TSTP Solution File: NUM845+2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM845+2 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 01:36:33 EDT 2024

% Result   : Theorem 40.42s 7.02s
% Output   : Refutation 40.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   81 (  41 unt;   6 typ;   0 def)
%            Number of atoms       :  111 ( 110 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives : 1028 (  33   ~;  23   |;   6   &; 959   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   79 (   0   ^  79   !;   0   ?;  79   :)

% Comments : 
%------------------------------------------------------------------------------
thf(vmul_type,type,
    vmul: $i > $i > $i ).

thf(vsucc_type,type,
    vsucc: $i > $i ).

thf(vd411_type,type,
    vd411: $i ).

thf(vplus_type,type,
    vplus: $i > $i > $i ).

thf(v1_type,type,
    v1: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

thf(55,plain,
    ! [A: $i,B: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(56,plain,
    ! [B: $i,A: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    inference(cnf,[status(esa)],[55]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    inference(lifteq,[status(thm)],[56]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
        = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
     => ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
          = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
       => ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
          = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(17,plain,
    ~ ! [A: $i] :
        ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
          = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
       => ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
          = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(19,plain,
    ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
    = ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(21,plain,
    ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
    = ( vmul @ ( vsucc @ vd411 ) @ sk1 ) ),
    inference(lifteq,[status(thm)],[19]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
        = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
     => ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).

thf(22,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
        = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
     => ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(23,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
       != ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
      | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(24,plain,
    ! [A: $i] :
      ( ( ( vplus @ ( vmul @ vd411 @ A ) @ A )
       != ( vmul @ ( vsucc @ vd411 ) @ A ) )
      | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
       != ( vmul @ ( vsucc @ vd411 ) @ A ) )
      | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) )
      | ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
       != ( vplus @ ( vmul @ vd411 @ A ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21,24]) ).

thf(159,plain,
    ( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
     != ( vmul @ ( vsucc @ vd411 ) @ sk1 ) )
    | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) )
      = ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( sk1 ))]]) ).

thf(200,plain,
    ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
    inference(simp,[status(thm)],[159]) ).

thf(297,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ ( vplus @ A @ B ) @ ( vsucc @ sk1 ) )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ B @ A )
       != ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,200]) ).

thf(298,plain,
    ( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( vd411 )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).

thf(599,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
        = ( vplus @ B @ A ) )
      | ( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
       != ( vplus @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[298,57]) ).

thf(600,plain,
    ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) )),bind(B,$thf( vsucc @ sk1 ))]]) ).

thf(299,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ A @ B )
        = ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ B @ A )
       != ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) @ ( vsucc @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[57,200]) ).

thf(300,plain,
    ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
    inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ))]]) ).

thf(716,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
        = ( vplus @ A @ B ) )
      | ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
       != ( vplus @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[300,57]) ).

thf(717,plain,
    ( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).

thf(597,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
        = ( vplus @ A @ B ) )
      | ( ( vplus @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) @ ( vsucc @ sk1 ) )
       != ( vplus @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[298,57]) ).

thf(598,plain,
    ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ))]]) ).

thf(1420,plain,
    ( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) ) ),
    inference(rewrite,[status(thm)],[598,300]) ).

thf(2038,plain,
    ( ( vplus @ ( vsucc @ sk1 ) @ ( vplus @ vd411 @ ( vmul @ vd411 @ sk1 ) ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
    inference(rewrite,[status(thm)],[717,1420]) ).

thf(2040,plain,
    ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
    inference(rewrite,[status(thm)],[600,2038]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vplus @ A @ ( vsucc @ B ) )
        = ( vsucc @ ( vplus @ A @ B ) ) )
      & ( ( vplus @ A @ v1 )
        = ( vsucc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

thf(64,plain,
    ! [A: $i,B: $i] :
      ( ( ( vplus @ A @ ( vsucc @ B ) )
        = ( vsucc @ ( vplus @ A @ B ) ) )
      & ( ( vplus @ A @ v1 )
        = ( vsucc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(65,plain,
    ( ! [A: $i,B: $i] :
        ( ( vplus @ A @ ( vsucc @ B ) )
        = ( vsucc @ ( vplus @ A @ B ) ) )
    & ! [A: $i] :
        ( ( vplus @ A @ v1 )
        = ( vsucc @ A ) ) ),
    inference(miniscope,[status(thm)],[64]) ).

