## TSTP Solution File: KLE089+1 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n083.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.75MB
% OS       : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Tue Jan 17 18:03:38 EST 2017

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  133 ( 116 unt;  11 typ;   0 def)
%            Number of atoms       :  366 ( 238 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  784 (  39   ~;  24   |;   4   &; 709   @)
%                                         (   2 <=>;   0  =>;   6  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg; 709 nst)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  201 (   0   ^ 201   !;   0   ?; 201   :)

%------------------------------------------------------------------------------
addition: \$i > \$i > \$i ).

thf(tp_antidomain,type,
antidomain: \$i > \$i ).

thf(tp_coantidomain,type,
coantidomain: \$i > \$i ).

thf(tp_codomain,type,
codomain: \$i > \$i ).

thf(tp_domain,type,
domain: \$i > \$i ).

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

thf(tp_multiplication,type,
multiplication: \$i > \$i > \$i ).

thf(tp_one,type,
one: \$i ).

thf(tp_sK1_X0,type,
sK1_X0: \$i ).

thf(tp_sK2_SY34,type,
sK2_SY34: \$i ).

thf(tp_zero,type,
zero: \$i ).

thf(1,axiom,
! [X0: \$i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).

thf(2,axiom,
! [X0: \$i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).

thf(3,axiom,
! [X0: \$i,X1: \$i] :
( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).

thf(4,axiom,
! [X0: \$i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).

thf(5,axiom,
! [X0: \$i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).

thf(6,axiom,
! [X0: \$i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).

thf(7,axiom,
! [X0: \$i,X1: \$i] :
( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
= ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).

thf(8,axiom,
! [X0: \$i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

thf(9,axiom,
! [A: \$i,B: \$i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

thf(10,axiom,
! [A: \$i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

thf(11,axiom,
! [A: \$i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).

thf(12,axiom,
! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

thf(13,axiom,
! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

thf(14,axiom,
! [A: \$i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).

thf(15,axiom,
! [A: \$i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).

thf(16,axiom,
! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

thf(17,axiom,
! [A: \$i] :
( ( addition @ A @ A )
= A ),

thf(18,axiom,
! [A: \$i] :
( ( addition @ A @ zero )
= A ),

thf(19,axiom,
! [C: \$i,B: \$i,A: \$i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),

thf(20,axiom,
! [A: \$i,B: \$i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),

thf(21,conjecture,
! [X0: \$i,X1: \$i] :
( ( ( multiplication @ ( domain @ X0 ) @ X1 )
= zero )
<= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
= ( antidomain @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(22,negated_conjecture,
( ( ! [X0: \$i,X1: \$i] :
( ( ( multiplication @ ( domain @ X0 ) @ X1 )
= zero )
<= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
= ( antidomain @ X1 ) ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[21]) ).

thf(23,plain,
( ( ! [X0: \$i,X1: \$i] :
( ( ( multiplication @ ( domain @ X0 ) @ X1 )
= zero )
<= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
= ( antidomain @ X1 ) ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[22]) ).

thf(24,plain,
( ( ! [X0: \$i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[1]) ).

thf(25,plain,
( ( ! [X0: \$i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= \$true ),
inference(unfold_def,[status(thm)],[2]) ).

thf(26,plain,
( ( ! [X0: \$i,X1: \$i] :
( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[3]) ).

thf(27,plain,
( ( ! [X0: \$i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= \$true ),
inference(unfold_def,[status(thm)],[4]) ).

thf(28,plain,
( ( ! [X0: \$i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[5]) ).

thf(29,plain,
( ( ! [X0: \$i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= \$true ),
inference(unfold_def,[status(thm)],[6]) ).

thf(30,plain,
( ( ! [X0: \$i,X1: \$i] :
( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
= ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[7]) ).

thf(31,plain,
( ( ! [X0: \$i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= \$true ),
inference(unfold_def,[status(thm)],[8]) ).

thf(32,plain,
( ( ! [A: \$i,B: \$i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[9]) ).

thf(33,plain,
( ( ! [A: \$i] :
( ( multiplication @ zero @ A )
= zero ) )
= \$true ),
inference(unfold_def,[status(thm)],[10]) ).

thf(34,plain,
( ( ! [A: \$i] :
( ( multiplication @ A @ zero )
= zero ) )
= \$true ),
inference(unfold_def,[status(thm)],[11]) ).

thf(35,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[12]) ).

thf(36,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[13]) ).

thf(37,plain,
( ( ! [A: \$i] :
( ( multiplication @ one @ A )
= A ) )
= \$true ),
inference(unfold_def,[status(thm)],[14]) ).

