TSTP Solution File: KLE131+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE131+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.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 : 600s
% DateTime : Sun Jul 17 02:11:28 EDT 2022
% Result : Theorem 265.94s 266.39s
% Output : CNFRefutation 265.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 47
% Syntax : Number of formulae : 191 ( 164 unt; 18 typ; 0 def)
% Number of atoms : 515 ( 342 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1452 ( 45 ~; 31 |; 4 &;1363 @)
% ( 2 <=>; 2 =>; 5 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 303 ( 0 ^ 303 !; 0 ?; 303 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_antidomain,type,
antidomain: $i > $i ).
thf(tp_backward_box,type,
backward_box: $i > $i > $i ).
thf(tp_backward_diamond,type,
backward_diamond: $i > $i > $i ).
thf(tp_c,type,
c: $i > $i ).
thf(tp_coantidomain,type,
coantidomain: $i > $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_divergence,type,
divergence: $i > $i ).
thf(tp_domain,type,
domain: $i > $i ).
thf(tp_domain_difference,type,
domain_difference: $i > $i > $i ).
thf(tp_forward_box,type,
forward_box: $i > $i > $i ).
thf(tp_forward_diamond,type,
forward_diamond: $i > $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_star,type,
star: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
=> ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
thf(2,axiom,
! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
thf(3,axiom,
! [X0: $i,X1: $i] :
( ( backward_box @ X0 @ X1 )
= ( c @ ( backward_diamond @ X0 @ ( c @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_box) ).
thf(4,axiom,
! [X0: $i,X1: $i] :
( ( forward_box @ X0 @ X1 )
= ( c @ ( forward_diamond @ X0 @ ( c @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_box) ).
thf(5,axiom,
! [X0: $i,X1: $i] :
( ( backward_diamond @ X0 @ X1 )
= ( codomain @ ( multiplication @ ( codomain @ X1 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
thf(6,axiom,
! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
thf(7,axiom,
! [X0: $i,X1: $i] :
( ( domain_difference @ X0 @ X1 )
= ( multiplication @ ( domain @ X0 ) @ ( antidomain @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_difference) ).
thf(8,axiom,
! [X0: $i] :
( ( c @ X0 )
= ( antidomain @ ( domain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(9,axiom,
! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(10,axiom,
! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(11,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(12,axiom,
! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(13,axiom,
! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(14,axiom,
! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(15,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(16,axiom,
! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(18,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(19,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(20,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(21,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(22,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(23,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(24,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(25,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(26,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(29,conjecture,
! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) )
= ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(30,negated_conjecture,
( ( ! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) )
= ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) )
= ( forward_diamond @ ( star @ X0 ) @ ( domain_difference @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
=> ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [X0: $i,X1: $i] :
( ( backward_box @ X0 @ X1 )
= ( c @ ( backward_diamond @ X0 @ ( c @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_box @ X0 @ X1 )
= ( c @ ( forward_diamond @ X0 @ ( c @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [X0: $i,X1: $i] :
( ( backward_diamond @ X0 @ X1 )
= ( codomain @ ( multiplication @ ( codomain @ X1 ) @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [X0: $i,X1: $i] :
( ( domain_difference @ X0 @ X1 )
= ( multiplication @ ( domain @ X0 ) @ ( antidomain @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,plain,
( ( ! [X0: $i] :
( ( c @ X0 )
= ( antidomain @ ( domain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( ! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,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)],[11]) ).
thf(43,plain,
( ( ! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(45,plain,
( ( ! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(46,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)],[15]) ).
thf(47,plain,
( ( ! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(51,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)],[20]) ).
thf(52,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)],[21]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(58,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
( ( ( ( divergence @ sK1_X0 )
= zero )
<= ! [SY150: $i] :
( ( addition @ ( domain @ SY150 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(61,plain,
( ( ~ ( ( ( divergence @ sK1_X0 )
= zero )
<= ! [SY150: $i] :
( ( addition @ ( domain @ SY150 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [SY150: $i] :
( ( addition @ ( domain @ SY150 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
& ( ( divergence @ sK1_X0 )
!= zero ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(63,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
!= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
| ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(64,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)],[48]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(66,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(69,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(73,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(76,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)],[64]) ).
thf(77,plain,
( ( ! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(78,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)],[46]) ).
thf(79,plain,
( ( ! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(80,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(81,plain,
( ( ! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(82,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)],[42]) ).
