TSTP Solution File: SYN075-1 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SYN075-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n032.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 : Mon Jun 24 19:53:12 EDT 2024

% Result   : Unsatisfiable 9.20s 2.67s
% Output   : Refutation 9.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   57 (   7 unt;   0 typ;   0 def)
%            Number of atoms       :  152 ( 108 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  420 (  78   ~;  87   |;   0   &; 255   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   89 (   0   ^  89   !;   0   ?;  89   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_f_type,type,
    big_f: $i > $i > $o ).

thf(f_type,type,
    f: $i > $i ).

thf(g_type,type,
    g: $i > $i ).

thf(h_type,type,
    h: $i > $i > $i ).

thf(a_type,type,
    a: $i ).

thf(b_type,type,
    b: $i ).

thf(3,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( A
       != ( g @ B ) )
      | ( big_f @ A @ ( f @ B ) )
      | ( ( f @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( g @ B ) )
      | ( big_f @ A @ ( f @ B ) )
      | ( ( f @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( g @ B ) )
      | ( big_f @ A @ ( f @ B ) )
      | ( ( f @ B )
        = B ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( g @ B ) )
      | ( ( f @ B )
        = B )
      | ( big_f @ A @ ( f @ B ) ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(30,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ( big_f @ ( g @ A ) @ ( f @ A ) ) ),
    inference(simp,[status(thm)],[29]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( B = b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( B = b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( B = b ) ),
    inference(cnf,[status(esa)],[39]) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ( B = b )
      | ~ ( big_f @ A @ B ) ),
    inference(lifteq,[status(thm)],[40]) ).

thf(323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f @ A )
        = A )
      | ( C = b )
      | ( ( big_f @ ( g @ A ) @ ( f @ A ) )
       != ( big_f @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[30,41]) ).

thf(324,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ( ( f @ A )
        = b ) ),
    inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( E )),bind(B,$thf( g @ E )),bind(C,$thf( f @ E ))]]) ).

thf(352,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ( ( f @ A )
        = b ) ),
    inference(simp,[status(thm)],[324]) ).

thf(716,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ( ( f @ A )
       != ( f @ A ) )
      | ( b != A ) ),
    inference(eqfactor_ordered,[status(thm)],[352]) ).

thf(717,plain,
    ( ( f @ b )
    = b ),
    inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( b ))]]) ).

thf(6,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( big_f @ ( h @ A @ B ) @ ( f @ A ) )
      | ( ( h @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( big_f @ ( h @ A @ B ) @ ( f @ A ) )
      | ( ( h @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( big_f @ ( h @ A @ B ) @ ( f @ A ) )
      | ( ( h @ A @ B )
        = B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
        = B )
      | ( big_f @ ( h @ A @ B ) @ ( f @ A ) ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ( b != A )
      | ( ( h @ A @ B )
        = B )
      | ( big_f @ ( h @ A @ B ) @ ( f @ A ) )
      | ( ( f @ b )
       != ( f @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[717,21]) ).

thf(772,plain,
    ! [A: $i] :
      ( ( b != b )
      | ( ( h @ b @ A )
        = A )
      | ( big_f @ ( h @ b @ A ) @ ( f @ b ) ) ),
    inference(pattern_uni,[status(thm)],[771:[bind(A,$thf( b ))]]) ).

thf(781,plain,
    ! [A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( big_f @ ( h @ b @ A ) @ ( f @ b ) ) ),
    inference(simp,[status(thm)],[772]) ).

thf(1,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ ( f @ B ) )
      | ( A
       != ( g @ B ) )
      | ( ( f @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ ( f @ B ) )
      | ( A
       != ( g @ B ) )
      | ( ( f @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ ( f @ B ) )
      | ( A
       != ( g @ B ) )
      | ( ( f @ B )
        = B ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( g @ B ) )
      | ( ( f @ B )
        = B )
      | ~ ( big_f @ A @ ( f @ B ) ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(27,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ~ ( big_f @ ( g @ A ) @ ( f @ A ) ) ),
    inference(simp,[status(thm)],[26]) ).

thf(1342,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
        = A )
      | ( ( f @ B )
        = B )
      | ( ( big_f @ ( g @ A ) @ ( f @ A ) )
       != ( big_f @ ( g @ B ) @ ( f @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,27]) ).

thf(1343,plain,
    ! [A: $i] :
      ( ( ( f @ A )
        = A )
      | ( ( f @ A )
        = A ) ),
    inference(pattern_uni,[status(thm)],[1342:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(1410,plain,
    ! [A: $i] :
      ( ( f @ A )
      = A ),
    inference(simp,[status(thm)],[1343]) ).

thf(1693,plain,
    ! [A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( big_f @ ( h @ b @ A ) @ b ) ),
    inference(rewrite,[status(thm)],[781,1410]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( A = a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( A = a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ A @ B )
      | ( A = a ) ),
    inference(cnf,[status(esa)],[36]) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ( A = a )
      | ~ ( big_f @ A @ B ) ),
    inference(lifteq,[status(thm)],[37]) ).

