TSTP Solution File: NUN133-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n014.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 12:46:07 EDT 2023

% Result   : Unsatisfiable 274.13s 274.00s
% Output   : CNFRefutation 274.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   45 (  37 unt;   8 typ;   0 def)
%            Number of atoms       :   37 (  36 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   57 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    s: $i > $i ).

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

tff(decl_28,type,
    cubes: $i > $i ).

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

cnf(sum_s,axiom,
    sum(s(X1)) = '+'(s(X1),sum(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).

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

cnf(goal,negated_conjecture,
    times(sum(s(a)),sum(s(a))) != cubes(s(a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(cubes_s,axiom,
    cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).

cnf(times_s,axiom,
    times(s(X1),X2) = '+'(X2,times(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).

cnf(plus_sum,axiom,
    '+'(sum(X1),sum(X1)) = times(X1,s(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).

cnf(induction_hypothesis,axiom,
    times(sum(a),sum(a)) = cubes(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_hypothesis) ).

cnf(plus_assoc,axiom,
    '+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).

cnf(distr,axiom,
    times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).

cnf(distr_001,axiom,
    times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr_001) ).

cnf(times_one,axiom,
    times(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).

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

cnf(times_assoc,axiom,
    times(X1,times(X2,X3)) = times(times(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_assoc) ).

cnf(c_0_13,axiom,
    sum(s(X1)) = '+'(s(X1),sum(X1)),
    sum_s ).

cnf(c_0_14,axiom,
    '+'(X1,X2) = '+'(X2,X1),
    plus_comm ).

cnf(c_0_15,negated_conjecture,
    times(sum(s(a)),sum(s(a))) != cubes(s(a)),
    goal ).

cnf(c_0_16,plain,
    sum(s(X1)) = '+'(sum(X1),s(X1)),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,axiom,
    cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
    cubes_s ).

cnf(c_0_18,axiom,
    times(s(X1),X2) = '+'(X2,times(X1,X2)),
    times_s ).

cnf(c_0_19,axiom,
    '+'(sum(X1),sum(X1)) = times(X1,s(X1)),
    plus_sum ).

cnf(c_0_20,negated_conjecture,
    cubes(s(a)) != times('+'(sum(a),s(a)),'+'(sum(a),s(a))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

cnf(c_0_21,plain,
    cubes(s(X1)) = '+'(cubes(X1),'+'('+'('+'(sum(X1),sum(X1)),s(X1)),times(X1,'+'('+'(sum(X1),sum(X1)),s(X1))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_14]),c_0_18]),c_0_14]) ).

cnf(c_0_22,axiom,
    times(sum(a),sum(a)) = cubes(a),
    induction_hypothesis ).

cnf(c_0_23,negated_conjecture,
    times('+'(sum(a),s(a)),'+'(sum(a),s(a))) != '+'(times(sum(a),sum(a)),'+'('+'('+'(sum(a),sum(a)),s(a)),times(a,'+'('+'(sum(a),sum(a)),s(a))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_24,axiom,
    '+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
    plus_assoc ).

cnf(c_0_25,axiom,
    times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
    distr ).

cnf(c_0_26,axiom,
    times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
    distr_001 ).

cnf(c_0_27,axiom,
    times(X1,one) = X1,
    times_one ).

cnf(c_0_28,axiom,
    times(X1,X2) = times(X2,X1),
    times_comm ).

cnf(c_0_29,axiom,
    times(X1,times(X2,X3)) = times(times(X1,X2),X3),
    times_assoc ).

cnf(c_0_30,negated_conjecture,
    '+'(sum(a),'+'(times(a,sum(a)),'+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(s(a),times(sum(a),s(a)))))))) != '+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),s(a)))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_26]),c_0_18]),c_0_14]),c_0_24]),c_0_26]),c_0_18]),c_0_19]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_25]),c_0_19]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]) ).

cnf(c_0_31,plain,
    s(X1) = '+'(one,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_27]) ).

cnf(c_0_32,plain,
    '+'(X1,X2) = '+'(X2,X1),
    c_0_14 ).

cnf(c_0_33,plain,
    times(X1,X2) = times(X2,X1),
    c_0_28 ).

cnf(c_0_34,plain,
    '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
    c_0_24 ).

cnf(c_0_35,plain,
    times(times(X1,X2),X3) = times(X1,times(X2,X3)),
    c_0_29 ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_25]),c_0_27]),c_0_28]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_31]),c_0_14]),c_0_24]),c_0_14]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_32,c_0_33,c_0_34,c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n014.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   : Sun Aug 27 09:53:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 274.13/274.00  % Version  : CSE_E---1.5
% 274.13/274.00  % Problem  : theBenchmark.p
% 274.13/274.00  % Proof found
% 274.13/274.00  % SZS status Theorem for theBenchmark.p
% 274.13/274.00  % SZS output start Proof
% See solution above
% 274.13/274.01  % Total time : 273.453000 s
% 274.13/274.01  % SZS output end Proof
% 274.13/274.01  % Total time : 273.469000 s
%------------------------------------------------------------------------------