TSTP Solution File: ROB014-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ROB014-2 : 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 14:07:18 EDT 2023

% Result   : Unsatisfiable 0.19s 0.69s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   36 (  21 unt;   8 typ;   0 def)
%            Number of atoms       :   37 (  32 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   22 (  13   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    9 (   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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (   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,
    e: $i ).

tff(decl_29,type,
    d: $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(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).

cnf(lemma_3_2,axiom,
    ( X1 = X2
    | negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).

cnf(condition,hypothesis,
    negate(add(negate(e),negate(add(d,negate(e))))) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).

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(prove_base_step,negated_conjecture,
    negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
    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(lemma_3_4,axiom,
    ( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
    | negate(add(X1,negate(X2))) != X3
    | ~ positive_integer(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_4) ).

cnf(one,axiom,
    positive_integer(one),
    file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-1.ax',one) ).

cnf(c_0_9,axiom,
    negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
    robbins_axiom ).

cnf(c_0_10,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_11,axiom,
    ( X1 = X2
    | negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
    lemma_3_2 ).

cnf(c_0_12,plain,
    negate(add(negate(add(X1,X2)),negate(add(negate(X2),X1)))) = X1,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,hypothesis,
    negate(add(negate(e),negate(add(d,negate(e))))) = d,
    condition ).

cnf(c_0_14,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    associativity_of_add ).

cnf(c_0_15,plain,
    ( X1 = X2
    | negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X3,X1)))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_16,hypothesis,
    negate(add(d,negate(add(e,negate(add(d,negate(e))))))) = negate(add(d,negate(e))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]),c_0_10]) ).

cnf(c_0_17,plain,
    add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
    prove_base_step ).

cnf(c_0_19,axiom,
    multiply(one,X1) = X1,
    one_times_x ).

cnf(c_0_20,hypothesis,
    ( X1 = negate(e)
    | negate(add(negate(e),negate(add(negate(add(d,negate(e))),X1)))) != negate(add(X1,d)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_13]) ).

cnf(c_0_21,hypothesis,
    negate(add(negate(add(d,negate(e))),negate(add(e,add(d,negate(add(d,negate(e)))))))) = d,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_16]),c_0_17]),c_0_10]) ).

cnf(c_0_22,negated_conjecture,
    negate(add(e,add(d,negate(add(d,negate(e)))))) != negate(e),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    ( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
    | negate(add(X1,negate(X2))) != X3
    | ~ positive_integer(X4) ),
    lemma_3_4 ).

cnf(c_0_24,axiom,
    positive_integer(one),
    one ).

cnf(c_0_25,hypothesis,
    negate(add(d,negate(add(e,add(d,negate(add(d,negate(e)))))))) != negate(add(d,negate(e))),
    inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_10]),c_0_22]),c_0_10]) ).

cnf(c_0_26,plain,
    ( negate(add(X1,negate(add(X2,add(X1,X3))))) = X3
    | negate(add(X1,negate(X2))) != X3 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24])]) ).

cnf(c_0_27,hypothesis,
    $false,
    inference(spm,[status(thm)],[c_0_25,c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ROB014-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 07:21:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.69  % Version  : CSE_E---1.5
% 0.19/0.69  % Problem  : theBenchmark.p
% 0.19/0.69  % Proof found
% 0.19/0.69  % SZS status Theorem for theBenchmark.p
% 0.19/0.69  % SZS output start Proof
% See solution above
% 0.19/0.70  % Total time : 0.116000 s
% 0.19/0.70  % SZS output end Proof
% 0.19/0.70  % Total time : 0.118000 s
%------------------------------------------------------------------------------