thf(1695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( B = a )
      | ( ( big_f @ ( h @ b @ A ) @ b )
       != ( big_f @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1693,38]) ).

thf(1696,plain,
    ! [A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( ( h @ b @ A )
        = a ) ),
    inference(pattern_uni,[status(thm)],[1695:[bind(A,$thf( E )),bind(B,$thf( h @ b @ E )),bind(C,$thf( b ))]]) ).

thf(1744,plain,
    ! [A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( ( h @ b @ A )
        = a ) ),
    inference(simp,[status(thm)],[1696]) ).

thf(1823,plain,
    ! [A: $i] :
      ( ( ( h @ b @ A )
        = A )
      | ( ( h @ b @ A )
       != ( h @ b @ A ) )
      | ( a != A ) ),
    inference(eqfactor_ordered,[status(thm)],[1744]) ).

thf(1826,plain,
    ( ( h @ b @ a )
    = a ),
    inference(pattern_uni,[status(thm)],[1823:[bind(A,$thf( a ))]]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( A != a )
      | ( B != b )
      | ( big_f @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( A != a )
      | ( B != b )
      | ( big_f @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ( A != a )
      | ( B != b )
      | ( big_f @ A @ B ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( A != a )
      | ( B != b )
      | ( big_f @ A @ B ) ),
    inference(lifteq,[status(thm)],[43]) ).

thf(45,plain,
    big_f @ a @ b,
    inference(simp,[status(thm)],[44]) ).

thf(7,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ~ ( big_f @ ( h @ A @ B ) @ ( f @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ~ ( big_f @ ( h @ A @ B ) @ ( f @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ~ ( big_f @ ( h @ A @ B ) @ ( f @ A ) ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ~ ( big_f @ ( h @ A @ B ) @ ( f @ A ) ) ),
    inference(lifteq,[status(thm)],[34]) ).

thf(89,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ( ( big_f @ ( h @ A @ B ) @ ( f @ A ) )
       != ( big_f @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[45,35]) ).

thf(91,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ A )
       != A )
      | ( ( h @ A @ B )
       != B )
      | ( ( h @ A @ B )
       != a )
      | ( ( f @ A )
       != b ) ),
    inference(simp,[status(thm)],[89]) ).

thf(2063,plain,
    ! [B: $i,A: $i] :
      ( ( A != A )
      | ( ( h @ A @ B )
       != B )
      | ( ( h @ A @ B )
       != a )
      | ( A != b ) ),
    inference(rewrite,[status(thm)],[91,1410]) ).

thf(2064,plain,
    ! [B: $i,A: $i] :
      ( ( ( h @ A @ B )
       != B )
      | ( ( h @ A @ B )
       != a )
      | ( A != b ) ),
    inference(simp,[status(thm)],[2063]) ).

thf(2066,plain,
    ! [B: $i,A: $i] :
      ( ( a != B )
      | ( ( h @ A @ B )
       != a )
      | ( A != b )
      | ( ( h @ b @ a )
       != ( h @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1826,2064]) ).

thf(2067,plain,
    ( ( a != a )
    | ( ( h @ b @ a )
     != a )
    | ( b != b ) ),
    inference(pattern_uni,[status(thm)],[2066:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).

thf(2111,plain,
    ( ( h @ b @ a )
   != a ),
    inference(simp,[status(thm)],[2067]) ).

thf(2120,plain,
    a != a,
    inference(rewrite,[status(thm)],[2111,1826]) ).

thf(2121,plain,
    $false,
    inference(simp,[status(thm)],[2120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SYN075-1 : TPTP v8.2.0. Released v1.0.0.
% 0.02/0.10  % Command  : run_Leo-III %s %d SAT
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Sun Jun 23 22:53:40 EDT 2024
% 0.10/0.29  % CPUTime  : 
% 0.79/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.03/0.88  % [INFO] 	 Parsing done (111ms). 
% 1.03/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.35/1.10  % [INFO] 	 nitpick registered as external prover. 
% 1.35/1.10  % [INFO] 	 Scanning for conjecture ... 
% 1.53/1.16  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.63/1.20  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.63/1.20  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.63/1.20  % [INFO] 	 Type checking passed. 
% 1.63/1.21  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 9.20/2.66  % [INFO] 	 Killing All external provers ... 
% 9.20/2.66  % Time passed: 2221ms (effective reasoning time: 1771ms)
% 9.20/2.66  % Axioms used in derivation (3): clause_2, clause_1, clause_3
% 9.20/2.66  % No. of inferences in proof: 57
% 9.20/2.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2221 ms resp. 1771 ms w/o parsing
% 9.20/2.73  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.20/2.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------