%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL078-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 18:22:29 EDT 2023

% Result   : Unsatisfiable 1.04s 1.10s
% Output   : CNFRefutation 1.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   28 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :   24 (  23 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   31 (   7 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    projection1: $i ).

tff(decl_25,type,
    pair: ( $i * $i ) > $i ).

tff(decl_26,type,
    projection2: $i ).

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

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

tff(decl_29,type,
    n: ( $i * $i ) > $i ).

tff(decl_30,type,
    identity: $i ).

cnf(abstraction,axiom,
    apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).

cnf(k_definition,axiom,
    apply(k(X1),X2) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).

cnf(extensionality2,axiom,
    ( X1 = X2
    | apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).

cnf(identity_definition,axiom,
    apply(identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).

cnf(prove_TRC1b,negated_conjecture,
    apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).

cnf(c_0_5,axiom,
    apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
    abstraction ).

cnf(c_0_6,axiom,
    apply(k(X1),X2) = X1,
    k_definition ).

cnf(c_0_7,axiom,
    ( X1 = X2
    | apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
    extensionality2 ).

cnf(c_0_8,axiom,
    apply(identity,X1) = X1,
    identity_definition ).

cnf(c_0_9,plain,
    apply(apply(apply(apply(abstraction,abstraction),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_6]) ).

cnf(c_0_10,plain,
    ( identity = X1
    | apply(X1,n(identity,X1)) != n(identity,X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_6]) ).

cnf(c_0_12,plain,
    ( k(X1) = X2
    | apply(X2,n(k(X1),X2)) != X1 ),
    inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_13,plain,
    apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
    prove_TRC1b ).

cnf(c_0_15,plain,
    ( k(X1) = apply(apply(apply(abstraction,abstraction),X2),X3)
    | apply(X3,apply(apply(X2,X3),n(k(X1),apply(apply(apply(abstraction,abstraction),X2),X3)))) != X1 ),
    inference(spm,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_16,plain,
    apply(abstraction,apply(apply(abstraction,abstraction),X1)) = k(identity),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]) ).

cnf(c_0_17,negated_conjecture,
    apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)) != k(k(identity)),
    inference(rw,[status(thm)],[c_0_14,c_0_5]) ).

cnf(c_0_18,plain,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_5])]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : COL078-1 : TPTP v8.1.2. Released v1.2.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n011.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   : Sun Aug 27 04:29:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 1.04/1.10  % Version  : CSE_E---1.5
% 1.04/1.10  % Problem  : theBenchmark.p
% 1.04/1.10  % Proof found
% 1.04/1.10  % SZS status Theorem for theBenchmark.p
% 1.04/1.10  % SZS output start Proof
% See solution above
% 1.04/1.10  % Total time : 0.510000 s
% 1.04/1.10  % SZS output end Proof
% 1.04/1.10  % Total time : 0.513000 s
%------------------------------------------------------------------------------