TSTP Solution File: SWW409-1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW409-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n012.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 18:25:05 EDT 2024

% Result   : Unsatisfiable 178.76s 30.90s
% Output   : Refutation 178.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   62 (  37 unt;   0 typ;   0 def)
%            Number of atoms       :   98 (  48 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  802 (  38   ~;  32   |;   0   &; 732   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  139 (   0   ^ 139   !;   0   ?; 139   :)

% Comments : 
%------------------------------------------------------------------------------
thf(heap_type,type,
    heap: $i > $o ).

thf(sep_type,type,
    sep: $i > $i > $i ).

thf(lseg_type,type,
    lseg: $i > $i > $i ).

thf(x2_type,type,
    x2: $i ).

thf(nil_type,type,
    nil: $i ).

thf(emp_type,type,
    emp: $i ).

thf(x1_type,type,
    x1: $i ).

thf(x3_type,type,
    x3: $i ).

thf(next_type,type,
    next: $i > $i > $i ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).

thf(50,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(51,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(lifteq,[status(thm)],[50]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).

thf(23,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(176,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( sep @ D @ ( sep @ C @ E ) ) )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ C @ ( sep @ D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[51,24]) ).

thf(177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( G )),bind(B,$thf( sep @ H @ I )),bind(C,$thf( lseg @ G @ G )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).

thf(263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(simp,[status(thm)],[177]) ).

thf(1030,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ B @ C )
        = E )
      | ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
       != ( sep @ ( lseg @ D @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[263,51]) ).

thf(1031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(pattern_uni,[status(thm)],[1030:[bind(A,$thf( K )),bind(B,$thf( lseg @ G @ G )),bind(C,$thf( I )),bind(D,$thf( G )),bind(E,$thf( sep @ ( lseg @ K @ K ) @ I ))]]) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(simp,[status(thm)],[1031]) ).

thf(11357,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ ( lseg @ C @ C ) @ B )
        = E )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ ( lseg @ D @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[1077,51]) ).

thf(11358,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[11357:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(11569,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(simp,[status(thm)],[11358]) ).

thf(67,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ D @ ( sep @ B @ ( sep @ A @ C ) ) )
        = ( sep @ E @ ( sep @ D @ F ) ) )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ E @ F ) ) ),
    inference(paramod_ordered,[status(thm)],[24,24]) ).

thf(68,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
      = ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ),
    inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( sep @ G @ H ))]]) ).

thf(115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
      = ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ),
    inference(simp,[status(thm)],[68]) ).

thf(5,axiom,
    heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).

thf(28,plain,
    heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(78,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) ) )
      | ( ( sep @ B @ ( sep @ A @ C ) )
       != ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[24,28]) ).

thf(100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) ) )
      | ( B
       != ( next @ x1 @ x3 ) )
      | ( ( sep @ A @ C )
       != emp ) ),
    inference(simp,[status(thm)],[78]) ).

thf(116,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ A @ ( sep @ ( next @ x1 @ x3 ) @ B ) ) ) ) )
      | ( ( sep @ A @ B )
       != emp ) ),
    inference(simp,[status(thm)],[100]) ).

thf(23710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ C @ ( sep @ ( next @ x1 @ x3 ) @ D ) ) ) ) )
      | ( A != emp )
      | ( ( sep @ ( lseg @ B @ B ) @ A )
       != ( sep @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[11569,116]) ).

thf(23711,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ B @ B ) @ ( sep @ ( next @ x1 @ x3 ) @ A ) ) ) ) )
      | ( A != emp ) ),
    inference(pattern_uni,[status(thm)],[23710:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( lseg @ F @ F )),bind(D,$thf( A ))]]) ).

thf(23925,plain,
    ! [A: $i] : ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ) ) ),
    inference(simp,[status(thm)],[23711]) ).

thf(24750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) ) ) )
      | ( ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) )
       != ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ E @ E ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[115,23925]) ).

thf(24751,plain,
    ! [A: $i] : ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[24750:[bind(A,$thf( lseg @ x3 @ nil )),bind(B,$thf( lseg @ I @ I )),bind(C,$thf( next @ x1 @ x3 )),bind(D,$thf( emp )),bind(E,$thf( I ))]]) ).

thf(25340,plain,
    ! [A: $i] : ( heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ),
    inference(simp,[status(thm)],[24751]) ).

thf(31432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) )
      | ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
       != ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ E @ E ) @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[115,25340]) ).

