TSTP Solution File: GRP012-4 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 22:25:26 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  111 (  79 unt;   5 typ;   0 def)
%            Number of atoms       :  143 ( 137 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   52 (  20   ~;  16   |;   0   &)
%                                         (  16 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :    5 (   5 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   91 (  84   !;   0   ?;  91   :)

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

tff(inverse_type,type,
    inverse: $i > $i ).

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

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

tff(identity_type,type,
    identity: $i ).

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

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

tff(3,plain,
    ( ! [X: $i] : ( multiply(inverse(X),X) = identity )
  <=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X: $i] : ( multiply(inverse(X),X) = identity ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

tff(5,plain,
    ! [X: $i] : ( multiply(inverse(X),X) = identity ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X: $i] : ( multiply(inverse(X),X) = identity ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X: $i] : ( multiply(inverse(X),X) = identity ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
    | ( multiply(inverse(a),a) = identity ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    multiply(inverse(a),a) = identity,
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X: $i] :
      refl(
        ( ( multiply(identity,X) = X )
      <=> ( multiply(identity,X) = X ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X: $i] : ( multiply(identity,X) = X )
  <=> ! [X: $i] : ( multiply(identity,X) = X ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X: $i] : ( multiply(identity,X) = X )
  <=> ! [X: $i] : ( multiply(identity,X) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [X: $i] : ( multiply(identity,X) = X ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

tff(14,plain,
    ! [X: $i] : ( multiply(identity,X) = X ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [X: $i] : ( multiply(identity,X) = X ),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X: $i] : ( multiply(identity,X) = X ),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [X: $i] : ( multiply(identity,X) = X )
    | ( multiply(identity,a) = a ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    multiply(identity,a) = a,
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    identity = multiply(inverse(a),a),
    inference(symmetry,[status(thm)],[9]) ).

tff(20,plain,
    multiply(identity,a) = multiply(multiply(inverse(a),a),a),
    inference(monotonicity,[status(thm)],[19]) ).

tff(21,plain,
    multiply(multiply(inverse(a),a),a) = multiply(identity,a),
    inference(symmetry,[status(thm)],[20]) ).

tff(22,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(
        ( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
      <=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

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

tff(25,axiom,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

tff(26,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(inverse(a),a),a) = multiply(inverse(a),multiply(a,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    multiply(multiply(inverse(a),a),a) = multiply(inverse(a),multiply(a,a)),
    inference(unit_resolution,[status(thm)],[29,28]) ).

tff(31,plain,
    multiply(inverse(a),multiply(a,a)) = multiply(multiply(inverse(a),a),a),
    inference(symmetry,[status(thm)],[30]) ).

tff(32,plain,
    multiply(inverse(a),multiply(a,a)) = a,
    inference(transitivity,[status(thm)],[31,21,18]) ).

tff(33,plain,
    multiply(inverse(a),multiply(inverse(a),multiply(a,a))) = multiply(inverse(a),a),
    inference(monotonicity,[status(thm)],[32]) ).

tff(34,plain,
    multiply(inverse(a),multiply(inverse(a),multiply(a,a))) = identity,
    inference(transitivity,[status(thm)],[33,9]) ).

tff(35,plain,
    multiply(multiply(inverse(a),multiply(inverse(a),multiply(a,a))),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(monotonicity,[status(thm)],[34]) ).

tff(36,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(inverse(a),multiply(inverse(a),multiply(a,a))),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(inverse(a),multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    multiply(multiply(inverse(a),multiply(inverse(a),multiply(a,a))),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(inverse(a),multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity)))),
    inference(unit_resolution,[status(thm)],[36,28]) ).

tff(38,plain,
    multiply(inverse(a),multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity)))) = multiply(multiply(inverse(a),multiply(inverse(a),multiply(a,a))),multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(symmetry,[status(thm)],[37]) ).

tff(39,plain,
    ^ [X: $i] :
      refl(
        ( ( multiply(X,identity) = X )
      <=> ( multiply(X,identity) = X ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X: $i] : ( multiply(X,identity) = X )
  <=> ! [X: $i] : ( multiply(X,identity) = X ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [X: $i] : ( multiply(X,identity) = X )
  <=> ! [X: $i] : ( multiply(X,identity) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ! [X: $i] : ( multiply(X,identity) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

tff(43,plain,
    ! [X: $i] : ( multiply(X,identity) = X ),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ! [X: $i] : ( multiply(X,identity) = X ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [X: $i] : ( multiply(X,identity) = X ),
    inference(modus_ponens,[status(thm)],[44,40]) ).