thf(83,plain,
( ( ! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(84,plain,
( ( ! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [X0: $i] :
( ( c @ X0 )
= ( antidomain @ ( domain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(86,plain,
( ( ! [X0: $i,X1: $i] :
( ( domain_difference @ X0 @ X1 )
= ( multiplication @ ( domain @ X0 ) @ ( antidomain @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(87,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(88,plain,
( ( ! [X0: $i,X1: $i] :
( ( backward_diamond @ X0 @ X1 )
= ( codomain @ ( multiplication @ ( codomain @ X1 ) @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(89,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_box @ X0 @ X1 )
= ( c @ ( forward_diamond @ X0 @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(90,plain,
( ( ! [X0: $i,X1: $i] :
( ( backward_box @ X0 @ X1 )
= ( c @ ( backward_diamond @ X0 @ ( c @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(91,plain,
( ( ! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(92,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
!= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
| ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(93,plain,
( ( ! [SY150: $i] :
( ( addition @ ( domain @ SY150 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SY150 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY150 ) ) ) ) )
& ( ( divergence @ sK1_X0 )
!= zero ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(94,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
| ~ ( ( ( divergence @ sK1_X0 )
!= zero ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(95,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)],[76]) ).
thf(96,plain,
! [SV1: $i] :
( ( ! [SY151: $i] :
( ( addition @ SV1 @ SY151 )
= ( addition @ SY151 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(97,plain,
! [SV2: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ( addition @ SY153 @ ( addition @ SY152 @ SV2 ) )
= ( addition @ ( addition @ SY153 @ SY152 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(98,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(99,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(100,plain,
! [SV5: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY154 @ SY155 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY154 ) @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(101,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(102,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(103,plain,
! [SV8: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ( multiplication @ SV8 @ ( addition @ SY156 @ SY157 ) )
= ( addition @ ( multiplication @ SV8 @ SY156 ) @ ( multiplication @ SV8 @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(104,plain,
! [SV9: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ( multiplication @ ( addition @ SV9 @ SY158 ) @ SY159 )
= ( addition @ ( multiplication @ SV9 @ SY159 ) @ ( multiplication @ SY158 @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(105,plain,
! [SV10: $i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(106,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(107,plain,
! [SV12: $i] :
( ( ( multiplication @ ( antidomain @ SV12 ) @ SV12 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(108,plain,
! [SV13: $i] :
( ( ! [SY160: $i] :
( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SY160 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY160 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY160 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(109,plain,
! [SV14: $i] :
( ( ( addition @ ( antidomain @ ( antidomain @ SV14 ) ) @ ( antidomain @ SV14 ) )
= one )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(110,plain,
! [SV15: $i] :
( ( ( domain @ SV15 )
= ( antidomain @ ( antidomain @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(111,plain,
! [SV16: $i] :
( ( ( multiplication @ SV16 @ ( coantidomain @ SV16 ) )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(112,plain,
! [SV17: $i] :
( ( ! [SY161: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SY161 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY161 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(113,plain,
! [SV18: $i] :
( ( ( addition @ ( coantidomain @ ( coantidomain @ SV18 ) ) @ ( coantidomain @ SV18 ) )
= one )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(114,plain,
! [SV19: $i] :
( ( ( codomain @ SV19 )
= ( coantidomain @ ( coantidomain @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(115,plain,
! [SV20: $i] :
( ( ( c @ SV20 )
= ( antidomain @ ( domain @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(116,plain,
! [SV21: $i] :
( ( ! [SY162: $i] :
( ( domain_difference @ SV21 @ SY162 )
= ( multiplication @ ( domain @ SV21 ) @ ( antidomain @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(117,plain,
! [SV22: $i] :
( ( ! [SY163: $i] :
( ( forward_diamond @ SV22 @ SY163 )
= ( domain @ ( multiplication @ SV22 @ ( domain @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(118,plain,
! [SV23: $i] :
( ( ! [SY164: $i] :
( ( backward_diamond @ SV23 @ SY164 )
= ( codomain @ ( multiplication @ ( codomain @ SY164 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(119,plain,
! [SV24: $i] :
( ( ! [SY165: $i] :
( ( forward_box @ SV24 @ SY165 )
= ( c @ ( forward_diamond @ SV24 @ ( c @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(120,plain,
! [SV25: $i] :
( ( ! [SY166: $i] :
( ( backward_box @ SV25 @ SY166 )
= ( c @ ( backward_diamond @ SV25 @ ( c @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(121,plain,
! [SV26: $i] :
( ( ( forward_diamond @ SV26 @ ( divergence @ SV26 ) )
= ( divergence @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(122,plain,
! [SV27: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( forward_diamond @ SY167 @ ( domain @ SV27 ) ) @ ( domain @ SY168 ) ) )
!= ( addition @ ( forward_diamond @ SY167 @ ( domain @ SV27 ) ) @ ( domain @ SY168 ) ) )
| ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( divergence @ SY167 ) @ ( forward_diamond @ ( star @ SY167 ) @ ( domain @ SY168 ) ) ) )
= ( addition @ ( divergence @ SY167 ) @ ( forward_diamond @ ( star @ SY167 ) @ ( domain @ SY168 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(123,plain,
( ( ~ ! [SX0: $i] :
( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
| ~ ( ( ( divergence @ sK1_X0 )
!= zero ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(124,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)],[95]) ).
