TSTP Solution File: LCL446-2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL446-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 00:10:03 EDT 2024

% Result   : Unsatisfiable 9.91s 2.71s
% Output   : Refutation 9.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   30 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :   47 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  480 (  20   ~;  16   |;   0   &; 444   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   95 (   0   ^  95   !;   0   ?;  95   :)

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

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

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

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

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

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

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

thf(1,negated_conjecture,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_p @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(5,plain,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_p @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,plain,
    ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_p @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OK_0) ).

thf(7,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ C @ D ) @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ B @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ C @ D ) @ D ) @ D ) @ ( c_PropLog_Othms @ E @ D ) @ ( tc_PropLog_Opl @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OS_0) ).

thf(10,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ C @ D ) @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ B @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ C @ D ) @ D ) @ D ) @ ( c_PropLog_Othms @ E @ D ) @ ( tc_PropLog_Opl @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,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 @ A @ D @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ D @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).

thf(8,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 @ A @ D @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ D @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,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 @ A @ D @ C ) @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ D @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(31,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ F @ ( c_PropLog_Othms @ G @ H ) @ ( tc_PropLog_Opl @ H ) )
      | ( c_in @ I @ ( c_PropLog_Othms @ G @ H ) @ ( tc_PropLog_Opl @ H ) )
      | ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ C @ D ) @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ B @ D ) @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ C @ D ) @ D ) @ D ) @ ( c_PropLog_Othms @ E @ D ) @ ( tc_PropLog_Opl @ D ) )
       != ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ F @ I @ H ) @ ( c_PropLog_Othms @ G @ H ) @ ( tc_PropLog_Opl @ H ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,9]) ).

thf(32,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ ( c_PropLog_Opl_Oop_A_N_62 @ C @ E @ B ) @ B ) @ ( c_PropLog_Othms @ A @ B ) @ ( tc_PropLog_Opl @ B ) )
      | ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ C @ B ) @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ E @ B ) @ B ) @ ( c_PropLog_Othms @ A @ B ) @ ( tc_PropLog_Opl @ B ) ) ),
    inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( V )),bind(B,$thf( T )),bind(C,$thf( W )),bind(D,$thf( R )),bind(E,$thf( E )),bind(F,$thf( c_PropLog_Opl_Oop_A_N_62 @ V @ ( c_PropLog_Opl_Oop_A_N_62 @ T @ W @ R ) @ R )),bind(G,$thf( E )),bind(H,$thf( R )),bind(I,$thf( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ V @ T @ R ) @ ( c_PropLog_Opl_Oop_A_N_62 @ V @ W @ R ) @ R ))]]) ).

thf(40,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ ( c_PropLog_Opl_Oop_A_N_62 @ C @ E @ B ) @ B ) @ ( c_PropLog_Othms @ A @ B ) @ ( tc_PropLog_Opl @ B ) )
      | ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ C @ B ) @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ E @ B ) @ B ) @ ( c_PropLog_Othms @ A @ B ) @ ( tc_PropLog_Opl @ B ) ) ),
    inference(simp,[status(thm)],[32]) ).

thf(227,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ H @ G @ F ) @ ( c_PropLog_Opl_Oop_A_N_62 @ H @ I @ F ) @ F ) @ ( c_PropLog_Othms @ E @ F ) @ ( tc_PropLog_Opl @ F ) )
      | ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) )
       != ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ H @ ( c_PropLog_Opl_Oop_A_N_62 @ G @ I @ F ) @ F ) @ ( c_PropLog_Othms @ E @ F ) @ ( tc_PropLog_Opl @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,40]) ).

thf(228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ B @ C ) @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ),
    inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( C )),bind(G,$thf( B )),bind(H,$thf( A )),bind(I,$thf( A ))]]) ).

thf(33,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ E @ H @ G ) @ ( c_PropLog_Othms @ F @ G ) @ ( tc_PropLog_Opl @ G ) )
      | ( c_in @ H @ ( c_PropLog_Othms @ F @ G ) @ ( tc_PropLog_Opl @ G ) )
      | ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) )
       != ( c_in @ E @ ( c_PropLog_Othms @ F @ G ) @ ( tc_PropLog_Opl @ G ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,9]) ).

thf(34,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ E @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ E @ C ) @ C ) @ B @ C ) @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ B @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( M )),bind(B,$thf( L )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( c_PropLog_Opl_Oop_A_N_62 @ M @ ( c_PropLog_Opl_Oop_A_N_62 @ L @ M @ K ) @ K )),bind(F,$thf( D )),bind(G,$thf( K )),bind(H,$thf( H ))]]) ).

thf(41,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ E @ ( c_PropLog_Opl_Oop_A_N_62 @ D @ E @ C ) @ C ) @ B @ C ) @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ( c_in @ B @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(simp,[status(thm)],[34]) ).

thf(380,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ F @ ( c_PropLog_Othms @ E @ G ) @ ( tc_PropLog_Opl @ G ) )
      | ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ B @ C ) @ ( c_PropLog_Opl_Oop_A_N_62 @ A @ A @ C ) @ C ) @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) )
       != ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ I @ ( c_PropLog_Opl_Oop_A_N_62 @ H @ I @ G ) @ G ) @ F @ G ) @ ( c_PropLog_Othms @ E @ G ) @ ( tc_PropLog_Opl @ G ) ) ) ),
    inference(paramod_ordered,[status(thm)],[228,41]) ).

thf(381,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ B @ C ) @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) ),
    inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( N )),bind(B,$thf( c_PropLog_Opl_Oop_A_N_62 @ J @ N @ O )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( c_PropLog_Opl_Oop_A_N_62 @ N @ N @ O )),bind(G,$thf( O )),bind(H,$thf( J )),bind(I,$thf( N ))]]) ).

thf(414,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ B @ C ) @ ( c_PropLog_Othms @ A @ C ) @ ( tc_PropLog_Opl @ C ) ),
    inference(simp,[status(thm)],[381]) ).

thf(416,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[6,414]) ).

thf(417,plain,
    $false,
    inference(simp,[status(thm)],[416]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : LCL446-2 : TPTP v8.2.0. Released v3.2.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 02:55:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/0.95  % [INFO] 	 Parsing done (98ms). 
% 1.22/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.59/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.71/1.23  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.85/1.24  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.24  % [INFO] 	 Type checking passed. 
% 1.85/1.24  % [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 ... 
% 9.91/2.70  % [INFO] 	 Killing All external provers ... 
% 9.91/2.71  % Time passed: 2182ms (effective reasoning time: 1736ms)
% 9.91/2.71  % Axioms used in derivation (3): cls_PropLog_Othms_OK_0, cls_PropLog_Othms_OS_0, cls_PropLog_Othms_OMP_0
% 9.91/2.71  % No. of inferences in proof: 23
% 9.91/2.71  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2182 ms resp. 1736 ms w/o parsing
% 9.96/2.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.96/2.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------