TSTP Solution File: SET844-2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET844-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 03:07:09 EDT 2024

% Result   : Unsatisfiable 4.82s 2.38s
% Output   : Refutation 4.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   38 (  15 unt;   9 typ;   0 def)
%            Number of atoms       :   62 (  14 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  423 (  30   ~;  27   |;   0   &; 366   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   49 (   0   ^  49   !;   0   ?;  49   :)

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

thf(v_m_type,type,
    v_m: $i ).

thf(c_Zorn_OTFin_type,type,
    c_Zorn_OTFin: $i > $i > $i ).

thf(v_S_type,type,
    v_S: $i ).

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

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(c_Zorn_Osucc_type,type,
    c_Zorn_Osucc: $i > $i > $i > $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_Union_type,type,
    c_Union: $i > $i > $i ).

thf(4,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(12,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
      | ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
      | ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
      | ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(23,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Union @ C @ ( tc_set @ E ) ) @ ( c_Zorn_OTFin @ D @ E ) @ ( tc_set @ ( tc_set @ E ) ) )
      | ( ( c_lessequals @ A @ A @ ( tc_set @ B ) )
       != ( c_lessequals @ C @ ( c_Zorn_OTFin @ D @ E ) @ ( tc_set @ ( tc_set @ ( tc_set @ E ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,14]) ).

thf(24,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( c_Zorn_OTFin @ F @ I )),bind(B,$thf( tc_set @ ( tc_set @ I ) )),bind(C,$thf( c_Zorn_OTFin @ F @ I )),bind(D,$thf( F )),bind(E,$thf( I ))]]) ).

thf(25,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
    inference(simp,[status(thm)],[24]) ).

thf(1,negated_conjecture,
    c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(7,plain,
    c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ 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_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( A
       != ( c_Zorn_Osucc @ B @ A @ C ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).

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

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

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

thf(34,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Zorn_Osucc @ B @ A @ C )
       != A )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( ( c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
       != ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,17]) ).

thf(35,plain,
    ! [A: $i] :
      ( ( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
       != v_m )
      | ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
      | ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( v_m )),bind(B,$thf( v_S )),bind(C,$thf( t_a ))]]) ).

thf(43,plain,
    ! [A: $i] :
      ( ( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
       != v_m )
      | ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
      | ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    inference(simp,[status(thm)],[35]) ).

thf(2,negated_conjecture,
    ( v_m
    = ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(8,plain,
    ( v_m
    = ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
    = v_m ),
    inference(lifteq,[status(thm)],[8]) ).

thf(77,plain,
    ! [A: $i] :
      ( ( v_m != v_m )
      | ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
      | ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    inference(rewrite,[status(thm)],[43,10]) ).

thf(78,plain,
    ! [A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
      | ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    inference(simp,[status(thm)],[77]) ).

thf(84,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ C @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) )
      | ( ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) )
       != ( c_in @ C @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[25,78]) ).

thf(85,plain,
    c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ),
    inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( v_S )),bind(B,$thf( t_a )),bind(C,$thf( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ))]]) ).

thf(3,negated_conjecture,
    ~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(9,plain,
    ~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(89,plain,
    $false,
    inference(rewrite,[status(thm)],[85,11]) ).

thf(90,plain,
    $false,
    inference(simp,[status(thm)],[89]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SET844-2 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n008.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon May 20 12:54:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.84/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/1.02  % [INFO] 	 Parsing done (110ms). 
% 1.15/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.52/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.52/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.63/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.79/1.37  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.85/1.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.38  % [INFO] 	 Type checking passed. 
% 1.85/1.38  % [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 ... 
% 4.82/2.37  % [INFO] 	 Killing All external provers ... 
% 4.82/2.38  % Time passed: 1900ms (effective reasoning time: 1340ms)
% 4.82/2.38  % Axioms used in derivation (3): cls_Set_Osubset__refl_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_Oeq__succ__upper_0
% 4.82/2.38  % No. of inferences in proof: 29
% 4.82/2.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1900 ms resp. 1340 ms w/o parsing
% 4.82/2.45  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.82/2.45  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------