thf(67,plain,
    ! [B: $i,A: $i] :
      ( ( vplus @ A @ ( vsucc @ B ) )
      = ( vsucc @ ( vplus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(70,plain,
    ! [B: $i,A: $i] :
      ( ( vplus @ A @ ( vsucc @ B ) )
      = ( vsucc @ ( vplus @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[67]) ).

thf(5209,plain,
    ( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
    = ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ),
    inference(rewrite,[status(thm)],[2040,70]) ).

thf(18,plain,
    ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) )
   != ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(20,plain,
    ( ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) )
   != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(309,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ A @ B )
       != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ B @ A )
       != ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ ( vsucc @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[57,20]) ).

thf(310,plain,
    ( ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) )
   != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( vsucc @ sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).

thf(8527,plain,
    ( ( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
     != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
    | ( ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) )
     != ( vplus @ ( vsucc @ sk1 ) @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5209,310]) ).

thf(8528,plain,
    ( ( vsucc @ ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) )
   != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[8527:[]]) ).

thf(9074,plain,
    ! [B: $i,A: $i] :
      ( ( ( vsucc @ ( vplus @ A @ B ) )
       != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ B @ A )
       != ( vplus @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,8528]) ).

thf(9075,plain,
    ( ( vsucc @ ( vplus @ sk1 @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) )
   != ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[9074:[bind(A,$thf( sk1 )),bind(B,$thf( vmul @ vd411 @ ( vsucc @ sk1 ) ))]]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
      & ( ( vmul @ A @ v1 )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ( ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
      & ( ( vmul @ A @ v1 )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(49,plain,
    ( ! [A: $i,B: $i] :
        ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
    & ! [A: $i] :
        ( ( vmul @ A @ v1 )
        = A ) ),
    inference(miniscope,[status(thm)],[48]) ).

thf(51,plain,
    ! [B: $i,A: $i] :
      ( ( vmul @ A @ ( vsucc @ B ) )
      = ( vplus @ ( vmul @ A @ B ) @ A ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ( vplus @ ( vmul @ A @ B ) @ A )
      = ( vmul @ A @ ( vsucc @ B ) ) ),
    inference(lifteq,[status(thm)],[51]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
        = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
     => ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
        = ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 6)') ).

thf(40,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
        = ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
     => ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
        = ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(41,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ A )
       != ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
      | ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
        = ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
    inference(cnf,[status(esa)],[40]) ).

thf(42,plain,
    ! [A: $i] :
      ( ( ( vplus @ ( vmul @ vd411 @ A ) @ A )
       != ( vmul @ ( vsucc @ vd411 ) @ A ) )
      | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
        = ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
    inference(lifteq,[status(thm)],[41]) ).

thf(2867,plain,
    ! [A: $i] :
      ( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
       != ( vmul @ ( vsucc @ vd411 ) @ A ) )
      | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
        = ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) )
      | ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )
       != ( vplus @ ( vmul @ vd411 @ A ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21,42]) ).

thf(2868,plain,
    ( ( ( vmul @ ( vsucc @ vd411 ) @ sk1 )
     != ( vmul @ ( vsucc @ vd411 ) @ sk1 ) )
    | ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
      = ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ sk1 ) @ ( vsucc @ vd411 ) ) ) ),
    inference(pattern_uni,[status(thm)],[2867:[bind(A,$thf( sk1 ))]]) ).

thf(3008,plain,
    ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
    = ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ sk1 ) @ ( vsucc @ vd411 ) ) ),
    inference(simp,[status(thm)],[2868]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( vplus @ ( vplus @ A @ B ) @ C )
      = ( vplus @ A @ ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

thf(61,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( vplus @ ( vplus @ A @ B ) @ C )
      = ( vplus @ A @ ( vplus @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(62,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( vplus @ ( vplus @ A @ B ) @ C )
      = ( vplus @ A @ ( vplus @ B @ C ) ) ),
    inference(cnf,[status(esa)],[61]) ).

