TSTP Solution File: BOO013-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 17:18:42 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   52
% Syntax   : Number of formulae    :  128 (  86 unt;   7 typ;   0 def)
%            Number of atoms       :  176 ( 165 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   62 (  17   ~;  13   |;   0   &)
%                                         (  32 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  155 ( 139   !;   0   ?; 155   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_type,type,
    c: $i ).

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

tff(add_type,type,
    add: ( $i * $i ) > $i ).

tff(multiply_type,type,
    multiply: ( $i * $i ) > $i ).

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

tff(additive_identity_type,type,
    additive_identity: $i ).

tff(multiplicative_identity_type,type,
    multiplicative_identity: $i ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ( add(multiply(a,b),X) = X )
      <=> ( add(multiply(a,b),X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] : ( add(multiply(a,b),X) = X )
  <=> ! [X: $i] : ( add(multiply(a,b),X) = X ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $i] :
      rewrite(
        ( ( add(additive_identity,X) = X )
      <=> ( add(multiply(a,b),X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $i] : ( add(additive_identity,X) = X )
  <=> ! [X: $i] : ( add(multiply(a,b),X) = X ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [X: $i] : ( add(additive_identity,X) = X )
  <=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ! [X: $i] : ( add(additive_identity,X) = X ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).

tff(7,plain,
    ! [X: $i] : ( add(additive_identity,X) = X ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [X: $i] : ( add(multiply(a,b),X) = X ),
    inference(modus_ponens,[status(thm)],[7,4]) ).

tff(9,plain,
    ! [X: $i] : ( add(multiply(a,b),X) = X ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X: $i] : ( add(multiply(a,b),X) = X ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ ! [X: $i] : ( add(multiply(a,b),X) = X )
    | ( add(multiply(a,b),c) = c ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    add(multiply(a,b),c) = c,
    inference(unit_resolution,[status(thm)],[11,10]) ).

tff(13,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( multiply(X,Y) = multiply(Y,X) )
      <=> ( multiply(X,Y) = multiply(Y,X) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
  <=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,plain,
    ( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
  <=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).

tff(17,plain,
    ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
    inference(modus_ponens,[status(thm)],[18,14]) ).

tff(20,plain,
    ( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
    | ( multiply(a,b) = multiply(b,a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(21,plain,
    multiply(a,b) = multiply(b,a),
    inference(unit_resolution,[status(thm)],[20,19]) ).

tff(22,plain,
    multiply(b,a) = multiply(a,b),
    inference(symmetry,[status(thm)],[21]) ).

tff(23,plain,
    add(multiply(b,a),c) = add(multiply(a,b),c),
    inference(monotonicity,[status(thm)],[22]) ).

tff(24,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(
        ( ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
      <=> ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).

tff(28,plain,
    ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
    inference(modus_ponens,[status(thm)],[29,25]) ).

tff(31,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) )
    | ( add(multiply(b,a),c) = multiply(add(b,c),add(a,c)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(32,plain,
    add(multiply(b,a),c) = multiply(add(b,c),add(a,c)),
    inference(unit_resolution,[status(thm)],[31,30]) ).

tff(33,plain,
    multiply(add(b,c),add(a,c)) = add(multiply(b,a),c),
    inference(symmetry,[status(thm)],[32]) ).

tff(34,plain,
    ( ( add(a,c) = multiplicative_identity )
  <=> ( add(a,c) = add(a,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( add(a,c) = multiplicative_identity )
  <=> ( add(a,c) = multiplicative_identity ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,axiom,
    add(a,c) = multiplicative_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_and_multiplicative_identity) ).

tff(37,plain,
    add(a,c) = multiplicative_identity,
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    add(a,c) = add(a,b),
    inference(modus_ponens,[status(thm)],[37,34]) ).

tff(39,plain,
    add(a,b) = add(a,c),
    inference(symmetry,[status(thm)],[38]) ).

tff(40,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( add(X,Y) = add(Y,X) )
      <=> ( add(X,Y) = add(Y,X) ) )),
    inference(bind,[status(th)],]) ).

tff(41,plain,
    ( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
  <=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
    inference(quant_intro,[status(thm)],[40]) ).

tff(42,plain,
    ( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
  <=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,axiom,
    ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).

tff(44,plain,
    ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
    inference(modus_ponens,[status(thm)],[43,42]) ).

tff(45,plain,
    ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
    inference(skolemize,[status(sab)],[44]) ).

tff(46,plain,
    ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
    inference(modus_ponens,[status(thm)],[45,41]) ).

tff(47,plain,
    ( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
    | ( add(a,b) = add(b,a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    add(a,b) = add(b,a),
    inference(unit_resolution,[status(thm)],[47,46]) ).