thf(31433,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[31432:[bind(A,$thf( next @ x1 @ x3 )),bind(B,$thf( lseg @ x2 @ x1 )),bind(C,$thf( lseg @ I @ I )),bind(D,$thf( sep @ ( lseg @ x3 @ nil ) @ emp )),bind(E,$thf( I ))]]) ).

thf(32051,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ),
    inference(simp,[status(thm)],[31433]) ).

thf(49277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ) )
      | ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
       != ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ E @ E ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[115,32051]) ).

thf(49278,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[49277:[bind(A,$thf( lseg @ x3 @ nil )),bind(B,$thf( lseg @ x2 @ x1 )),bind(C,$thf( lseg @ I @ I )),bind(D,$thf( emp )),bind(E,$thf( I ))]]) ).

thf(49905,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ) ),
    inference(simp,[status(thm)],[49278]) ).

thf(83588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ A ) ) ) )
      | ( ( sep @ ( lseg @ B @ B ) @ A )
       != ( sep @ ( lseg @ C @ C ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[11569,49905]) ).

thf(83589,plain,
    heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[83588:[bind(A,$thf( emp )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_2) ).

thf(44,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(45,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    inference(cnf,[status(esa)],[44]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    inference(lifteq,[status(thm)],[45]) ).

thf(84705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) )
      | ( ( heap @ ( sep @ ( next @ x1 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ emp ) ) ) )
       != ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[83589,46]) ).

thf(84706,plain,
    ( ( x3 = x1 )
    | ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ ( sep @ ( lseg @ x2 @ x1 ) @ emp ) ) ) ),
    inference(pattern_uni,[status(thm)],[84705:[bind(A,$thf( x1 )),bind(B,$thf( x3 )),bind(C,$thf( nil )),bind(D,$thf( sep @ ( lseg @ x2 @ x1 ) @ emp ))]]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_3) ).

thf(58,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(59,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(1,negated_conjecture,
    ~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).

thf(18,plain,
    ~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(19,plain,
    ~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ),
    inference(polarity_switch,[status(thm)],[18]) ).

thf(12787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) )
       != ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ) ) ),
    inference(paramod_ordered,[status(thm)],[59,19]) ).

thf(12788,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ x2 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[12787:[bind(A,$thf( x2 )),bind(B,$thf( B )),bind(C,$thf( emp ))]]) ).

thf(12938,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ x2 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
    inference(simp,[status(thm)],[12788]) ).

thf(13571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ B @ ( sep @ A @ C ) ) )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ ( lseg @ x2 @ D ) @ ( sep @ ( lseg @ D @ nil ) @ emp ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,12938]) ).

thf(13572,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x2 @ A ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[13571:[bind(A,$thf( lseg @ x2 @ G )),bind(B,$thf( lseg @ G @ nil )),bind(C,$thf( emp )),bind(D,$thf( G ))]]) ).

thf(13767,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x2 @ A ) @ emp ) ) ),
    inference(simp,[status(thm)],[13572]) ).

thf(85461,plain,
    ( ( x3 = x1 )
    | $false ),
    inference(rewrite,[status(thm)],[84706,13767]) ).

thf(85462,plain,
    x3 = x1,
    inference(simp,[status(thm)],[85461]) ).

thf(2,axiom,
    x1 != x3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).

thf(20,plain,
    x1 != x3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(21,plain,
    x1 != x3,
    inference(polarity_switch,[status(thm)],[20]) ).

thf(22,plain,
    x3 != x1,
    inference(lifteq,[status(thm)],[21]) ).

thf(85463,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[85462,22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW409-1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d SAT
% 0.11/0.31  % Computer : n012.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Wed Jun 19 07:48:25 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.86/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.94  % [INFO] 	 Parsing done (107ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.14  % [INFO] 	 nitpick registered as external prover. 
% 1.49/1.14  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ... 
% 1.84/1.23  % [INFO] 	 Axiom selection finished. Selected 16 axioms (removed 0 axioms). 
% 1.97/1.25  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.97/1.26  % [INFO] 	 Type checking passed. 
% 1.97/1.26  % [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 ... 
% 178.76/30.90  % [INFO] 	 Killing All external provers ... 
% 178.76/30.90  % Time passed: 30400ms (effective reasoning time: 29950ms)
% 178.76/30.90  % Axioms used in derivation (6): premise_5, associative_commutative, normalization, unfolding_3, premise_3, unfolding_2
% 178.76/30.90  % No. of inferences in proof: 62
% 178.76/30.90  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 30400 ms resp. 29950 ms w/o parsing
% 178.76/30.94  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 178.76/30.94  % [INFO] 	 Killing All external provers ... 
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