TSTP Solution File: GRP767-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 Sep 16 22:29:48 EDT 2022

% Result   : Unsatisfiable 11.08s 7.33s
% Output   : Proof 11.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   78
% Syntax   : Number of formulae    :  232 ( 168 unt;   9 typ;   0 def)
%            Number of atoms       :  304 ( 290 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  100 (  32   ~;  28   |;   0   &)
%                                         (  40 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of FOOLs       :   13 (  13 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  264 ( 240   !;   0   ?; 264   :)

% Comments : 
%------------------------------------------------------------------------------
tff(j_type,type,
    j: $i > $i ).

tff(x1_type,type,
    x1: $i ).

tff(product_type,type,
    product: ( $i * $i ) > $i ).

tff(x0_type,type,
    x0: $i ).

tff(quotient_type,type,
    quotient: ( $i * $i ) > $i ).

tff(one_type,type,
    one: $i ).

tff(difference_type,type,
    difference: ( $i * $i ) > $i ).

tff(i_type,type,
    i: $i > $i ).

tff(eta_type,type,
    eta: $i > $i ).

tff(1,plain,
    ^ [A: $i] :
      refl(
        ( ( j(A) = quotient(one,A) )
      <=> ( j(A) = quotient(one,A) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [A: $i] : ( j(A) = quotient(one,A) )
  <=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [A: $i] : ( j(A) = quotient(one,A) )
  <=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [A: $i] : ( j(A) = quotient(one,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).

tff(5,plain,
    ! [A: $i] : ( j(A) = quotient(one,A) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [A: $i] : ( j(A) = quotient(one,A) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [A: $i] : ( j(A) = quotient(one,A) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
    | ( j(x1) = quotient(one,x1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    j(x1) = quotient(one,x1),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    quotient(one,x1) = j(x1),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( difference(A,product(A,B)) = B )
      <=> ( difference(A,product(A,B)) = B ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
  <=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
  <=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).

tff(15,plain,
    ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
    | ( difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1),
    inference(unit_resolution,[status(thm)],[18,17]) ).

tff(20,plain,
    ^ [A: $i] :
      refl(
        ( ( product(A,one) = A )
      <=> ( product(A,one) = A ) )),
    inference(bind,[status(th)],]) ).

tff(21,plain,
    ( ! [A: $i] : ( product(A,one) = A )
  <=> ! [A: $i] : ( product(A,one) = A ) ),
    inference(quant_intro,[status(thm)],[20]) ).

tff(22,plain,
    ( ! [A: $i] : ( product(A,one) = A )
  <=> ! [A: $i] : ( product(A,one) = A ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,axiom,
    ! [A: $i] : ( product(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).

tff(24,plain,
    ! [A: $i] : ( product(A,one) = A ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ! [A: $i] : ( product(A,one) = A ),
    inference(skolemize,[status(sab)],[24]) ).

tff(26,plain,
    ! [A: $i] : ( product(A,one) = A ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ( ~ ! [A: $i] : ( product(A,one) = A )
    | ( product(x0,one) = x0 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    product(x0,one) = x0,
    inference(unit_resolution,[status(thm)],[27,26]) ).

tff(29,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( product(quotient(A,B),B) = A )
      <=> ( product(quotient(A,B),B) = A ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
  <=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
  <=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).

tff(33,plain,
    ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
    | ( product(quotient(one,x0),x0) = one ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    product(quotient(one,x0),x0) = one,
    inference(unit_resolution,[status(thm)],[36,35]) ).

tff(38,plain,
    product(x0,product(quotient(one,x0),x0)) = product(x0,one),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( product(A,difference(A,B)) = B )
      <=> ( product(A,difference(A,B)) = B ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
  <=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
  <=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).

tff(43,plain,
    ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
    inference(modus_ponens,[status(thm)],[44,40]) ).

tff(46,plain,
    ( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
    | ( product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))) = product(x0,product(quotient(one,x0),x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(47,plain,
    product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))) = product(x0,product(quotient(one,x0),x0)),
    inference(unit_resolution,[status(thm)],[46,45]) ).

