TSTP Solution File: NUM841+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : NUM841+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.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 : Fri May 19 11:42:18 EDT 2023

% Result   : Theorem 4.00s 1.98s
% Output   : Refutation 4.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  104 (  32 unt;  12 typ;   0 def)
%            Number of atoms       :  180 (  82 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  544 (  42   ~;  28   |;  14   &; 414   @)
%                                         (   4 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  184 (   0   ^; 166   !;  18   ?; 184   :)

% Comments : 
%------------------------------------------------------------------------------
thf(greater_type,type,
    greater: $i > $i > $o ).

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

thf(vd344_type,type,
    vd344: $i ).

thf(vd347_type,type,
    vd347: $i ).

thf(vd345_type,type,
    vd345: $i ).

thf(vd348_type,type,
    vd348: $i ).

thf(leq_type,type,
    leq: $i > $i > $o ).

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

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

thf(vskolem2_type,type,
    vskolem2: $i > $i ).

thf(geq_type,type,
    geq: $i > $i > $o ).

thf(less_type,type,
    less: $i > $i > $o ).

thf(22,axiom,
    ! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).

thf(120,plain,
    ! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( less @ B @ C )
          & ( leq @ A @ B ) )
        | ( ( leq @ B @ C )
          & ( less @ A @ B ) ) )
     => ( less @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).

thf(78,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( less @ B @ C )
          & ( leq @ A @ B ) )
        | ( ( leq @ B @ C )
          & ( less @ A @ B ) ) )
     => ( less @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( greater @ A @ B )
     => ( less @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

thf(147,plain,
    ! [A: $i,B: $i] :
      ( ( greater @ A @ B )
     => ( less @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( geq @ A @ B )
     => ( leq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).

thf(53,plain,
    ! [A: $i,B: $i] :
      ( ( geq @ A @ B )
     => ( leq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ! [C: $i] :
          ( ( vplus @ C @ A )
         != ( vplus @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).

thf(109,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ! [C: $i] :
          ( ( vplus @ C @ A )
         != ( vplus @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vplus @ A @ C )
        = ( vplus @ B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).

thf(173,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vplus @ A @ C )
        = ( vplus @ B @ C ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( greater @ A @ B )
      | ~ ( less @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

thf(181,plain,
    ! [A: $i,B: $i] :
      ( ~ ( greater @ A @ B )
      | ~ ( less @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( leq @ B @ C )
        & ( leq @ A @ B ) )
     => ( leq @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).

thf(48,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( leq @ B @ C )
        & ( leq @ A @ B ) )
     => ( leq @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( A != v1 )
     => ( A
        = ( vsucc @ ( vskolem2 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).

thf(50,plain,
    ! [A: $i] :
      ( ( A != v1 )
     => ( A
        = ( vsucc @ ( vskolem2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( vsucc @ A )
     != v1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).

thf(87,plain,
    ! [A: $i] :
      ( ( vsucc @ A )
     != v1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(21,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(117,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)],[21]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

thf(102,plain,
    ! [A: $i,B: $i] :
      ( ( vplus @ B @ A )
      = ( vplus @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(26,axiom,
    greater @ ( vplus @ vd347 @ vd345 ) @ ( vplus @ vd348 @ vd345 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(213, 351, 1)') ).

thf(134,plain,
    greater @ ( vplus @ vd347 @ vd345 ) @ ( vplus @ vd348 @ vd345 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ~ ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) )
      | ~ ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

thf(105,plain,
    ! [A: $i,B: $i] :
      ( ~ ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) )
      | ~ ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( less @ B @ A )
    <=> ? [C: $i] :
          ( A
          = ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

thf(161,plain,
    ! [A: $i,B: $i] :
      ( ( ( less @ B @ A )
       => ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) ) )
      & ( ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) )
       => ( less @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vsucc @ A )
        = ( vsucc @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).

thf(64,plain,
    ! [A: $i,B: $i] :
      ( ( ( vsucc @ A )
        = ( vsucc @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( less @ A @ B )
     => ( greater @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

thf(149,plain,
    ! [A: $i,B: $i] :
      ( ( less @ A @ B )
     => ( greater @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less @ B @ C )
        & ( less @ A @ B ) )
     => ( less @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).

thf(81,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less @ B @ C )
        & ( less @ A @ B ) )
     => ( less @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( leq @ A @ B )
     => ( geq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).

thf(76,plain,
    ! [A: $i,B: $i] :
      ( ( leq @ A @ B )
     => ( geq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ? [C: $i] :
            ( A
            = ( vplus @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(15,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(91,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)],[15]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ( greater @ A @ B )
      | ( less @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

thf(155,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ( greater @ A @ B )
      | ( less @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(45,axiom,
    ( ( vplus @ vd345 @ vd347 )
    = ( vplus @ vd347 @ vd345 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(213, 351, 0)') ).

thf(198,plain,
    ( ( vplus @ vd345 @ vd347 )
    = ( vplus @ vd347 @ vd345 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( B
     != ( vplus @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

thf(130,plain,
    ! [A: $i,B: $i] :
      ( B
     != ( vplus @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(27,axiom,
    greater @ vd344 @ vd345,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).

thf(135,plain,
    greater @ vd344 @ vd345,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(34,axiom,
    greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd347 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(212, 350, 0)') ).

