%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG011-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 : Wed Aug 30 16:00:04 EDT 2023

% Result   : Unsatisfiable 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   30 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   58 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   72 (  39   ~;  33   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   43 (   8 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    f: ( $i * $i ) > $i ).

tff(decl_23,type,
    c: $i > $o ).

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

tff(decl_25,type,
    a1: $i ).

tff(decl_26,type,
    a2: $i ).

cnf(partitions_exclusive,hypothesis,
    ( ~ c(X1)
    | ~ d(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive) ).

cnf(conjecture_1,negated_conjecture,
    ( d(f(X1,X2))
    | ~ c(X1)
    | ~ c(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).

cnf(conjecture_2,negated_conjecture,
    ( c(f(X1,X2))
    | ~ d(X1)
    | ~ d(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).

cnf(f_is_associative,axiom,
    f(X1,f(X2,X3)) = f(f(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).

cnf(partitions_union,axiom,
    ( c(X1)
    | d(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).

cnf(partition_d_not_empty,hypothesis,
    d(a2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d_not_empty) ).

cnf(partition_c_not_empty,hypothesis,
    c(a1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_c_not_empty) ).

cnf(c_0_7,hypothesis,
    ( ~ c(X1)
    | ~ d(X1) ),
    partitions_exclusive ).

cnf(c_0_8,negated_conjecture,
    ( d(f(X1,X2))
    | ~ c(X1)
    | ~ c(X2) ),
    conjecture_1 ).

cnf(c_0_9,negated_conjecture,
    ( c(f(X1,X2))
    | ~ d(X1)
    | ~ d(X2) ),
    conjecture_2 ).

cnf(c_0_10,axiom,
    f(X1,f(X2,X3)) = f(f(X1,X2),X3),
    f_is_associative ).

cnf(c_0_11,hypothesis,
    ( ~ c(f(X1,X2))
    | ~ c(X2)
    | ~ c(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( c(f(X1,f(X2,X3)))
    | ~ d(f(X1,X2))
    | ~ d(X3) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,hypothesis,
    ( ~ d(f(X1,X2))
    | ~ d(X3)
    | ~ c(f(X2,X3))
    | ~ c(X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,axiom,
    ( c(X1)
    | d(X1) ),
    partitions_union ).

cnf(c_0_15,hypothesis,
    ( c(f(X1,X2))
    | ~ d(X3)
    | ~ c(f(X2,X3))
    | ~ c(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    ( c(f(X1,X2))
    | ~ d(X3)
    | ~ d(X2)
    | ~ c(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_9]) ).

cnf(c_0_17,hypothesis,
    d(a2),
    partition_d_not_empty ).

cnf(c_0_18,negated_conjecture,
    ( ~ d(X1)
    | ~ c(f(X2,X1))
    | ~ c(X3)
    | ~ c(X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_19,hypothesis,
    ( c(f(X1,X2))
    | ~ d(X2)
    | ~ c(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ d(X1)
    | ~ c(X2)
    | ~ c(X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,hypothesis,
    ( ~ c(X1)
    | ~ c(X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

cnf(c_0_22,hypothesis,
    c(a1),
    partition_c_not_empty ).

cnf(c_0_23,hypothesis,
    ~ c(X1),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,hypothesis,
    $false,
    inference(sr,[status(thm)],[c_0_22,c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ALG011-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 03:11:02 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.60  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.004000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.006000 s
%------------------------------------------------------------------------------