tff(48,plain,
    ( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
    | ( j(x0) = quotient(one,x0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    j(x0) = quotient(one,x0),
    inference(unit_resolution,[status(thm)],[48,7]) ).

tff(50,plain,
    quotient(one,x0) = j(x0),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    product(x0,quotient(one,x0)) = product(x0,j(x0)),
    inference(monotonicity,[status(thm)],[50]) ).

tff(52,plain,
    product(x0,j(x0)) = product(x0,quotient(one,x0)),
    inference(symmetry,[status(thm)],[51]) ).

tff(53,plain,
    difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))) = difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))),
    inference(monotonicity,[status(thm)],[52]) ).

tff(54,plain,
    difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))),
    inference(symmetry,[status(thm)],[53]) ).

tff(55,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
      <=> ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
  <=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
  <=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,axiom,
    ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).

tff(59,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
    inference(skolemize,[status(sab)],[59]) ).

tff(61,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
    inference(modus_ponens,[status(thm)],[60,56]) ).

tff(62,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
    | ( difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(63,plain,
    difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0),
    inference(unit_resolution,[status(thm)],[62,61]) ).

tff(64,plain,
    quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) = difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) = difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))),
    inference(transitivity,[status(thm)],[64,54]) ).

tff(66,plain,
    product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)) = product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))),
    inference(monotonicity,[status(thm)],[65]) ).

tff(67,plain,
    product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)) = x0,
    inference(transitivity,[status(thm)],[66,47,38,28]) ).

tff(68,plain,
    product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))) = product(x0,j(product(x1,x0))),
    inference(monotonicity,[status(thm)],[67]) ).

tff(69,plain,
    product(x0,j(product(x1,x0))) = product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))),
    inference(symmetry,[status(thm)],[68]) ).

tff(70,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( quotient(product(A,B),B) = A )
      <=> ( quotient(product(A,B),B) = A ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
  <=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,plain,
    ( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
  <=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,axiom,
    ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).

tff(74,plain,
    ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
    inference(modus_ponens,[status(thm)],[75,71]) ).

tff(77,plain,
    ( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
    | ( quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(78,plain,
    quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))),
    inference(unit_resolution,[status(thm)],[77,76]) ).

tff(79,plain,
    ( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
    | ( product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(80,plain,
    product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1),
    inference(unit_resolution,[status(thm)],[79,45]) ).

tff(81,plain,
    ( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
    | ( product(quotient(one,product(x1,x0)),product(x1,x0)) = one ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    product(quotient(one,product(x1,x0)),product(x1,x0)) = one,
    inference(unit_resolution,[status(thm)],[81,35]) ).

tff(83,plain,
    ( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
    | ( j(product(x1,x0)) = quotient(one,product(x1,x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(84,plain,
    j(product(x1,x0)) = quotient(one,product(x1,x0)),
    inference(unit_resolution,[status(thm)],[83,7]) ).

tff(85,plain,
    product(j(product(x1,x0)),product(x1,x0)) = product(quotient(one,product(x1,x0)),product(x1,x0)),
    inference(monotonicity,[status(thm)],[84]) ).

tff(86,plain,
    product(j(product(x1,x0)),product(x1,x0)) = one,
    inference(transitivity,[status(thm)],[85,82]) ).

tff(87,plain,
    quotient(product(j(product(x1,x0)),product(x1,x0)),x0) = quotient(one,x0),
    inference(monotonicity,[status(thm)],[86]) ).

tff(88,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
      <=> ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) )),
    inference(bind,[status(th)],]) ).

tff(89,plain,
    ( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
  <=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
    inference(quant_intro,[status(thm)],[88]) ).

tff(90,plain,
    ( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
  <=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(91,axiom,
    ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).

tff(92,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
    inference(modus_ponens,[status(thm)],[91,90]) ).

tff(93,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
    inference(skolemize,[status(sab)],[92]) ).

tff(94,plain,
    ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
    inference(modus_ponens,[status(thm)],[93,89]) ).

tff(95,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
    | ( difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(96,plain,
    difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0),
    inference(unit_resolution,[status(thm)],[95,94]) ).

