TSTP Solution File: SYO633-1 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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  7 11:05:27 EDT 2024

% Result   : Unsatisfiable 10.38s 2.87s
% Output   : Refutation 10.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   57 (  14 unt;   5 typ;   0 def)
%            Number of atoms       :  170 (   5 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 1180 ( 130   ~; 108   |;   0   &; 942   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  143 (   0   ^ 143   !;   0   ?; 143   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
    '\'E\'': $i > $i > $o ).

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

thf(s_type,type,
    s: $i > $i ).

thf('\'0\'_type',type,
    '\'0\'': $i ).

thf('\'AP\'_type',type,
    '\'AP\'': $i > $i > $i ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_12) ).

thf(32,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(33,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    inference(cnf,[status(esa)],[32]) ).

thf(4,axiom,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_04) ).

thf(20,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_05) ).

thf(21,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_10) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(151,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ $true
      | ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(rewrite,[status(thm)],[29,20,21]) ).

thf(152,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
    inference(simp,[status(thm)],[151]) ).

thf(809,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    inference(rewrite,[status(thm)],[33,20,21,152]) ).

thf(810,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) ),
    inference(simp,[status(thm)],[809]) ).

thf(9,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_09) ).

thf(26,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(27,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(442,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) ) ),
    inference(rewrite,[status(thm)],[27,20,21,152]) ).

thf(443,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) ) ),
    inference(simp,[status(thm)],[442]) ).

thf(819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ ( s @ '\'0\'' ) )
      | ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
       != ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[810,443]) ).

thf(820,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ '\'0\'' ) ),
    inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).

thf(831,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ '\'0\'' ) ),
    inference(simp,[status(thm)],[820]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_07) ).

thf(23,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(24,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ $true
      | ~ $true
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | ~ $true
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ '\'0\'' ) ),
    inference(rewrite,[status(thm)],[24,20,21,152]) ).

thf(396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ C ) ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[395]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_03) ).

thf(18,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(19,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ $true
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ '\'0\'' )
      | ~ $true ),
    inference(rewrite,[status(thm)],[19,20,21]) ).

thf(37,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[36]) ).

thf(155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ $true
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
    inference(rewrite,[status(thm)],[37,152]) ).

thf(156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[155]) ).

thf(158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[156]) ).

thf(450,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ B ) ) @ ( s @ '\'0\'' ) )
       != ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) ) ) ),
    inference(paramod_ordered,[status(thm)],[443,158]) ).

thf(451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
    inference(pattern_uni,[status(thm)],[450:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ G )),bind(E,$thf( E ))]]) ).

thf(468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[451]) ).

thf(494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' )
      | ( ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
       != ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[468]) ).

thf(505,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ '\'0\'' ) ),
    inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( B ))]]) ).

thf(524,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ '\'0\'' ) ),
    inference(simp,[status(thm)],[505]) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ C ) @ '\'0\'' )
      | ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
       != ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[810,524]) ).

thf(815,plain,
    ! [A: $i] :
      ~ ( '\'E\'' @ ( f @ A ) @ '\'0\'' ),
    inference(pattern_uni,[status(thm)],[814:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).

thf(839,plain,
    ! [A: $i] :
      ~ ( '\'E\'' @ ( f @ A ) @ '\'0\'' ),
    inference(simp,[status(thm)],[815]) ).

thf(840,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
      | $false ),
    inference(rewrite,[status(thm)],[396,839]) ).

thf(841,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
    inference(simp,[status(thm)],[840]) ).

thf(861,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
    inference(simp,[status(thm)],[841]) ).

thf(919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
      | ( ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
       != ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[810,861]) ).

thf(920,plain,
    ! [A: $i] :
      ~ ( '\'E\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
    inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( E )),bind(B,$thf( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E )),bind(C,$thf( C ))]]) ).

thf(945,plain,
    ! [A: $i] :
      ~ ( '\'E\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
    inference(simp,[status(thm)],[920]) ).

thf(948,plain,
    $false,
    inference(rewrite,[status(thm)],[831,945]) ).

thf(949,plain,
    $false,
    inference(simp,[status(thm)],[948]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n006.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  6 20:12:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.96/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (121ms). 
% 1.18/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.21  % [INFO] 	 13 axioms and no conjecture found. 
% 1.85/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.27  % [INFO] 	 Type checking passed. 
% 2.01/1.27  % [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 ... 
% 10.38/2.86  % [INFO] 	 Killing All external provers ... 
% 10.38/2.86  % Time passed: 2337ms (effective reasoning time: 1881ms)
% 10.38/2.86  % Axioms used in derivation (7): clause_12_09, clause_4_12, clause_5_03, clause_2_07, clause_6_04, clause_1_10, clause_8_05
% 10.38/2.87  % No. of inferences in proof: 52
% 10.38/2.87  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2337 ms resp. 1881 ms w/o parsing
% 10.62/2.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.62/2.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------