TSTP Solution File: ARI712_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI712_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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 Sep  6 17:02:42 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   30 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :   41 (  34 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   29 (  14   ~;   0   |;   0   &)
%                                         (  15 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :   20 (   3 avg)
%            Number arithmetic     : 1758 (   0 atm;1475 fun; 283 num;   0 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   2 prp; 0-2 aty)
%            Number of functors    :   11 (   4 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(d_type,type,
    d: $int ).

tff(c_type,type,
    c: $int ).

tff(b_type,type,
    b: $int ).

tff(a_type,type,
    a: $int ).

tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( 0 = 0 )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( $sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$product(-1,$product(c,d)))))))))))))))) = 0 )
  <=> ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) = 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    $sum($product(a,a),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d)))))))))))))))) = $sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$product(-1,$product(c,d)))))))))))))))),
    inference(rewrite,[status(thm)],]) ).

tff(5,plain,
    ( ( $sum($product(a,a),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d)))))))))))))))) = 0 )
  <=> ( $sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$product(-1,$product(c,d)))))))))))))))) = 0 ) ),
    inference(monotonicity,[status(thm)],[4]) ).

tff(6,plain,
    ( ( $sum($product(a,a),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d)))))))))))))))) = 0 )
  <=> ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) = 0 ) ),
    inference(transitivity,[status(thm)],[5,3]) ).

tff(7,plain,
    ( ( $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 )
  <=> ( $sum($product(a,a),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d)))))))))))))))) = 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,plain,
    ( ( $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 )
  <=> ( $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    ( ( $sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0 )
  <=> ( $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    $sum($sum($sum($product(a,a),$product($sum($product($product(a,b),c),$product($product(b,d),a)),$sum($sum($product($product(c,c),a),$product($product(d,d),b)),1))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq) ).

tff(11,plain,
    $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0,
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    $sum($product(a,a),$sum($product($sum($product(a,$product(b,c)),$product(a,$product(b,d))),$sum(1,$sum($product(a,$product(c,c)),$product(b,$product(d,d))))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0,
    inference(modus_ponens,[status(thm)],[11,8]) ).

tff(13,plain,
    $sum($product(a,a),$sum($product(a,$product(b,c)),$sum($product(a,$product(b,d)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(a,$product(a,$product(b,$product(c,$product(c,d))))),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d)))))))))))))))) = 0,
    inference(modus_ponens,[status(thm)],[12,7]) ).

tff(14,plain,
    $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) = 0,
    inference(modus_ponens,[status(thm)],[13,6]) ).

tff(15,plain,
    ( ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) = 0 )
  <=> ( 0 = 0 ) ),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    ( ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) = 0 )
  <=> $true ),
    inference(transitivity,[status(thm)],[15,2]) ).

tff(17,plain,
    ( ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) != 0 )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[16]) ).

tff(18,plain,
    ( ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) != 0 )
  <=> $false ),
    inference(transitivity,[status(thm)],[17,1]) ).

tff(19,plain,
    ( ( $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0 )
  <=> ( $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) != 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( ( $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0 )
  <=> ( $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ( $sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))) != 0 )
  <=> ( $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    $sum($product(1,$product($product($product($product($product(d,d),d),b),b),a)),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(2,a),$product(-1,$product(a,a))),b),$product(2,c)),$product(-1,$product($product($product($product($product(d,d),c),b),b),a))),$product(c,a)),$product(c,b)),$product(-1,$product($product(c,b),a))),$product(-1,$product($product($product($product($product(c,c),c),b),a),a))),$product(2,d)),$product(d,c)),$product(-1,$product($product(d,b),a))),$product(c,c)),$product(-1,$product($product($product($product($product(d,c),c),b),a),a))))) != 0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

tff(23,plain,
    $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0,
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    $sum($product(a,$product(b,$product(b,$product(d,$product(d,d))))),$sum($product(-2,a),$sum($product(a,a),$sum($product(-1,b),$sum($product(-2,c),$sum($product(a,$product(b,$product(b,$product(c,$product(d,d))))),$sum($product(-1,$product(a,c)),$sum($product(-1,$product(b,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,$product(b,$product(c,$product(c,c))))),$sum($product(-2,d),$sum($product(-1,$product(c,d)),$sum($product(a,$product(b,d)),$sum($product(-1,$product(c,c)),$product(a,$product(a,$product(b,$product(c,$product(c,d))))))))))))))))))) != 0,
    inference(modus_ponens,[status(thm)],[23,20]) ).

tff(25,plain,
    $sum($product(2,a),$sum($product(-1,$product(a,a)),$sum(b,$sum($product(2,c),$sum($product(2,d),$sum($product(c,c),$sum($product(-1,$product(a,$product(b,c))),$sum($product(-1,$product(a,$product(b,d))),$sum($product(-1,$product(a,$product(b,$product(b,$product(c,$product(d,d)))))),$sum($product(-1,$product(a,$product(b,$product(b,$product(d,$product(d,d)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,c)))))),$sum($product(-1,$product(a,$product(a,$product(b,$product(c,$product(c,d)))))),$sum($product(a,c),$sum($product(b,c),$product(c,d))))))))))))))) != 0,
    inference(modus_ponens,[status(thm)],[24,19]) ).

tff(26,plain,
    $false,
    inference(modus_ponens,[status(thm)],[25,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : ARI712_1 : TPTP v8.1.0. Released v6.3.0.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 30 02:04:05 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.13/0.39  % SZS status Theorem
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------