tff(97,plain,
    difference(x0,product(product(x0,j(product(x1,x0))),x1)) = j(x0),
    inference(transitivity,[status(thm)],[96,87,50]) ).

tff(98,plain,
    product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(x0,j(x0)),
    inference(monotonicity,[status(thm)],[97]) ).

tff(99,plain,
    product(x0,j(x0)) = product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))),
    inference(symmetry,[status(thm)],[98]) ).

tff(100,plain,
    ^ [A: $i] :
      refl(
        ( ( product(i(A),A) = product(A,j(A)) )
      <=> ( product(i(A),A) = product(A,j(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(101,plain,
    ( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
  <=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
    inference(quant_intro,[status(thm)],[100]) ).

tff(102,plain,
    ( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
  <=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(103,axiom,
    ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).

tff(104,plain,
    ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
    inference(modus_ponens,[status(thm)],[103,102]) ).

tff(105,plain,
    ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
    inference(skolemize,[status(sab)],[104]) ).

tff(106,plain,
    ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
    inference(modus_ponens,[status(thm)],[105,101]) ).

tff(107,plain,
    ( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
    | ( product(i(x0),x0) = product(x0,j(x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(108,plain,
    product(i(x0),x0) = product(x0,j(x0)),
    inference(unit_resolution,[status(thm)],[107,106]) ).

tff(109,plain,
    ( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
    | ( difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(110,plain,
    difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0,
    inference(unit_resolution,[status(thm)],[109,17]) ).

tff(111,plain,
    one = product(quotient(one,x0),x0),
    inference(symmetry,[status(thm)],[37]) ).

tff(112,plain,
    difference(quotient(one,x0),one) = difference(quotient(one,x0),product(quotient(one,x0),x0)),
    inference(monotonicity,[status(thm)],[111]) ).

tff(113,plain,
    ^ [A: $i] :
      refl(
        ( ( i(A) = difference(A,one) )
      <=> ( i(A) = difference(A,one) ) )),
    inference(bind,[status(th)],]) ).

tff(114,plain,
    ( ! [A: $i] : ( i(A) = difference(A,one) )
  <=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
    inference(quant_intro,[status(thm)],[113]) ).

tff(115,plain,
    ( ! [A: $i] : ( i(A) = difference(A,one) )
  <=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(116,axiom,
    ! [A: $i] : ( i(A) = difference(A,one) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).

tff(117,plain,
    ! [A: $i] : ( i(A) = difference(A,one) ),
    inference(modus_ponens,[status(thm)],[116,115]) ).

tff(118,plain,
    ! [A: $i] : ( i(A) = difference(A,one) ),
    inference(skolemize,[status(sab)],[117]) ).

tff(119,plain,
    ! [A: $i] : ( i(A) = difference(A,one) ),
    inference(modus_ponens,[status(thm)],[118,114]) ).

tff(120,plain,
    ( ~ ! [A: $i] : ( i(A) = difference(A,one) )
    | ( i(quotient(one,x0)) = difference(quotient(one,x0),one) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(121,plain,
    i(quotient(one,x0)) = difference(quotient(one,x0),one),
    inference(unit_resolution,[status(thm)],[120,119]) ).

tff(122,plain,
    i(quotient(one,x0)) = x0,
    inference(transitivity,[status(thm)],[121,112,110]) ).

tff(123,plain,
    i(i(quotient(one,x0))) = i(x0),
    inference(monotonicity,[status(thm)],[122]) ).

tff(124,plain,
    product(i(i(quotient(one,x0))),x0) = product(i(x0),x0),
    inference(monotonicity,[status(thm)],[123]) ).

tff(125,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
      <=> ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) )),
    inference(bind,[status(th)],]) ).

tff(126,plain,
    ( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
  <=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
    inference(quant_intro,[status(thm)],[125]) ).

tff(127,plain,
    ( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
  <=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(128,axiom,
    ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).

tff(129,plain,
    ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
    inference(modus_ponens,[status(thm)],[128,127]) ).

tff(130,plain,
    ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
    inference(skolemize,[status(sab)],[129]) ).