thf(154,plain,
    greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd347 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ( less @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

thf(72,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ( less @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
     => ( greater @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).

thf(143,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
     => ( greater @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( greater @ A @ B )
     => ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).

thf(158,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( greater @ A @ B )
     => ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ( geq @ B @ A )
    <=> ( ( greater @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).

thf(186,plain,
    ! [A: $i,B: $i] :
      ( ( ( geq @ B @ A )
       => ( ( greater @ B @ A )
          | ( B = A ) ) )
      & ( ( ( greater @ B @ A )
          | ( B = A ) )
       => ( geq @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( leq @ B @ A )
    <=> ( ( less @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).

thf(55,plain,
    ! [A: $i,B: $i] :
      ( ( ( leq @ B @ A )
       => ( ( less @ B @ A )
          | ( B = A ) ) )
      & ( ( ( less @ B @ A )
          | ( B = A ) )
       => ( leq @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ? [C: $i] :
          ( A
          = ( vplus @ B @ C ) )
      | ? [C: $i] :
          ( B
          = ( vplus @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).

thf(114,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ? [C: $i] :
          ( A
          = ( vplus @ B @ C ) )
      | ? [C: $i] :
          ( B
          = ( vplus @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
     => ( less @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).

thf(151,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
     => ( less @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A = B )
     => ( ( vplus @ A @ C )
        = ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).

thf(168,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A = B )
     => ( ( vplus @ A @ C )
        = ( vplus @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(30,axiom,
    greater @ vd347 @ vd348,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).

thf(146,plain,
    greater @ vd347 @ vd348,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ( ( vplus @ ( vsucc @ A ) @ B )
      = ( vsucc @ ( vplus @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).

thf(183,plain,
    ! [A: $i,B: $i] :
      ( ( vplus @ ( vsucc @ A ) @ B )
      = ( vsucc @ ( vplus @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( vplus @ v1 @ A )
      = ( vsucc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

thf(195,plain,
    ! [A: $i] :
      ( ( vplus @ v1 @ A )
      = ( vsucc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ( greater @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).

thf(126,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ( greater @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( greater @ B @ A )
    <=> ? [C: $i] :
          ( B
          = ( vplus @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

thf(136,plain,
    ! [A: $i,B: $i] :
      ( ( ( greater @ B @ A )
       => ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) ) )
      & ( ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) )
       => ( greater @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1,conjecture,
    greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(214, 352, 0)') ).

thf(2,negated_conjecture,
    ~ ( greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(47,plain,
    ~ ( greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(46,axiom,
    ( ( vplus @ vd348 @ vd345 )
    = ( vplus @ vd345 @ vd348 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(213, 351, 2)') ).

thf(200,plain,
    ( ( vplus @ vd348 @ vd345 )
    = ( vplus @ vd345 @ vd348 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( vsucc @ A )
       != ( vsucc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).

thf(68,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( vsucc @ A )
       != ( vsucc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( less @ A @ B )
     => ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).

thf(178,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( less @ A @ B )
     => ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

thf(122,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
      | ~ ? [C: $i] :
            ( B
            = ( vplus @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( vsucc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).

thf(83,plain,
    ! [A: $i] :
      ( ( vsucc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(202,plain,
    $false,
    inference(cvc4,[status(thm)],[120,78,147,53,109,173,181,48,50,87,117,102,134,105,161,64,149,81,76,98,91,155,198,130,135,154,72,143,158,186,55,114,151,168,146,183,195,126,136,47,200,68,178,122,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM841+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n001.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 18:19:05 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.95/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/0.98  % [INFO] 	 Parsing done (136ms). 
% 1.33/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.77/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.77/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.77/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.26  % [INFO] 	 Found a conjecture and 44 axioms. Running axiom selection ... 
% 1.98/1.31  % [INFO] 	 Axiom selection finished. Selected 44 axioms (removed 0 axioms). 
% 2.19/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.19/1.37  % [INFO] 	 Type checking passed. 
% 2.39/1.37  % [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 ... 
% 4.00/1.97  % External prover 'cvc4' found a proof!
% 4.00/1.97  % [INFO] 	 Killing All external provers ... 
% 4.00/1.97  % Time passed: 1457ms (effective reasoning time: 975ms)
% 4.00/1.97  % 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)>
% 4.00/1.97  % Axioms used in derivation (44): ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), holds(213, 351, 0), def(cond(conseq(axiom(3)), 16), 1), ass(cond(goal(88), 0), 3), ass(cond(goal(202), 0), 2), ass(cond(goal(202), 0), 1), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(52, 0), 0), holds(conjunct1(211), 346, 0), ass(cond(12, 0), 0), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(81, 0), 0), ass(cond(goal(193), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 2), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), ass(cond(184, 0), 0), ass(cond(goal(88), 0), 2), ass(cond(147, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(73, 0), 0), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), ass(cond(20, 0), 0), holds(213, 351, 1), ass(cond(158, 0), 0), ass(cond(33, 0), 0), holds(213, 351, 2), qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), ass(cond(61, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), holds(conjunct2(211), 349, 0), ass(cond(168, 0), 0), ass(cond(43, 0), 0), holds(212, 350, 0)
% 4.00/1.97  % No. of inferences in proof: 92
% 4.00/1.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1457 ms resp. 975 ms w/o parsing
% 4.19/2.04  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.19/2.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------