%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ROB011-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 14:07:17 EDT 2023

% Result   : Unsatisfiable 0.16s 0.55s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (  18 unt;   9 typ;   0 def)
%            Number of atoms       :   18 (  17 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    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    negate: $i > $i ).

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

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

tff(decl_26,type,
    positive_integer: $i > $o ).

tff(decl_27,type,
    successor: $i > $i ).

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

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

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

cnf(robbins_axiom,axiom,
    negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).

cnf(condition,hypothesis,
    negate(add(a,negate(b))) = c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).

cnf(prove_base_step,negated_conjecture,
    negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_base_step) ).

cnf(one_times_x,axiom,
    multiply(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-1.ax',one_times_x) ).

cnf(associativity_of_add,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).

cnf(c_0_6,axiom,
    negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
    robbins_axiom ).

cnf(c_0_7,hypothesis,
    negate(add(a,negate(b))) = c,
    condition ).

cnf(c_0_8,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_9,negated_conjecture,
    negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
    prove_base_step ).

cnf(c_0_10,axiom,
    multiply(one,X1) = X1,
    one_times_x ).

cnf(c_0_11,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    associativity_of_add ).

cnf(c_0_12,hypothesis,
    negate(add(c,negate(add(a,b)))) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    negate(add(a,negate(add(b,add(a,c))))) != c,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_15,hypothesis,
    negate(add(a,negate(add(c,add(a,b))))) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_12]),c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    negate(add(a,negate(add(a,add(c,b))))) != c,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_8]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : ROB011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n031.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon Aug 28 07:25:55 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.16/0.54  start to proof: theBenchmark
% 0.16/0.55  % Version  : CSE_E---1.5
% 0.16/0.55  % Problem  : theBenchmark.p
% 0.16/0.55  % Proof found
% 0.16/0.55  % SZS status Theorem for theBenchmark.p
% 0.16/0.55  % SZS output start Proof
% See solution above
% 0.16/0.55  % Total time : 0.005000 s
% 0.16/0.55  % SZS output end Proof
% 0.16/0.55  % Total time : 0.008000 s
%------------------------------------------------------------------------------