tff(131,plain,
    ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
    inference(modus_ponens,[status(thm)],[130,126]) ).

tff(132,plain,
    ( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
    | ( product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(133,plain,
    product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
    inference(unit_resolution,[status(thm)],[132,131]) ).

tff(134,plain,
    product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) = product(i(i(quotient(one,x0))),x0),
    inference(symmetry,[status(thm)],[133]) ).

tff(135,plain,
    ^ [A: $i] :
      refl(
        ( ( eta(A) = product(i(A),A) )
      <=> ( eta(A) = product(i(A),A) ) )),
    inference(bind,[status(th)],]) ).

tff(136,plain,
    ( ! [A: $i] : ( eta(A) = product(i(A),A) )
  <=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
    inference(quant_intro,[status(thm)],[135]) ).

tff(137,plain,
    ( ! [A: $i] : ( eta(A) = product(i(A),A) )
  <=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(138,axiom,
    ! [A: $i] : ( eta(A) = product(i(A),A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).

tff(139,plain,
    ! [A: $i] : ( eta(A) = product(i(A),A) ),
    inference(modus_ponens,[status(thm)],[138,137]) ).

tff(140,plain,
    ! [A: $i] : ( eta(A) = product(i(A),A) ),
    inference(skolemize,[status(sab)],[139]) ).

tff(141,plain,
    ! [A: $i] : ( eta(A) = product(i(A),A) ),
    inference(modus_ponens,[status(thm)],[140,136]) ).

tff(142,plain,
    ( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
    | ( eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(143,plain,
    eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
    inference(unit_resolution,[status(thm)],[142,141]) ).

tff(144,plain,
    product(i(quotient(one,x0)),quotient(one,x0)) = eta(quotient(one,x0)),
    inference(symmetry,[status(thm)],[143]) ).

tff(145,plain,
    i(j(x0)) = i(quotient(one,x0)),
    inference(monotonicity,[status(thm)],[49]) ).

tff(146,plain,
    i(quotient(one,x0)) = i(j(x0)),
    inference(symmetry,[status(thm)],[145]) ).

tff(147,plain,
    product(i(quotient(one,x0)),quotient(one,x0)) = product(i(j(x0)),j(x0)),
    inference(monotonicity,[status(thm)],[146,50]) ).

tff(148,plain,
    product(i(j(x0)),j(x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
    inference(symmetry,[status(thm)],[147]) ).

tff(149,plain,
    i(j(x0)) = x0,
    inference(transitivity,[status(thm)],[145,121,112,110]) ).

tff(150,plain,
    product(i(j(x0)),j(x0)) = product(x0,j(x0)),
    inference(monotonicity,[status(thm)],[149]) ).

tff(151,plain,
    product(x0,j(x0)) = product(i(j(x0)),j(x0)),
    inference(symmetry,[status(thm)],[150]) ).

tff(152,plain,
    product(x0,j(x0)) = eta(quotient(one,x0)),
    inference(transitivity,[status(thm)],[151,148,144]) ).

tff(153,plain,
    product(product(x0,j(x0)),product(quotient(one,x0),x0)) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
    inference(monotonicity,[status(thm)],[152]) ).

tff(154,plain,
    ( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
    | ( product(quotient(one,x1),x1) = one ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(155,plain,
    product(quotient(one,x1),x1) = one,
    inference(unit_resolution,[status(thm)],[154,35]) ).

tff(156,plain,
    product(quotient(one,x1),x1) = product(quotient(one,x0),x0),
    inference(transitivity,[status(thm)],[155,111]) ).

tff(157,plain,
    eta(quotient(one,x0)) = product(x0,j(x0)),
    inference(transitivity,[status(thm)],[143,147,150]) ).

tff(158,plain,
    product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(x0,j(x0)),product(quotient(one,x0),x0)),
    inference(monotonicity,[status(thm)],[157,156]) ).

tff(159,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
      <=> ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) )),
    inference(bind,[status(th)],]) ).

tff(160,plain,
    ( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
  <=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
    inference(quant_intro,[status(thm)],[159]) ).