tff(46,plain,
    ( ~ ! [X: $i] : ( multiply(X,identity) = X )
    | ( multiply(inverse(multiply(a,b)),identity) = inverse(multiply(a,b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(47,plain,
    multiply(inverse(multiply(a,b)),identity) = inverse(multiply(a,b)),
    inference(unit_resolution,[status(thm)],[46,45]) ).

tff(48,plain,
    inverse(multiply(a,b)) = multiply(inverse(multiply(a,b)),identity),
    inference(symmetry,[status(thm)],[47]) ).

tff(49,plain,
    multiply(b,inverse(multiply(a,b))) = multiply(b,multiply(inverse(multiply(a,b)),identity)),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    multiply(b,multiply(inverse(multiply(a,b)),identity)) = multiply(b,inverse(multiply(a,b))),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(a,multiply(b,inverse(multiply(a,b)))),
    inference(monotonicity,[status(thm)],[32,50]) ).

tff(52,plain,
    multiply(a,multiply(b,inverse(multiply(a,b)))) = multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(symmetry,[status(thm)],[51]) ).

tff(53,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(a,b),inverse(multiply(a,b))) = multiply(a,multiply(b,inverse(multiply(a,b)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(54,plain,
    multiply(multiply(a,b),inverse(multiply(a,b))) = multiply(a,multiply(b,inverse(multiply(a,b)))),
    inference(unit_resolution,[status(thm)],[53,28]) ).

tff(55,plain,
    ^ [X: $i] :
      refl(
        ( ( multiply(X,inverse(X)) = identity )
      <=> ( multiply(X,inverse(X)) = identity ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
  <=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
  <=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,axiom,
    ! [X: $i] : ( multiply(X,inverse(X)) = identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).

tff(59,plain,
    ! [X: $i] : ( multiply(X,inverse(X)) = identity ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ! [X: $i] : ( multiply(X,inverse(X)) = identity ),
    inference(skolemize,[status(sab)],[59]) ).

tff(61,plain,
    ! [X: $i] : ( multiply(X,inverse(X)) = identity ),
    inference(modus_ponens,[status(thm)],[60,56]) ).

tff(62,plain,
    ( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
    | ( multiply(multiply(a,b),inverse(multiply(a,b))) = identity ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(63,plain,
    multiply(multiply(a,b),inverse(multiply(a,b))) = identity,
    inference(unit_resolution,[status(thm)],[62,61]) ).

tff(64,plain,
    identity = multiply(multiply(a,b),inverse(multiply(a,b))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    ( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
    | ( multiply(identity,inverse(identity)) = identity ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(66,plain,
    multiply(identity,inverse(identity)) = identity,
    inference(unit_resolution,[status(thm)],[65,61]) ).

tff(67,plain,
    ( ~ ! [X: $i] : ( multiply(identity,X) = X )
    | ( multiply(identity,inverse(identity)) = inverse(identity) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    multiply(identity,inverse(identity)) = inverse(identity),
    inference(unit_resolution,[status(thm)],[67,16]) ).

tff(69,plain,
    inverse(identity) = multiply(identity,inverse(identity)),
    inference(symmetry,[status(thm)],[68]) ).

tff(70,plain,
    inverse(identity) = multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(transitivity,[status(thm)],[69,66,64,54,52]) ).

tff(71,plain,
    multiply(inverse(a),inverse(identity)) = multiply(inverse(a),multiply(multiply(inverse(a),multiply(a,a)),multiply(b,multiply(inverse(multiply(a,b)),identity)))),
    inference(monotonicity,[status(thm)],[70]) ).

tff(72,plain,
    identity = multiply(identity,inverse(identity)),
    inference(symmetry,[status(thm)],[66]) ).

tff(73,plain,
    identity = inverse(identity),
    inference(transitivity,[status(thm)],[72,68]) ).

tff(74,plain,
    multiply(inverse(a),identity) = multiply(inverse(a),inverse(identity)),
    inference(monotonicity,[status(thm)],[73]) ).