thf(63,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( vplus @ ( vplus @ A @ B ) @ C )
      = ( vplus @ A @ ( vplus @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[62]) ).

thf(4993,plain,
    ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[3008,54,63]) ).

thf(5013,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ A @ B )
        = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ ( vmul @ vd411 @ sk1 ) @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) )
       != ( vplus @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4993,57]) ).

thf(5014,plain,
    ( ( vplus @ ( vplus @ sk1 @ ( vsucc @ vd411 ) ) @ ( vmul @ vd411 @ sk1 ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[5013:[bind(A,$thf( vplus @ sk1 @ ( vsucc @ vd411 ) )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).

thf(5305,plain,
    ( ( vplus @ sk1 @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[5014,63]) ).

thf(5325,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ A @ B )
        = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ sk1 @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) )
       != ( vplus @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5305,57]) ).

thf(5326,plain,
    ( ( vplus @ ( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) ) @ sk1 )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[5325:[bind(A,$thf( vplus @ ( vsucc @ vd411 ) @ ( vmul @ vd411 @ sk1 ) )),bind(B,$thf( sk1 ))]]) ).

thf(5814,plain,
    ( ( vplus @ ( vsucc @ vd411 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[5326,63]) ).

thf(5839,plain,
    ! [B: $i,A: $i] :
      ( ( ( vplus @ A @ B )
        = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ ( vsucc @ vd411 ) @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) )
       != ( vplus @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5814,57]) ).

thf(5840,plain,
    ( ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ ( vsucc @ vd411 ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[5839:[bind(A,$thf( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 )),bind(B,$thf( vsucc @ vd411 ))]]) ).

thf(6227,plain,
    ( ( vsucc @ ( vplus @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) @ vd411 ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[5840,70]) ).

thf(6288,plain,
    ! [B: $i,A: $i] :
      ( ( ( vsucc @ ( vplus @ ( vplus @ A @ B ) @ vd411 ) )
        = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ B @ A )
       != ( vplus @ ( vmul @ vd411 @ sk1 ) @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,6227]) ).

thf(6289,plain,
    ( ( vsucc @ ( vplus @ ( vplus @ sk1 @ ( vmul @ vd411 @ sk1 ) ) @ vd411 ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[6288:[bind(A,$thf( sk1 )),bind(B,$thf( vmul @ vd411 @ sk1 ))]]) ).

thf(7232,plain,
    ( ( vsucc @ ( vplus @ sk1 @ ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[6289,63]) ).

thf(7363,plain,
    ! [B: $i,A: $i] :
      ( ( ( vsucc @ ( vplus @ sk1 @ ( vmul @ A @ ( vsucc @ B ) ) ) )
        = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) )
      | ( ( vplus @ ( vmul @ A @ B ) @ A )
       != ( vplus @ ( vmul @ vd411 @ sk1 ) @ vd411 ) ) ),
    inference(paramod_ordered,[status(thm)],[54,7232]) ).

thf(7364,plain,
    ( ( vsucc @ ( vplus @ sk1 @ ( vmul @ vd411 @ ( vsucc @ sk1 ) ) ) )
    = ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[7363:[bind(A,$thf( vd411 )),bind(B,$thf( sk1 ))]]) ).

thf(9266,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[9075,7364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM845+2 : TPTP v8.2.0. Released v4.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n014.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 06:19:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.88/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.97  % [INFO] 	 Parsing done (126ms). 
% 1.21/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 1.85/1.29  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 2.04/1.33  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.04/1.33  % [INFO] 	 Type checking passed. 
% 2.04/1.33  % [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 ... 
% 40.42/7.01  % [INFO] 	 Killing All external provers ... 
% 40.42/7.01  % Time passed: 6504ms (effective reasoning time: 6031ms)
% 40.42/7.01  % Solved by 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)>
% 40.42/7.02  % Axioms used in derivation (6): ass(cond(conseq(263), 1), 6), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(33, 0), 0), ass(cond(61, 0), 0), ass(cond(conseq(263), 1), 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))
% 40.42/7.02  % No. of inferences in proof: 75
% 40.42/7.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6504 ms resp. 6031 ms w/o parsing
% 40.42/7.09  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.42/7.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------