tff(161,plain,
    ( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
  <=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(162,axiom,
    ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).

tff(163,plain,
    ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
    inference(modus_ponens,[status(thm)],[162,161]) ).

tff(164,plain,
    ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
    inference(skolemize,[status(sab)],[163]) ).

tff(165,plain,
    ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
    inference(modus_ponens,[status(thm)],[164,160]) ).

tff(166,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
    | ( product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(167,plain,
    product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1),
    inference(unit_resolution,[status(thm)],[166,165]) ).

tff(168,plain,
    product(product(eta(quotient(one,x0)),quotient(one,x1)),x1) = product(eta(quotient(one,x0)),product(quotient(one,x1),x1)),
    inference(symmetry,[status(thm)],[167]) ).

tff(169,plain,
    product(eta(quotient(one,x0)),quotient(one,x1)) = product(product(x0,j(x0)),quotient(one,x1)),
    inference(monotonicity,[status(thm)],[157]) ).

tff(170,plain,
    product(product(x0,j(x0)),quotient(one,x1)) = product(eta(quotient(one,x0)),quotient(one,x1)),
    inference(symmetry,[status(thm)],[169]) ).

tff(171,plain,
    product(product(product(x0,j(x0)),quotient(one,x1)),x1) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1),
    inference(monotonicity,[status(thm)],[170]) ).

tff(172,plain,
    product(product(product(x0,j(x0)),quotient(one,x1)),x1) = product(product(x0,j(product(x1,x0))),x1),
    inference(transitivity,[status(thm)],[171,168,158,153,134,124,108,99,80]) ).

tff(173,plain,
    quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = quotient(product(product(x0,j(product(x1,x0))),x1),x1),
    inference(monotonicity,[status(thm)],[172]) ).

tff(174,plain,
    ( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
    | ( quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = product(product(x0,j(x0)),quotient(one,x1)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(175,plain,
    quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = product(product(x0,j(x0)),quotient(one,x1)),
    inference(unit_resolution,[status(thm)],[174,76]) ).

tff(176,plain,
    product(product(x0,j(x0)),quotient(one,x1)) = quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1),
    inference(symmetry,[status(thm)],[175]) ).

tff(177,plain,
    product(product(x0,j(x0)),quotient(one,x1)) = product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))),
    inference(transitivity,[status(thm)],[176,173,78,69]) ).

tff(178,plain,
    difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))),
    inference(monotonicity,[status(thm)],[177]) ).

tff(179,plain,
    difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))),
    inference(symmetry,[status(thm)],[178]) ).

tff(180,plain,
    ( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
    | ( eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(181,plain,
    eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))),
    inference(unit_resolution,[status(thm)],[180,141]) ).

tff(182,plain,
    product(i(j(j(x0))),j(j(x0))) = eta(j(j(x0))),
    inference(symmetry,[status(thm)],[181]) ).

tff(183,plain,
    ( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
    | ( difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(184,plain,
    difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0),
    inference(unit_resolution,[status(thm)],[183,17]) ).

tff(185,plain,
    quotient(one,quotient(one,x0)) = quotient(one,j(x0)),
    inference(monotonicity,[status(thm)],[50]) ).

tff(186,plain,
    quotient(one,j(x0)) = quotient(one,quotient(one,x0)),
    inference(symmetry,[status(thm)],[185]) ).

tff(187,plain,
    ( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
    | ( j(j(x0)) = quotient(one,j(x0)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(188,plain,
    j(j(x0)) = quotient(one,j(x0)),
    inference(unit_resolution,[status(thm)],[187,7]) ).

tff(189,plain,
    j(j(x0)) = quotient(one,quotient(one,x0)),
    inference(transitivity,[status(thm)],[188,186]) ).

tff(190,plain,
    product(j(j(x0)),quotient(one,x0)) = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
    inference(monotonicity,[status(thm)],[189]) ).

tff(191,plain,
    product(quotient(one,quotient(one,x0)),quotient(one,x0)) = product(j(j(x0)),quotient(one,x0)),
    inference(symmetry,[status(thm)],[190]) ).