thf(125,plain,
! [SV28: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV28 )
= ( addition @ SV28 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(126,plain,
! [SV2: $i,SV29: $i] :
( ( ! [SY169: $i] :
( ( addition @ SY169 @ ( addition @ SV29 @ SV2 ) )
= ( addition @ ( addition @ SY169 @ SV29 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(127,plain,
! [SV30: $i,SV5: $i] :
( ( ! [SY170: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV30 @ SY170 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV30 ) @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(128,plain,
! [SV31: $i,SV8: $i] :
( ( ! [SY171: $i] :
( ( multiplication @ SV8 @ ( addition @ SV31 @ SY171 ) )
= ( addition @ ( multiplication @ SV8 @ SV31 ) @ ( multiplication @ SV8 @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(129,plain,
! [SV32: $i,SV9: $i] :
( ( ! [SY172: $i] :
( ( multiplication @ ( addition @ SV9 @ SV32 ) @ SY172 )
= ( addition @ ( multiplication @ SV9 @ SY172 ) @ ( multiplication @ SV32 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(130,plain,
! [SV33: $i,SV13: $i] :
( ( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SV33 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(131,plain,
! [SV34: $i,SV17: $i] :
( ( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SV34 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV34 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV35: $i,SV21: $i] :
( ( ( domain_difference @ SV21 @ SV35 )
= ( multiplication @ ( domain @ SV21 ) @ ( antidomain @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV36: $i,SV22: $i] :
( ( ( forward_diamond @ SV22 @ SV36 )
= ( domain @ ( multiplication @ SV22 @ ( domain @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV37: $i,SV23: $i] :
( ( ( backward_diamond @ SV23 @ SV37 )
= ( codomain @ ( multiplication @ ( codomain @ SV37 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV38: $i,SV24: $i] :
( ( ( forward_box @ SV24 @ SV38 )
= ( c @ ( forward_diamond @ SV24 @ ( c @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV39: $i,SV25: $i] :
( ( ( backward_box @ SV25 @ SV39 )
= ( c @ ( backward_diamond @ SV25 @ ( c @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV40: $i,SV27: $i] :
( ( ! [SY173: $i] :
( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SY173 ) ) )
!= ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SY173 ) ) )
| ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SY173 ) ) ) )
= ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SY173 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(138,plain,
( ( ~ ! [SX0: $i] :
( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(139,plain,
( ( ~ ( ( ( divergence @ sK1_X0 )
!= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(142,plain,
! [SV2: $i,SV29: $i,SV41: $i] :
( ( ( addition @ SV41 @ ( addition @ SV29 @ SV2 ) )
= ( addition @ ( addition @ SV41 @ SV29 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV42: $i,SV30: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV30 @ SV42 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV30 ) @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV43: $i,SV31: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV31 @ SV43 ) )
= ( addition @ ( multiplication @ SV8 @ SV31 ) @ ( multiplication @ SV8 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV44: $i,SV32: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV32 ) @ SV44 )
= ( addition @ ( multiplication @ SV9 @ SV44 ) @ ( multiplication @ SV32 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV45: $i,SV40: $i,SV27: $i] :
( ( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) )
!= ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) )
| ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) )
= ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(147,plain,
( ( ! [SX0: $i] :
( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(148,plain,
( ( ( ( divergence @ sK1_X0 )
!= zero ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV45: $i,SV40: $i,SV27: $i] :
( ( ( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) )
!= ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) ) )
= $true )
| ( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) )
= ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV46: $i] :
( ( ( addition @ ( domain @ SV46 ) @ ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SV46 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SV46 ) ) ) ) )
= ( forward_diamond @ ( star @ sK1_X0 ) @ ( domain_difference @ ( domain @ SV46 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(153,plain,
( ( ( divergence @ sK1_X0 )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV47: $i] :
( ( ! [SY174: $i] :
( ( ( addition @ SV47 @ SY174 )
!= SY174 )
| ( leq @ SV47 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV48: $i] :
( ( ! [SY175: $i] :
( ~ ( leq @ SV48 @ SY175 )
| ( ( addition @ SV48 @ SY175 )
= SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV45: $i,SV40: $i,SV27: $i] :
( ( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) )
= ( addition @ ( forward_diamond @ SV40 @ ( domain @ SV27 ) ) @ ( domain @ SV45 ) ) )
= $false )
| ( ( ( addition @ ( domain @ SV27 ) @ ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) )
= ( addition @ ( divergence @ SV40 ) @ ( forward_diamond @ ( star @ SV40 ) @ ( domain @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV49: $i,SV47: $i] :
( ( ( ( addition @ SV47 @ SV49 )
!= SV49 )
| ( leq @ SV47 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV50: $i,SV48: $i] :
( ( ~ ( leq @ SV48 @ SV50 )
| ( ( addition @ SV48 @ SV50 )
= SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV49: $i,SV47: $i] :
( ( ( ( ( addition @ SV47 @ SV49 )
!= SV49 ) )
= $true )
| ( ( leq @ SV47 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(160,plain,
! [SV50: $i,SV48: $i] :
( ( ( ~ ( leq @ SV48 @ SV50 ) )
= $true )
| ( ( ( addition @ SV48 @ SV50 )
= SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(161,plain,
! [SV49: $i,SV47: $i] :
( ( ( ( addition @ SV47 @ SV49 )
= SV49 )
= $false )
| ( ( leq @ SV47 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV50: $i,SV48: $i] :
( ( ( leq @ SV48 @ SV50 )
= $false )
| ( ( ( addition @ SV48 @ SV50 )
= SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(163,plain,
! [SV51: $i] :
( ( ( addition @ SV51 @ zero )
= SV51 )
= $true ),
inference(rename,[status(thm)],[98]) ).
