TSTP Solution File: KLE090-10 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 : Unsatisfiable 26.03s 26.29s
% Output : CNFRefutation 26.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 40
% Syntax : Number of formulae : 139 ( 125 unt; 14 typ; 0 def)
% Number of atoms : 321 ( 215 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 687 ( 6 ~; 0 |; 0 &; 681 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 206 ( 0 ^ 206 !; 0 ?; 206 :)
% 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_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_ifeq2,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $i ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_goals_X1,type,
sK1_goals_X1: $i ).
thf(tp_sK2_goals_X0,type,
sK2_goals_X0: $i ).
thf(tp_true,type,
true: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
thf(2,axiom,
! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',codomain2) ).
thf(4,axiom,
! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
thf(5,axiom,
! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(6,axiom,
! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(8,axiom,
! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(16,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(19,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
!= ( antidomain @ sK2_goals_X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_1) ).
thf(27,negated_conjecture,
( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
= sK1_goals_X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,plain,
( ( ! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(31,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(32,plain,
( ( ! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(33,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(34,plain,
( ( ! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,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(36,plain,
( ( ! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,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)],[13]) ).
thf(42,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)],[14]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(52,plain,
( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
!= ( antidomain @ sK2_goals_X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
( ( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
= sK1_goals_X1 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,plain,
( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
!= ( antidomain @ sK2_goals_X0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(56,plain,
( ( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
= sK1_goals_X1 )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(57,plain,
( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
!= ( antidomain @ sK2_goals_X0 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(73,plain,
( ( ! [X0: $i] :
( ( multiplication @ ( antidomain @ X0 ) @ X0 )
= zero ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(74,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)],[35]) ).
thf(75,plain,
( ( ! [X0: $i] :
( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
= one ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(76,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(77,plain,
( ( ! [X0: $i] :
( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
= zero ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(78,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)],[31]) ).
thf(79,plain,
( ( ! [X0: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
= one ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(80,plain,
( ( ! [X0: $i] :
( ( codomain @ X0 )
= ( coantidomain @ ( coantidomain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(81,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(82,plain,
( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
= ( antidomain @ sK2_goals_X0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SY40 @ SY41 )
= SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( ifeq @ SV2 @ SV2 @ SY42 @ SY43 )
= SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY44: $i] :
( ( addition @ SV3 @ SY44 )
= ( addition @ SY44 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(86,plain,
! [SV4: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( addition @ SV4 @ ( addition @ SY45 @ SY46 ) )
= ( addition @ ( addition @ SV4 @ SY45 ) @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(87,plain,
! [SV5: $i] :
( ( ( addition @ SV5 @ zero )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(88,plain,
! [SV6: $i] :
( ( ( addition @ SV6 @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(89,plain,
! [SV7: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( multiplication @ SV7 @ ( multiplication @ SY47 @ SY48 ) )
= ( multiplication @ ( multiplication @ SV7 @ SY47 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(90,plain,
! [SV8: $i] :
( ( ( multiplication @ SV8 @ one )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(91,plain,
! [SV9: $i] :
( ( ( multiplication @ one @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV10: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( multiplication @ SV10 @ ( addition @ SY49 @ SY50 ) )
= ( addition @ ( multiplication @ SV10 @ SY49 ) @ ( multiplication @ SV10 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV11: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( multiplication @ ( addition @ SV11 @ SY51 ) @ SY52 )
= ( addition @ ( multiplication @ SV11 @ SY52 ) @ ( multiplication @ SY51 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV12: $i] :
( ( ( multiplication @ SV12 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(95,plain,
! [SV13: $i] :
( ( ( multiplication @ zero @ SV13 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(96,plain,