thf(38,plain,
( ( ! [A: \$i] :
( ( multiplication @ A @ one )
= A ) )
= \$true ),
inference(unfold_def,[status(thm)],[15]) ).

thf(39,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[16]) ).

thf(40,plain,
( ( ! [A: \$i] :
( ( addition @ A @ A )
= A ) )
= \$true ),
inference(unfold_def,[status(thm)],[17]) ).

thf(41,plain,
( ( ! [A: \$i] :
( ( addition @ A @ zero )
= A ) )
= \$true ),
inference(unfold_def,[status(thm)],[18]) ).

thf(42,plain,
( ( ! [C: \$i,B: \$i,A: \$i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[19]) ).

thf(43,plain,
( ( ! [A: \$i,B: \$i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[20]) ).

thf(44,plain,
( ( ! [SY34: \$i] :
( ( ( multiplication @ ( domain @ sK1_X0 ) @ SY34 )
= zero )
<= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ SY34 ) )
= ( antidomain @ SY34 ) ) ) )
= \$false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).

thf(45,plain,
( ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
= zero )
<= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
= ( antidomain @ sK2_SY34 ) ) )
= \$false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).

thf(46,plain,
( ( ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
= zero )
<= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
= ( antidomain @ sK2_SY34 ) ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[45]) ).

thf(47,plain,
( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
= ( antidomain @ sK2_SY34 ) )
& ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[46]) ).

thf(48,plain,
( ( ! [A: \$i,B: \$i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) )
& ! [A: \$i,B: \$i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[32]) ).

thf(49,plain,
( ( ! [A: \$i,B: \$i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= \$true ),
inference(copy,[status(thm)],[43]) ).

thf(50,plain,
( ( ! [C: \$i,B: \$i,A: \$i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= \$true ),
inference(copy,[status(thm)],[42]) ).

thf(51,plain,
( ( ! [A: \$i] :
( ( addition @ A @ zero )
= A ) )
= \$true ),
inference(copy,[status(thm)],[41]) ).

thf(52,plain,
( ( ! [A: \$i] :
( ( addition @ A @ A )
= A ) )
= \$true ),
inference(copy,[status(thm)],[40]) ).

thf(53,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= \$true ),
inference(copy,[status(thm)],[39]) ).

thf(54,plain,
( ( ! [A: \$i] :
( ( multiplication @ A @ one )
= A ) )
= \$true ),
inference(copy,[status(thm)],[38]) ).

thf(55,plain,
( ( ! [A: \$i] :
( ( multiplication @ one @ A )
= A ) )
= \$true ),
inference(copy,[status(thm)],[37]) ).

thf(56,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= \$true ),
inference(copy,[status(thm)],[36]) ).

thf(57,plain,
( ( ! [A: \$i,B: \$i,C: \$i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= \$true ),
inference(copy,[status(thm)],[35]) ).

thf(58,plain,
( ( ! [A: \$i] :
( ( multiplication @ A @ zero )
= zero ) )
= \$true ),
inference(copy,[status(thm)],[34]) ).

thf(59,plain,
( ( ! [A: \$i] :
( ( multiplication @ zero @ A )
= zero ) )
= \$true ),
inference(copy,[status(thm)],[33]) ).

thf(60,plain,
( ( ! [A: \$i,B: \$i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) )
& ! [A: \$i,B: \$i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ) )
= \$true ),
inference(copy,[status(thm)],[48]) ).

thf(61,plain,
( ( ! [X0: \$i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= \$true ),
inference(copy,[status(thm)],[31]) ).

thf(62,plain,
( ( ! [X0: \$i,X1: \$i] :
( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
= ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ) )
= \$true ),
inference(copy,[status(thm)],[30]) ).

thf(63,plain,
( ( ! [X0: \$i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= \$true ),
inference(copy,[status(thm)],[29]) ).

thf(64,plain,
( ( ! [X0: \$i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= \$true ),
inference(copy,[status(thm)],[28]) ).

thf(65,plain,
( ( ! [X0: \$i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= \$true ),
inference(copy,[status(thm)],[27]) ).

thf(66,plain,
( ( ! [X0: \$i,X1: \$i] :
( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ) )
= \$true ),
inference(copy,[status(thm)],[26]) ).

thf(67,plain,
( ( ! [X0: \$i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= \$true ),
inference(copy,[status(thm)],[25]) ).

thf(68,plain,
( ( ! [X0: \$i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= \$true ),
inference(copy,[status(thm)],[24]) ).

thf(69,plain,
( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
= ( antidomain @ sK2_SY34 ) )
& ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) )
= \$true ),
inference(copy,[status(thm)],[47]) ).

thf(70,plain,
( ( ~ ( ~ ! [SX0: \$i,SX1: \$i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: \$i,SX1: \$i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[60]) ).

