TSTP Solution File: LCL434-2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL434-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 00:10:00 EDT 2024

% Result   : Unsatisfiable 7.02s 2.40s
% Output   : Refutation 7.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :   64 (  20 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  335 (  30   ~;  26   |;   0   &; 279   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :   63 (   0   ^  63   !;   0   ?;  63   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(v_pa_type,type,
    v_pa: $i ).

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(v_p_type,type,
    v_p: $i ).

thf(v_H_type,type,
    v_H: $i ).

thf(tc_PropLog_Opl_type,type,
    tc_PropLog_Opl: $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(c_PropLog_Opl_Oop_A_N_62_type,type,
    c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).

thf(c_PropLog_Othms_type,type,
    c_PropLog_Othms: $i > $i > $i ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ A @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__right_0) ).

thf(13,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ A @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ A @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(2,negated_conjecture,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(8,plain,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(624,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ A @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
       != ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,9]) ).

thf(625,plain,
    ~ ( c_in @ v_pa @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(pattern_uni,[status(thm)],[624:[bind(A,$thf( v_pa )),bind(B,$thf( v_H )),bind(C,$thf( t_a )),bind(D,$thf( v_p ))]]) ).

thf(1,negated_conjecture,
    c_in @ v_pa @ ( c_insert @ v_p @ v_H @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_PropLog_Opl @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(7,plain,
    c_in @ v_pa @ ( c_insert @ v_p @ v_H @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_PropLog_Opl @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(16,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(17,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_in @ A @ C @ D )
      | ( ( c_in @ v_pa @ ( c_insert @ v_p @ v_H @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_PropLog_Opl @ t_a ) )
       != ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[7,17]) ).

thf(203,plain,
    ( ( v_p = v_pa )
    | ( c_in @ v_pa @ v_H @ ( tc_PropLog_Opl @ t_a ) ) ),
    inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( v_pa )),bind(B,$thf( v_p )),bind(C,$thf( v_H )),bind(D,$thf( tc_PropLog_Opl @ t_a ))]]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ B ) @ ( c_PropLog_Othms @ C @ B ) @ ( tc_PropLog_Opl @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms__I_0) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ B ) @ ( c_PropLog_Othms @ C @ B ) @ ( tc_PropLog_Opl @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ B ) @ ( c_PropLog_Othms @ C @ B ) @ ( tc_PropLog_Opl @ B ) )
     != ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) ),
    inference(paramod_ordered,[status(thm)],[12,9]) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ B )
       != ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_pa @ t_a ) )
      | ( ( c_PropLog_Othms @ C @ B )
       != ( c_PropLog_Othms @ v_H @ t_a ) )
      | ( ( tc_PropLog_Opl @ B )
       != ( tc_PropLog_Opl @ t_a ) ) ),
    inference(simp,[status(thm)],[21]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != v_p )
      | ( A != v_pa )
      | ( B != t_a )
      | ( C != v_H )
      | ( B != t_a )
      | ( ( tc_PropLog_Opl @ B )
       != ( tc_PropLog_Opl @ t_a ) ) ),
    inference(simp,[status(thm)],[22]) ).

thf(32,plain,
    v_p != v_pa,
    inference(simp,[status(thm)],[25]) ).

thf(300,plain,
    c_in @ v_pa @ v_H @ ( tc_PropLog_Opl @ t_a ),
    inference(simplifyReflect,[status(thm)],[203,32]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( ( c_in @ v_pa @ v_H @ ( tc_PropLog_Opl @ t_a ) )
       != ( c_in @ A @ B @ ( tc_PropLog_Opl @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[300,11]) ).

thf(340,plain,
    c_in @ v_pa @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ),
    inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( v_pa )),bind(B,$thf( v_H )),bind(C,$thf( t_a ))]]) ).

thf(682,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[625,340]) ).

thf(683,plain,
    $false,
    inference(simp,[status(thm)],[682]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL434-2 : TPTP v8.2.0. Released v3.2.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 01:47:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.95/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.14/1.03  % [INFO] 	 Parsing done (109ms). 
% 1.14/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.80/1.30  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.80/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.80/1.31  % [INFO] 	 Type checking passed. 
% 1.80/1.32  % [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 ... 
% 7.02/2.39  % [INFO] 	 Killing All external provers ... 
% 7.02/2.40  % Time passed: 1856ms (effective reasoning time: 1356ms)
% 7.02/2.40  % Axioms used in derivation (4): cls_PropLog_Oweaken__right_0, cls_Set_OinsertE_0, cls_PropLog_Othms__I_0, cls_PropLog_Othms_OH_0
% 7.02/2.40  % No. of inferences in proof: 30
% 7.02/2.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1856 ms resp. 1356 ms w/o parsing
% 7.02/2.43  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.02/2.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------