TSTP Solution File: SYN310-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN310-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 : Tue May 21 08:17:57 EDT 2024

% Result   : Unsatisfiable 11.56s 3.80s
% Output   : Refutation 11.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   49 (  19 unt;   6 typ;   0 def)
%            Number of atoms       :   91 (  12 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  368 (  27   ~;  24   |;   0   &; 317   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   72 (   0   ^  72   !;   0   ?;  72   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p_type,type,
    p: $i > $i > $i > $o ).

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

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

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

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

thf(c_type,type,
    c: $i ).

thf(6,negated_conjecture,
    p @ ( f @ ( g @ a ) ) @ ( f @ ( g @ b ) ) @ ( f @ ( g @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).

thf(9,plain,
    p @ ( f @ ( g @ a ) ) @ ( f @ ( g @ b ) ) @ ( f @ ( g @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ ( f @ A ) @ B @ C )
      | ( p @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ ( f @ A ) @ B @ C )
      | ( p @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ ( f @ A ) @ B @ C )
      | ( p @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(52,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ ( f @ ( g @ a ) ) @ ( f @ ( g @ b ) ) @ ( f @ ( g @ c ) ) )
       != ( p @ ( f @ A ) @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9,14]) ).

thf(53,plain,
    p @ ( g @ a ) @ ( f @ ( g @ b ) ) @ ( f @ ( g @ c ) ),
    inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( g @ a )),bind(B,$thf( f @ ( g @ b ) )),bind(C,$thf( f @ ( g @ c ) ))]]) ).

thf(2,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ B @ A @ C ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ B @ A @ C )
      | ( ( p @ ( g @ a ) @ ( f @ ( g @ b ) ) @ ( f @ ( g @ c ) ) )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[53,13]) ).

thf(68,plain,
    p @ ( f @ ( g @ b ) ) @ ( g @ a ) @ ( f @ ( g @ c ) ),
    inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( g @ a )),bind(B,$thf( f @ ( g @ b ) )),bind(C,$thf( f @ ( g @ c ) ))]]) ).

thf(102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ ( f @ ( g @ b ) ) @ ( g @ a ) @ ( f @ ( g @ c ) ) )
       != ( p @ ( f @ A ) @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[68,14]) ).

thf(103,plain,
    p @ ( g @ b ) @ ( g @ a ) @ ( f @ ( g @ c ) ),
    inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( g @ b )),bind(B,$thf( g @ a )),bind(C,$thf( f @ ( g @ c ) ))]]) ).

thf(1,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ C )
      | ( p @ C @ B @ A ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ C @ B @ A )
      | ( ( p @ ( g @ b ) @ ( g @ a ) @ ( f @ ( g @ c ) ) )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[103,17]) ).

thf(114,plain,
    p @ ( f @ ( g @ c ) ) @ ( g @ a ) @ ( g @ b ),
    inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( g @ b )),bind(B,$thf( g @ a )),bind(C,$thf( f @ ( g @ c ) ))]]) ).

thf(167,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ ( f @ ( g @ c ) ) @ ( g @ a ) @ ( g @ b ) )
       != ( p @ ( f @ A ) @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[114,14]) ).

thf(168,plain,
    p @ ( g @ c ) @ ( g @ a ) @ ( g @ b ),
    inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( g @ c )),bind(B,$thf( g @ a )),bind(C,$thf( g @ b ))]]) ).

thf(3,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ ( g @ C ) )
      | ( p @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ ( g @ C ) )
      | ( p @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p @ A @ B @ ( g @ C ) )
      | ( p @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(182,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ ( g @ c ) @ ( g @ a ) @ ( g @ b ) )
       != ( p @ A @ B @ ( g @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[168,16]) ).

thf(183,plain,
    p @ ( g @ c ) @ ( g @ a ) @ b,
    inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( g @ c )),bind(B,$thf( g @ a )),bind(C,$thf( b ))]]) ).

thf(191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ C @ B @ A )
      | ( ( p @ ( g @ c ) @ ( g @ a ) @ b )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[183,17]) ).

thf(192,plain,
    p @ b @ ( g @ a ) @ ( g @ c ),
    inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( g @ c )),bind(B,$thf( g @ a )),bind(C,$thf( b ))]]) ).

thf(217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ b @ ( g @ a ) @ ( g @ c ) )
       != ( p @ A @ B @ ( g @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[192,16]) ).

thf(218,plain,
    p @ b @ ( g @ a ) @ c,
    inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( b )),bind(B,$thf( g @ a )),bind(C,$thf( c ))]]) ).

thf(224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ B @ A @ C )
      | ( ( p @ b @ ( g @ a ) @ c )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[218,13]) ).

thf(225,plain,
    p @ ( g @ a ) @ b @ c,
    inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( b )),bind(B,$thf( g @ a )),bind(C,$thf( c ))]]) ).

thf(239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ C @ B @ A )
      | ( ( p @ ( g @ a ) @ b @ c )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[225,17]) ).

thf(240,plain,
    p @ c @ b @ ( g @ a ),
    inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( g @ a )),bind(B,$thf( b )),bind(C,$thf( c ))]]) ).

thf(319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ A @ B @ C )
      | ( ( p @ c @ b @ ( g @ a ) )
       != ( p @ A @ B @ ( g @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[240,16]) ).

thf(320,plain,
    p @ c @ b @ a,
    inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( c )),bind(B,$thf( b )),bind(C,$thf( a ))]]) ).

thf(336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p @ C @ B @ A )
      | ( ( p @ c @ b @ a )
       != ( p @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[320,17]) ).

thf(337,plain,
    p @ a @ b @ c,
    inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( c )),bind(B,$thf( b )),bind(C,$thf( a ))]]) ).

thf(5,negated_conjecture,
    ~ ( p @ a @ b @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).

thf(7,plain,
    ~ ( p @ a @ b @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,plain,
    ~ ( p @ a @ b @ c ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(441,plain,
    $false,
    inference(rewrite,[status(thm)],[337,15]) ).

thf(442,plain,
    $false,
    inference(simp,[status(thm)],[441]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN310-1 : TPTP v8.2.0. Released v1.2.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n018.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Mon May 20 15:17:09 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 1.24/1.13  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.51/1.29  % [INFO] 	 Parsing done (164ms). 
% 1.51/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.10/1.71  % [INFO] 	 nitpick registered as external prover. 
% 2.10/1.72  % [INFO] 	 Scanning for conjecture ... 
% 2.36/1.83  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.43/1.88  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.43/1.88  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.43/1.88  % [INFO] 	 Type checking passed. 
% 2.43/1.88  % [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 ... 
% 11.56/3.79  % [INFO] 	 Killing All external provers ... 
% 11.56/3.79  % Time passed: 3228ms (effective reasoning time: 2473ms)
% 11.56/3.80  % Axioms used in derivation (0): 
% 11.56/3.80  % No. of inferences in proof: 43
% 11.56/3.80  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3228 ms resp. 2473 ms w/o parsing
% 11.84/3.87  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.84/3.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------