity ).

cnf(c_0_9,axiom,
    equalish(add(X1,n0),X1),
    adding_zero ).

cnf(c_0_10,plain,
    ( equalish(X1,X2)
    | ~ equalish(X1,add(X2,n0)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,axiom,
    equalish(add(X1,X2),add(X2,X1)),
    commutativity_of_plus ).

cnf(c_0_12,axiom,
    ( equalish(X2,X1)
    | ~ equalish(X1,X2) ),
    symmetry ).

cnf(c_0_13,plain,
    equalish(add(n0,X1),X1),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    equalish(X1,add(n0,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,axiom,
    ( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
    | ~ less(X1,X2) ),
    less_lemma ).

cnf(c_0_16,hypothesis,
    less(a,a),
    impossible_a_is_less_than_itself ).

cnf(c_0_17,plain,
    ( equalish(X1,add(n0,X2))
    | ~ equalish(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_14]) ).

cnf(c_0_18,hypothesis,
    equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,axiom,
    ( equalish(X1,X3)
    | ~ equalish(add(X1,X2),add(X3,X2)) ),
    plus_substitution ).

cnf(c_0_20,hypothesis,
    equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),add(n0,a)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ~ equalish(successor(X1),n0),
    prove_a_contradiction ).

cnf(c_0_22,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n018.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 12:07:44 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.73  % Version  : CSE_E---1.5
% 0.19/0.73  % Problem  : theBenchmark.p
% 0.19/0.73  % Proof found
% 0.19/0.73  % SZS status Theorem for theBenchmark.p
% 0.19/0.73  % SZS output start Proof
% See solution above
% 0.19/0.73  % Total time : 0.147000 s
% 0.19/0.73  % SZS output end Proof
% 0.19/0.73  % Total time : 0.150000 s
%------------------------------------------------------------------------------