tff(49,plain,
    add(b,a) = add(a,b),
    inference(symmetry,[status(thm)],[48]) ).

tff(50,plain,
    add(b,a) = add(a,c),
    inference(transitivity,[status(thm)],[49,39]) ).

tff(51,plain,
    ( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
    | ( add(b,c) = add(c,b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    add(b,c) = add(c,b),
    inference(unit_resolution,[status(thm)],[51,46]) ).

tff(53,plain,
    add(c,b) = add(b,c),
    inference(symmetry,[status(thm)],[52]) ).

tff(54,plain,
    ^ [X: $i] :
      refl(
        ( ( multiply(X,add(a,b)) = X )
      <=> ( multiply(X,add(a,b)) = X ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [X: $i] : ( multiply(X,add(a,b)) = X )
  <=> ! [X: $i] : ( multiply(X,add(a,b)) = X ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,plain,
    ^ [X: $i] :
      rewrite(
        ( ( multiply(X,multiplicative_identity) = X )
      <=> ( multiply(X,add(a,b)) = X ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
  <=> ! [X: $i] : ( multiply(X,add(a,b)) = X ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
  <=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,axiom,
    ! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).

tff(60,plain,
    ! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ! [X: $i] : ( multiply(X,add(a,b)) = X ),
    inference(modus_ponens,[status(thm)],[60,57]) ).

tff(62,plain,
    ! [X: $i] : ( multiply(X,add(a,b)) = X ),
    inference(skolemize,[status(sab)],[61]) ).

tff(63,plain,
    ! [X: $i] : ( multiply(X,add(a,b)) = X ),
    inference(modus_ponens,[status(thm)],[62,55]) ).

tff(64,plain,
    ( ~ ! [X: $i] : ( multiply(X,add(a,b)) = X )
    | ( multiply(add(c,b),add(a,b)) = add(c,b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(65,plain,
    multiply(add(c,b),add(a,b)) = add(c,b),
    inference(unit_resolution,[status(thm)],[64,63]) ).

tff(66,plain,
    multiply(add(c,b),add(a,b)) = multiply(add(b,c),add(a,c)),
    inference(monotonicity,[status(thm)],[53,39]) ).

tff(67,plain,
    multiply(add(b,c),add(a,c)) = multiply(add(c,b),add(a,b)),
    inference(symmetry,[status(thm)],[66]) ).

tff(68,plain,
    add(multiply(a,b),c) = add(multiply(b,a),c),
    inference(symmetry,[status(thm)],[23]) ).

tff(69,plain,
    c = add(multiply(a,b),c),
    inference(symmetry,[status(thm)],[12]) ).

tff(70,plain,
    c = add(b,c),
    inference(transitivity,[status(thm)],[69,68,32,67,65,53]) ).

tff(71,plain,
    multiply(c,add(b,a)) = multiply(add(b,c),add(a,c)),
    inference(monotonicity,[status(thm)],[70,50]) ).

tff(72,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(
        ( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
      <=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
    inference(bind,[status(th)],]) ).

tff(73,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
    inference(quant_intro,[status(thm)],[72]) ).

tff(74,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,axiom,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).

tff(76,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
    inference(modus_ponens,[status(thm)],[75,74]) ).

tff(77,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
    inference(skolemize,[status(sab)],[76]) ).

tff(78,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
    inference(modus_ponens,[status(thm)],[77,73]) ).

tff(79,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
    | ( multiply(c,add(b,a)) = add(multiply(c,b),multiply(c,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(80,plain,
    multiply(c,add(b,a)) = add(multiply(c,b),multiply(c,a)),
    inference(unit_resolution,[status(thm)],[79,78]) ).

tff(81,plain,
    add(multiply(c,b),multiply(c,a)) = multiply(c,add(b,a)),
    inference(symmetry,[status(thm)],[80]) ).

tff(82,plain,
    ( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
    | ( multiply(a,c) = multiply(c,a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(83,plain,
    multiply(a,c) = multiply(c,a),
    inference(unit_resolution,[status(thm)],[82,19]) ).

tff(84,plain,
    ( ( multiply(a,c) = additive_identity )
  <=> ( multiply(a,c) = multiply(a,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,plain,
    ( ( multiply(a,c) = additive_identity )
  <=> ( multiply(a,c) = additive_identity ) ),
    inference(rewrite,[status(thm)],]) ).

tff(86,axiom,
    multiply(a,c) = additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_a_additive_identity) ).

tff(87,plain,
    multiply(a,c) = additive_identity,
    inference(modus_ponens,[status(thm)],[86,85]) ).