tff(75,plain,
    ( ~ ! [X: $i] : ( multiply(X,identity) = X )
    | ( multiply(inverse(a),identity) = inverse(a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    multiply(inverse(a),identity) = inverse(a),
    inference(unit_resolution,[status(thm)],[75,45]) ).

tff(77,plain,
    inverse(a) = multiply(inverse(a),identity),
    inference(symmetry,[status(thm)],[76]) ).

tff(78,plain,
    inverse(a) = multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(transitivity,[status(thm)],[77,74,71,38,35]) ).

tff(79,plain,
    multiply(inverse(b),inverse(a)) = multiply(inverse(b),multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity)))),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    multiply(inverse(b),multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity)))) = multiply(inverse(b),inverse(a)),
    inference(symmetry,[status(thm)],[79]) ).

tff(81,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(inverse(b),identity),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(inverse(b),multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    multiply(multiply(inverse(b),identity),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(inverse(b),multiply(identity,multiply(b,multiply(inverse(multiply(a,b)),identity)))),
    inference(unit_resolution,[status(thm)],[81,28]) ).

tff(83,plain,
    ( ~ ! [X: $i] : ( multiply(X,identity) = X )
    | ( multiply(inverse(b),identity) = inverse(b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(84,plain,
    multiply(inverse(b),identity) = inverse(b),
    inference(unit_resolution,[status(thm)],[83,45]) ).

tff(85,plain,
    multiply(multiply(inverse(b),identity),multiply(b,multiply(inverse(multiply(a,b)),identity))) = multiply(inverse(b),multiply(b,inverse(multiply(a,b)))),
    inference(monotonicity,[status(thm)],[84,50]) ).

tff(86,plain,
    multiply(inverse(b),multiply(b,inverse(multiply(a,b)))) = multiply(multiply(inverse(b),identity),multiply(b,multiply(inverse(multiply(a,b)),identity))),
    inference(symmetry,[status(thm)],[85]) ).

tff(87,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(inverse(b),b),inverse(multiply(a,b))) = multiply(inverse(b),multiply(b,inverse(multiply(a,b)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(88,plain,
    multiply(multiply(inverse(b),b),inverse(multiply(a,b))) = multiply(inverse(b),multiply(b,inverse(multiply(a,b)))),
    inference(unit_resolution,[status(thm)],[87,28]) ).

tff(89,plain,
    ( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
    | ( multiply(inverse(multiply(a,b)),multiply(a,b)) = identity ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(90,plain,
    multiply(inverse(multiply(a,b)),multiply(a,b)) = identity,
    inference(unit_resolution,[status(thm)],[89,7]) ).

tff(91,plain,
    identity = multiply(inverse(multiply(a,b)),multiply(a,b)),
    inference(symmetry,[status(thm)],[90]) ).

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

tff(93,plain,
    multiply(inverse(b),b) = identity,
    inference(unit_resolution,[status(thm)],[92,7]) ).

tff(94,plain,
    multiply(inverse(b),b) = multiply(inverse(multiply(a,b)),multiply(a,b)),
    inference(transitivity,[status(thm)],[93,91]) ).

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

tff(96,plain,
    multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(multiply(inverse(b),b),inverse(multiply(a,b))),
    inference(symmetry,[status(thm)],[95]) ).

tff(97,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
    | ( multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(98,plain,
    multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))),
    inference(unit_resolution,[status(thm)],[97,28]) ).

tff(99,plain,
    multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) = multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))),
    inference(symmetry,[status(thm)],[98]) ).

tff(100,plain,
    multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) = multiply(inverse(multiply(a,b)),identity),
    inference(monotonicity,[status(thm)],[63]) ).

tff(101,plain,
    multiply(inverse(multiply(a,b)),identity) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))),
    inference(symmetry,[status(thm)],[100]) ).

tff(102,plain,
    inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)),
    inference(transitivity,[status(thm)],[48,101,99,96,88,86,82,80]) ).

tff(103,plain,
    ( ( inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) )
  <=> ( inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(104,axiom,
    inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).

tff(105,plain,
    inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
    inference(modus_ponens,[status(thm)],[104,103]) ).

tff(106,plain,
    $false,
    inference(unit_resolution,[status(thm)],[105,102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n002.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Aug 31 14:17:14 EDT 2022
% 0.13/0.33  % 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.
% 0.19/0.51  % SZS status Unsatisfiable
% 0.19/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------