! [SV14: $i] :
( ( ! [SY53: $i] :
( ( ifeq @ ( leq @ SV14 @ SY53 ) @ true @ ( addition @ SV14 @ SY53 ) @ SY53 )
= SY53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(97,plain,
! [SV15: $i] :
( ( ! [SY54: $i] :
( ( ifeq2 @ ( addition @ SV15 @ SY54 ) @ SY54 @ ( leq @ SV15 @ SY54 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(98,plain,
! [SV16: $i] :
( ( ( multiplication @ ( antidomain @ SV16 ) @ SV16 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(99,plain,
! [SV17: $i] :
( ( ! [SY55: $i] :
( ( addition @ ( antidomain @ ( multiplication @ SV17 @ SY55 ) ) @ ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SY55 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SY55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(100,plain,
! [SV18: $i] :
( ( ( addition @ ( antidomain @ ( antidomain @ SV18 ) ) @ ( antidomain @ SV18 ) )
= one )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(101,plain,
! [SV19: $i] :
( ( ( domain @ SV19 )
= ( antidomain @ ( antidomain @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(102,plain,
! [SV20: $i] :
( ( ( multiplication @ SV20 @ ( coantidomain @ SV20 ) )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(103,plain,
! [SV21: $i] :
( ( ! [SY56: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ SV21 @ SY56 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SY56 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(104,plain,
! [SV22: $i] :
( ( ( addition @ ( coantidomain @ ( coantidomain @ SV22 ) ) @ ( coantidomain @ SV22 ) )
= one )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(105,plain,
! [SV23: $i] :
( ( ( codomain @ SV23 )
= ( coantidomain @ ( coantidomain @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(106,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(107,plain,
! [SV24: $i,SV1: $i] :
( ( ! [SY57: $i] :
( ( ifeq2 @ SV1 @ SV1 @ SV24 @ SY57 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(108,plain,
! [SV25: $i,SV2: $i] :
( ( ! [SY58: $i] :
( ( ifeq @ SV2 @ SV2 @ SV25 @ SY58 )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(109,plain,
! [SV26: $i,SV3: $i] :
( ( ( addition @ SV3 @ SV26 )
= ( addition @ SV26 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(110,plain,
! [SV27: $i,SV4: $i] :
( ( ! [SY59: $i] :
( ( addition @ SV4 @ ( addition @ SV27 @ SY59 ) )
= ( addition @ ( addition @ SV4 @ SV27 ) @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(111,plain,
! [SV28: $i,SV7: $i] :
( ( ! [SY60: $i] :
( ( multiplication @ SV7 @ ( multiplication @ SV28 @ SY60 ) )
= ( multiplication @ ( multiplication @ SV7 @ SV28 ) @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
! [SV29: $i,SV10: $i] :
( ( ! [SY61: $i] :
( ( multiplication @ SV10 @ ( addition @ SV29 @ SY61 ) )
= ( addition @ ( multiplication @ SV10 @ SV29 ) @ ( multiplication @ SV10 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV30: $i,SV11: $i] :
( ( ! [SY62: $i] :
( ( multiplication @ ( addition @ SV11 @ SV30 ) @ SY62 )
= ( addition @ ( multiplication @ SV11 @ SY62 ) @ ( multiplication @ SV30 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV31: $i,SV14: $i] :
( ( ( ifeq @ ( leq @ SV14 @ SV31 ) @ true @ ( addition @ SV14 @ SV31 ) @ SV31 )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV32: $i,SV15: $i] :
( ( ( ifeq2 @ ( addition @ SV15 @ SV32 ) @ SV32 @ ( leq @ SV15 @ SV32 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV33: $i,SV17: $i] :
( ( ( addition @ ( antidomain @ ( multiplication @ SV17 @ SV33 ) ) @ ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
= ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV34: $i,SV21: $i] :
( ( ( addition @ ( coantidomain @ ( multiplication @ SV21 @ SV34 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SV34 ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV35: $i,SV24: $i,SV1: $i] :
( ( ( ifeq2 @ SV1 @ SV1 @ SV24 @ SV35 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV36: $i,SV25: $i,SV2: $i] :
( ( ( ifeq @ SV2 @ SV2 @ SV25 @ SV36 )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV37: $i,SV27: $i,SV4: $i] :
( ( ( addition @ SV4 @ ( addition @ SV27 @ SV37 ) )
= ( addition @ ( addition @ SV4 @ SV27 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV38: $i,SV28: $i,SV7: $i] :
( ( ( multiplication @ SV7 @ ( multiplication @ SV28 @ SV38 ) )
= ( multiplication @ ( multiplication @ SV7 @ SV28 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV39: $i,SV29: $i,SV10: $i] :
( ( ( multiplication @ SV10 @ ( addition @ SV29 @ SV39 ) )
= ( addition @ ( multiplication @ SV10 @ SV29 ) @ ( multiplication @ SV10 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV40: $i,SV30: $i,SV11: $i] :
( ( ( multiplication @ ( addition @ SV11 @ SV30 ) @ SV40 )
= ( addition @ ( multiplication @ SV11 @ SV40 ) @ ( multiplication @ SV30 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,123,122,121,120,119,118,117,116,115,114,109,106,105,104,102,101,100,98,95,94,91,90,88,87,82]) ).
thf(125,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 13:56:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 25
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.37 .
% 0.13/0.38 (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full)......
% 26.03/26.29
% 26.03/26.29 ********************************
% 26.03/26.29 * All subproblems solved! *
% 26.03/26.29 ********************************
% 26.03/26.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.03/26.29
% 26.03/26.29 %**** Beginning of derivation protocol ****
% 26.03/26.29 % SZS output start CNFRefutation
% See solution above
% 26.03/26.29
% 26.03/26.29 %**** End of derivation protocol ****
% 26.03/26.29 %**** no. of clauses in derivation: 125 ****
% 26.03/26.29 %**** clause counter: 124 ****
% 26.03/26.29
% 26.03/26.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------