tff(88,plain,
    multiply(a,c) = multiply(a,b),
    inference(modus_ponens,[status(thm)],[87,84]) ).

tff(89,plain,
    multiply(a,b) = multiply(a,c),
    inference(symmetry,[status(thm)],[88]) ).

tff(90,plain,
    multiply(a,b) = multiply(c,a),
    inference(transitivity,[status(thm)],[89,83]) ).

tff(91,plain,
    add(multiply(c,b),multiply(a,b)) = add(multiply(c,b),multiply(c,a)),
    inference(monotonicity,[status(thm)],[90]) ).

tff(92,plain,
    ( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
    | ( multiply(c,b) = multiply(b,c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(93,plain,
    multiply(c,b) = multiply(b,c),
    inference(unit_resolution,[status(thm)],[92,19]) ).

tff(94,plain,
    multiply(b,c) = multiply(c,b),
    inference(symmetry,[status(thm)],[93]) ).

tff(95,plain,
    add(multiply(b,c),multiply(b,a)) = add(multiply(c,b),multiply(a,b)),
    inference(monotonicity,[status(thm)],[94,22]) ).

tff(96,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
    | ( multiply(b,add(c,a)) = add(multiply(b,c),multiply(b,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(97,plain,
    multiply(b,add(c,a)) = add(multiply(b,c),multiply(b,a)),
    inference(unit_resolution,[status(thm)],[96,78]) ).

tff(98,plain,
    ( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
    | ( add(a,c) = add(c,a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(99,plain,
    add(a,c) = add(c,a),
    inference(unit_resolution,[status(thm)],[98,46]) ).

tff(100,plain,
    add(a,b) = add(c,a),
    inference(transitivity,[status(thm)],[39,99]) ).

tff(101,plain,
    multiply(b,add(a,b)) = multiply(b,add(c,a)),
    inference(monotonicity,[status(thm)],[100]) ).

tff(102,plain,
    ( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
    | ( multiply(add(a,b),b) = multiply(b,add(a,b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(103,plain,
    multiply(add(a,b),b) = multiply(b,add(a,b)),
    inference(unit_resolution,[status(thm)],[102,19]) ).

tff(104,plain,
    ^ [X: $i] :
      refl(
        ( ( multiply(add(a,b),X) = X )
      <=> ( multiply(add(a,b),X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(105,plain,
    ( ! [X: $i] : ( multiply(add(a,b),X) = X )
  <=> ! [X: $i] : ( multiply(add(a,b),X) = X ) ),
    inference(quant_intro,[status(thm)],[104]) ).

tff(106,plain,
    ^ [X: $i] :
      rewrite(
        ( ( multiply(multiplicative_identity,X) = X )
      <=> ( multiply(add(a,b),X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(107,plain,
    ( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
  <=> ! [X: $i] : ( multiply(add(a,b),X) = X ) ),
    inference(quant_intro,[status(thm)],[106]) ).

tff(108,plain,
    ( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
  <=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,axiom,
    ! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).

tff(110,plain,
    ! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
    inference(modus_ponens,[status(thm)],[109,108]) ).

tff(111,plain,
    ! [X: $i] : ( multiply(add(a,b),X) = X ),
    inference(modus_ponens,[status(thm)],[110,107]) ).

tff(112,plain,
    ! [X: $i] : ( multiply(add(a,b),X) = X ),
    inference(skolemize,[status(sab)],[111]) ).

tff(113,plain,
    ! [X: $i] : ( multiply(add(a,b),X) = X ),
    inference(modus_ponens,[status(thm)],[112,105]) ).

tff(114,plain,
    ( ~ ! [X: $i] : ( multiply(add(a,b),X) = X )
    | ( multiply(add(a,b),b) = b ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(115,plain,
    multiply(add(a,b),b) = b,
    inference(unit_resolution,[status(thm)],[114,113]) ).

tff(116,plain,
    b = multiply(add(a,b),b),
    inference(symmetry,[status(thm)],[115]) ).

tff(117,plain,
    b = c,
    inference(transitivity,[status(thm)],[116,103,101,97,95,91,81,71,33,23,12]) ).

tff(118,plain,
    ( ( b != c )
  <=> ( b != c ) ),
    inference(rewrite,[status(thm)],]) ).

tff(119,axiom,
    b != c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_a) ).

tff(120,plain,
    b != c,
    inference(modus_ponens,[status(thm)],[119,118]) ).

tff(121,plain,
    $false,
    inference(unit_resolution,[status(thm)],[120,117]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n025.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 03:01:14 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.
% 0.20/0.43  % SZS status Unsatisfiable
% 0.20/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------