TSTP Solution File: KLE089+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE089+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 : n011.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 02:11:18 EDT 2022
% Result : Theorem 0.61s 0.80s
% Output : CNFRefutation 0.61s
% 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 ( 3 avg)
% Number of connectives : 784 ( 39 ~; 24 |; 4 &; 709 @)
% ( 2 <=>; 0 =>; 6 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% 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 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(19,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(20,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
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
% 0.03/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n011.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 : 600
% 0.13/0.33 % DateTime : Thu Jun 16 09:58:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 20
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 .
% 0.13/0.35 (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)......
% 0.61/0.80
% 0.61/0.80 ********************************
% 0.61/0.80 * All subproblems solved! *
% 0.61/0.80 ********************************
% 0.61/0.80 % 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)
% 0.61/0.80
% 0.61/0.80 %**** Beginning of derivation protocol ****
% 0.61/0.80 % SZS output start CNFRefutation
% See solution above
% 0.61/0.80
% 0.61/0.80 %**** End of derivation protocol ****
% 0.61/0.80 %**** no. of clauses in derivation: 122 ****
% 0.61/0.80 %**** clause counter: 121 ****
% 0.61/0.80
% 0.61/0.80 % 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)
%------------------------------------------------------------------------------