thf(71,plain,
( ( ~ ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
!= ( antidomain @ sK2_SY34 ) )
| ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[69]) ).

thf(72,plain,
! [SV1: \$i] :
( ( ! [SY35: \$i] :
( ( addition @ SV1 @ SY35 )
= ( addition @ SY35 @ SV1 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(73,plain,
! [SV2: \$i] :
( ( ! [SY36: \$i,SY37: \$i] :
( ( addition @ SY37 @ ( addition @ SY36 @ SV2 ) )
= ( addition @ ( addition @ SY37 @ SY36 ) @ SV2 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(74,plain,
! [SV3: \$i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(75,plain,
! [SV4: \$i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(76,plain,
! [SV5: \$i] :
( ( ! [SY38: \$i,SY39: \$i] :
( ( multiplication @ SV5 @ ( multiplication @ SY38 @ SY39 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY38 ) @ SY39 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(77,plain,
! [SV6: \$i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(78,plain,
! [SV7: \$i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(79,plain,
! [SV8: \$i] :
( ( ! [SY40: \$i,SY41: \$i] :
( ( multiplication @ SV8 @ ( addition @ SY40 @ SY41 ) )
= ( addition @ ( multiplication @ SV8 @ SY40 ) @ ( multiplication @ SV8 @ SY41 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(80,plain,
! [SV9: \$i] :
( ( ! [SY42: \$i,SY43: \$i] :
( ( multiplication @ ( addition @ SV9 @ SY42 ) @ SY43 )
= ( addition @ ( multiplication @ SV9 @ SY43 ) @ ( multiplication @ SY42 @ SY43 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(81,plain,
! [SV10: \$i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(82,plain,
! [SV11: \$i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(83,plain,
! [SV12: \$i] :
( ( ( multiplication @ ( antidomain @ SV12 ) @ SV12 )
= zero )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(84,plain,
! [SV13: \$i] :
( ( ! [SY44: \$i] :
( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SY44 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY44 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY44 ) ) ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(85,plain,
! [SV14: \$i] :
( ( ( addition @ ( antidomain @ ( antidomain @ SV14 ) ) @ ( antidomain @ SV14 ) )
= one )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(86,plain,
! [SV15: \$i] :
( ( ( domain @ SV15 )
= ( antidomain @ ( antidomain @ SV15 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(87,plain,
! [SV16: \$i] :
( ( ( multiplication @ SV16 @ ( coantidomain @ SV16 ) )
= zero )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(88,plain,
! [SV17: \$i] :
( ( ! [SY45: \$i] :
( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SY45 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY45 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY45 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(89,plain,
! [SV18: \$i] :
( ( ( addition @ ( coantidomain @ ( coantidomain @ SV18 ) ) @ ( coantidomain @ SV18 ) )
= one )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(90,plain,
! [SV19: \$i] :
( ( ( codomain @ SV19 )
= ( coantidomain @ ( coantidomain @ SV19 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(91,plain,
( ( ~ ! [SX0: \$i,SX1: \$i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: \$i,SX1: \$i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(92,plain,
( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
!= ( antidomain @ sK2_SY34 ) )
| ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(93,plain,
! [SV20: \$i,SV1: \$i] :
( ( ( addition @ SV1 @ SV20 )
= ( addition @ SV20 @ SV1 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(94,plain,
! [SV2: \$i,SV21: \$i] :
( ( ! [SY46: \$i] :
( ( addition @ SY46 @ ( addition @ SV21 @ SV2 ) )
= ( addition @ ( addition @ SY46 @ SV21 ) @ SV2 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(95,plain,
! [SV22: \$i,SV5: \$i] :
( ( ! [SY47: \$i] :
( ( multiplication @ SV5 @ ( multiplication @ SV22 @ SY47 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV22 ) @ SY47 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(96,plain,
! [SV23: \$i,SV8: \$i] :
( ( ! [SY48: \$i] :
( ( multiplication @ SV8 @ ( addition @ SV23 @ SY48 ) )
= ( addition @ ( multiplication @ SV8 @ SV23 ) @ ( multiplication @ SV8 @ SY48 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(97,plain,
! [SV24: \$i,SV9: \$i] :
( ( ! [SY49: \$i] :
( ( multiplication @ ( addition @ SV9 @ SV24 ) @ SY49 )
= ( addition @ ( multiplication @ SV9 @ SY49 ) @ ( multiplication @ SV24 @ SY49 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(98,plain,
! [SV25: \$i,SV13: \$i] :
( ( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SV25 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV25 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV25 ) ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(99,plain,
! [SV26: \$i,SV17: \$i] :
( ( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SV26 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV26 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV26 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(100,plain,
( ( ~ ! [SX0: \$i,SX1: \$i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(101,plain,
( ( ~ ! [SX0: \$i,SX1: \$i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(102,plain,
( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
!= ( antidomain @ sK2_SY34 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(103,plain,
( ( ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(104,plain,
! [SV2: \$i,SV21: \$i,SV27: \$i] :
( ( ( addition @ SV27 @ ( addition @ SV21 @ SV2 ) )
= ( addition @ ( addition @ SV27 @ SV21 ) @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(105,plain,
! [SV28: \$i,SV22: \$i,SV5: \$i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV22 @ SV28 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV22 ) @ SV28 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(106,plain,
! [SV29: \$i,SV23: \$i,SV8: \$i] :
( ( ( multiplication @ SV8 @ ( addition @ SV23 @ SV29 ) )
= ( addition @ ( multiplication @ SV8 @ SV23 ) @ ( multiplication @ SV8 @ SV29 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(107,plain,
! [SV30: \$i,SV24: \$i,SV9: \$i] :
( ( ( multiplication @ ( addition @ SV9 @ SV24 ) @ SV30 )
= ( addition @ ( multiplication @ SV9 @ SV30 ) @ ( multiplication @ SV24 @ SV30 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(108,plain,
( ( ! [SX0: \$i,SX1: \$i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(109,plain,
( ( ! [SX0: \$i,SX1: \$i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).