thf(164,plain,
! [SV52: $i] :
( ( ( addition @ SV52 @ SV52 )
= SV52 )
= $true ),
inference(rename,[status(thm)],[99]) ).
thf(165,plain,
! [SV53: $i] :
( ( ( multiplication @ SV53 @ one )
= SV53 )
= $true ),
inference(rename,[status(thm)],[101]) ).
thf(166,plain,
! [SV54: $i] :
( ( ( multiplication @ one @ SV54 )
= SV54 )
= $true ),
inference(rename,[status(thm)],[102]) ).
thf(167,plain,
! [SV55: $i] :
( ( ( multiplication @ SV55 @ zero )
= zero )
= $true ),
inference(rename,[status(thm)],[105]) ).
thf(168,plain,
! [SV56: $i] :
( ( ( multiplication @ zero @ SV56 )
= zero )
= $true ),
inference(rename,[status(thm)],[106]) ).
thf(169,plain,
! [SV57: $i] :
( ( ( multiplication @ ( antidomain @ SV57 ) @ SV57 )
= zero )
= $true ),
inference(rename,[status(thm)],[107]) ).
thf(170,plain,
! [SV58: $i] :
( ( ( addition @ ( antidomain @ ( antidomain @ SV58 ) ) @ ( antidomain @ SV58 ) )
= one )
= $true ),
inference(rename,[status(thm)],[109]) ).
thf(171,plain,
! [SV59: $i] :
( ( ( domain @ SV59 )
= ( antidomain @ ( antidomain @ SV59 ) ) )
= $true ),
inference(rename,[status(thm)],[110]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[111,171,170,169,168,167,166,165,164,163,162,161,156,153,152,145,144,143,142,136,135,134,133,132,131,130,125,121,115,114,113]) ).
thf(173,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : KLE131+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 09:45:41 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.38
% 0.15/0.38 No.of.Axioms: 28
% 0.15/0.38
% 0.15/0.38 Length.of.Defs: 0
% 0.15/0.38
% 0.15/0.38 Contains.Choice.Funs: false
% 0.15/0.39 .
% 0.15/0.40 (rf:0,axioms:28,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:30,loop_count:0,foatp_calls:0,translation:fof_full).........eprover: CPU time limit exceeded, terminating
% 74.35/74.63 .eprover: CPU time limit exceeded, terminating
% 148.37/148.78 .
% 148.49/148.80 (rf:0,axioms:28,ps:2,u:1,ude:false,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:30,loop_count:0,foatp_calls:0,translation:fof_full)........eprover: CPU time limit exceeded, terminating
% 186.56/186.97 ..eprover: CPU time limit exceeded, terminating
% 224.70/225.09
% 224.70/225.09 (rf:0,axioms:28,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:30,loop_count:0,foatp_calls:0,translation:fof_full)..........eprover: CPU time limit exceeded, terminating
% 260.78/261.27 ..
% 265.94/266.39
% 265.94/266.39 ********************************
% 265.94/266.39 * All subproblems solved! *
% 265.94/266.39 ********************************
% 265.94/266.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:36,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:172,loop_count:10,foatp_calls:2,translation:fof_full)
% 265.94/266.40
% 265.94/266.40 %**** Beginning of derivation protocol ****
% 265.94/266.40 % SZS output start CNFRefutation
% See solution above
% 265.94/266.41
% 265.94/266.41 %**** End of derivation protocol ****
% 265.94/266.41 %**** no. of clauses in derivation: 173 ****
% 265.94/266.41 %**** clause counter: 172 ****
% 265.94/266.41
% 265.94/266.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:36,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:172,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------