tff(192,plain,
    ( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
    | ( product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(193,plain,
    product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one,
    inference(unit_resolution,[status(thm)],[192,35]) ).

tff(194,plain,
    one = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
    inference(symmetry,[status(thm)],[193]) ).

tff(195,plain,
    one = product(j(j(x0)),quotient(one,x0)),
    inference(transitivity,[status(thm)],[194,191]) ).

tff(196,plain,
    difference(j(j(x0)),one) = difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))),
    inference(monotonicity,[status(thm)],[195]) ).

tff(197,plain,
    ( ~ ! [A: $i] : ( i(A) = difference(A,one) )
    | ( i(j(j(x0))) = difference(j(j(x0)),one) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(198,plain,
    i(j(j(x0))) = difference(j(j(x0)),one),
    inference(unit_resolution,[status(thm)],[197,119]) ).

tff(199,plain,
    i(j(j(x0))) = j(x0),
    inference(transitivity,[status(thm)],[198,196,184,50]) ).

tff(200,plain,
    product(i(j(j(x0))),j(j(x0))) = product(j(x0),j(j(x0))),
    inference(monotonicity,[status(thm)],[199]) ).

tff(201,plain,
    product(j(x0),j(j(x0))) = product(i(j(j(x0))),j(j(x0))),
    inference(symmetry,[status(thm)],[200]) ).

tff(202,plain,
    ( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
    | ( product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(203,plain,
    product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))),
    inference(unit_resolution,[status(thm)],[202,106]) ).

tff(204,plain,
    product(x0,j(x0)) = eta(j(j(x0))),
    inference(transitivity,[status(thm)],[151,203,201,182]) ).

tff(205,plain,
    product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
    inference(monotonicity,[status(thm)],[204]) ).

tff(206,plain,
    product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
    inference(symmetry,[status(thm)],[205]) ).

tff(207,plain,
    ( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
    | ( product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(208,plain,
    product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
    inference(unit_resolution,[status(thm)],[207,131]) ).

tff(209,plain,
    i(i(j(j(x0)))) = i(j(x0)),
    inference(monotonicity,[status(thm)],[199]) ).

tff(210,plain,
    i(i(j(j(x0)))) = x0,
    inference(transitivity,[status(thm)],[209,145,121,112,110]) ).

tff(211,plain,
    product(i(i(j(j(x0)))),j(product(x1,x0))) = product(x0,j(product(x1,x0))),
    inference(monotonicity,[status(thm)],[210]) ).

tff(212,plain,
    product(x0,j(product(x1,x0))) = product(i(i(j(j(x0)))),j(product(x1,x0))),
    inference(symmetry,[status(thm)],[211]) ).

tff(213,plain,
    product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
    inference(transitivity,[status(thm)],[68,212,208,206]) ).

tff(214,plain,
    difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
    inference(monotonicity,[status(thm)],[213]) ).

tff(215,plain,
    difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))),
    inference(symmetry,[status(thm)],[214]) ).

tff(216,plain,
    ( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
    | ( difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(217,plain,
    difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))),
    inference(unit_resolution,[status(thm)],[216,17]) ).

tff(218,plain,
    product(j(j(x0)),j(product(x1,x0))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
    inference(symmetry,[status(thm)],[217]) ).

tff(219,plain,
    product(j(j(x0)),j(product(x1,x0))) = j(x1),
    inference(transitivity,[status(thm)],[218,215,179,19,10]) ).

tff(220,plain,
    ( ( product(j(j(x0)),j(product(x1,x0))) != j(x1) )
  <=> ( product(j(j(x0)),j(product(x1,x0))) != j(x1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(221,axiom,
    product(j(j(x0)),j(product(x1,x0))) != j(x1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(222,plain,
    product(j(j(x0)),j(product(x1,x0))) != j(x1),
    inference(modus_ponens,[status(thm)],[221,220]) ).

tff(223,plain,
    $false,
    inference(unit_resolution,[status(thm)],[222,219]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n004.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 : Wed Aug 31 20:54:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 11.08/7.33  % SZS status Unsatisfiable
% 11.08/7.33  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------