thf(110,plain,
( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
= ( antidomain @ sK2_SY34 ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).

thf(111,plain,
( ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
!= zero ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(112,plain,
! [SV31: \$i] :
( ( ! [SY50: \$i] :
( ( ( addition @ SV31 @ SY50 )
!= SY50 )
| ( leq @ SV31 @ SY50 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(113,plain,
! [SV32: \$i] :
( ( ! [SY51: \$i] :
( ~ ( leq @ SV32 @ SY51 )
| ( ( addition @ SV32 @ SY51 )
= SY51 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(114,plain,
( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
= zero )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(115,plain,
! [SV33: \$i,SV31: \$i] :
( ( ( ( addition @ SV31 @ SV33 )
!= SV33 )
| ( leq @ SV31 @ SV33 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(116,plain,
! [SV34: \$i,SV32: \$i] :
( ( ~ ( leq @ SV32 @ SV34 )
| ( ( addition @ SV32 @ SV34 )
= SV34 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(117,plain,
! [SV33: \$i,SV31: \$i] :
( ( ( ( ( addition @ SV31 @ SV33 )
!= SV33 ) )
= \$true )
| ( ( leq @ SV31 @ SV33 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).

thf(118,plain,
! [SV34: \$i,SV32: \$i] :
( ( ( ~ ( leq @ SV32 @ SV34 ) )
= \$true )
| ( ( ( addition @ SV32 @ SV34 )
= SV34 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(119,plain,
! [SV33: \$i,SV31: \$i] :
( ( ( ( addition @ SV31 @ SV33 )
= SV33 )
= \$false )
| ( ( leq @ SV31 @ SV33 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(120,plain,
! [SV34: \$i,SV32: \$i] :
( ( ( leq @ SV32 @ SV34 )
= \$false )
| ( ( ( addition @ SV32 @ SV34 )
= SV34 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(121,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[74,120,119,114,110,107,106,105,104,99,98,93,90,89,87,86,85,83,82,81,78,77,75]) ).

thf(122,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[121]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.03/0.23  % Computer : n083.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.75MB
% 0.03/0.23  % OS       : Linux 3.10.0-327.36.3.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Sat Jan 14 16:34:33 CST 2017
% 0.03/0.23  % CPUTime  :
% 0.03/0.24
% 0.03/0.24   No.of.Axioms: 20
% 0.03/0.24
% 0.03/0.24   Length.of.Defs: 0
% 0.03/0.24
% 0.03/0.24   Contains.Choice.Funs: false
% 0.03/0.25  .
% 0.03/0.25  (rf:0,axioms:20,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.06/0.65
% 0.06/0.65  ********************************
% 0.06/0.65  *   All subproblems solved!    *
% 0.06/0.65  ********************************
% 0.06/0.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.65
% 0.06/0.65  %**** Beginning of derivation protocol ****
% 0.06/0.65  % SZS output start CNFRefutation
% See solution above
% 0.06/0.65  % SZS output end CNFRefutation
% 0.06/0.65
% 0.06/0.65  %**** End of derivation protocol ****
% 0.06/0.65  %**** no. of clauses in derivation: 122 ****
% 0.06/0.65  %**** clause counter: 121 ****
% 0.06/0.65
% 0.06/0.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```