TSTP Solution File: LCL163-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL163-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 06:52:33 EDT 2023

% Result   : Unsatisfiable 6.24s 6.27s
% Output   : CNFRefutation 6.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   35 (  27 unt;   8 typ;   0 def)
%            Number of atoms       :   27 (  26 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   38 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    not: $i > $i ).

tff(decl_23,type,
    truth: $i ).

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

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

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

tff(decl_27,type,
    implies: ( $i * $i ) > $i ).

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

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

cnf(axiom_2,axiom,
    xor(X1,falsehood) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).

cnf(xor_commutativity,axiom,
    xor(X1,X2) = xor(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).

cnf(axiom_7,axiom,
    xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_7) ).

cnf(axiom_3,axiom,
    xor(X1,X1) = falsehood,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_3) ).

cnf(axiom_8,axiom,
    and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_8) ).

cnf(and_star_commutativity,axiom,
    and_star(X1,X2) = and_star(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).

cnf(prove_wajsberg_axiom,negated_conjecture,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).

cnf(implies_definition,axiom,
    implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).

cnf(c_0_8,axiom,
    xor(X1,falsehood) = X1,
    axiom_2 ).

cnf(c_0_9,axiom,
    xor(X1,X2) = xor(X2,X1),
    xor_commutativity ).

cnf(c_0_10,axiom,
    xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
    axiom_7 ).

cnf(c_0_11,axiom,
    xor(X1,X1) = falsehood,
    axiom_3 ).

cnf(c_0_12,axiom,
    and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
    axiom_8 ).

cnf(c_0_13,axiom,
    and_star(X1,X2) = and_star(X2,X1),
    and_star_commutativity ).

cnf(c_0_14,plain,
    xor(falsehood,X1) = X1,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_15,plain,
    xor(X1,xor(truth,xor(truth,X2))) = xor(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_10]),c_0_11]),c_0_8]),c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    prove_wajsberg_axiom ).

cnf(c_0_17,axiom,
    implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
    implies_definition ).

cnf(c_0_18,plain,
    and_star(X1,xor(truth,and_star(xor(truth,X2),X1))) = and_star(X2,xor(truth,and_star(xor(truth,X1),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_9]),c_0_13]),c_0_9]),c_0_13]) ).

cnf(c_0_19,plain,
    xor(truth,xor(truth,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).

cnf(c_0_20,plain,
    xor(X1,xor(X2,truth)) = xor(X2,xor(truth,X1)),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))) != xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).

cnf(c_0_22,plain,
    and_star(xor(truth,X1),xor(truth,and_star(xor(truth,X2),xor(truth,X1)))) = and_star(X2,xor(truth,and_star(X1,X2))),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    xor(X1,xor(truth,X2)) = xor(X2,xor(truth,X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_9]) ).

cnf(c_0_24,negated_conjecture,
    xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))) != xor(truth,and_star(xor(truth,y),xor(truth,and_star(x,xor(truth,y))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).

cnf(c_0_25,plain,
    and_star(xor(truth,X1),xor(truth,and_star(X2,xor(truth,X1)))) = and_star(xor(truth,X2),xor(truth,and_star(X1,xor(truth,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11]),c_0_8]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL163-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 07:10:10 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 6.24/6.27  % Version  : CSE_E---1.5
% 6.24/6.27  % Problem  : theBenchmark.p
% 6.24/6.27  % Proof found
% 6.24/6.27  % SZS status Theorem for theBenchmark.p
% 6.24/6.27  % SZS output start Proof
% See solution above
% 6.24/6.28  % Total time : 5.684000 s
% 6.24/6.28  % SZS output end Proof
% 6.24/6.28  % Total time : 5.687000 s
%------------------------------------------------------------------------------