TSTP Solution File: KLE044-10 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE044-10 : 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 : n020.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 02:11:04 EDT 2022
% Result : Unsatisfiable 43.71s 43.91s
% Output : CNFRefutation 43.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 127 ( 114 unt; 13 typ; 0 def)
% Number of atoms : 296 ( 197 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 766 ( 6 ~; 0 |; 0 &; 760 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 224 ( 0 ^ 224 !; 0 ?; 224 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_ifeq2,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(tp_ifeq3,type,
ifeq3: $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_X0,type,
sK1_goals_X0: $i ).
thf(tp_sK2_goals_X0,type,
sK2_goals_X0: $i ).
thf(tp_star,type,
star: $i > $i ).
thf(tp_true,type,
true: $i ).
thf(tp_tuple,type,
tuple: $i > $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
thf(3,axiom,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
thf(4,axiom,
! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(9,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(10,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(11,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(13,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(14,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(15,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(16,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(17,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
( tuple @ ( leq @ ( star @ ( addition @ one @ sK2_goals_X0 ) ) @ ( star @ sK2_goals_X0 ) ) @ ( leq @ ( star @ sK1_goals_X0 ) @ ( star @ ( addition @ one @ sK1_goals_X0 ) ) ) )
!= ( tuple @ true @ true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,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)],[9]) ).
thf(34,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)],[10]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ( ( tuple @ ( leq @ ( star @ ( addition @ one @ sK2_goals_X0 ) ) @ ( star @ sK2_goals_X0 ) ) @ ( leq @ ( star @ sK1_goals_X0 ) @ ( star @ ( addition @ one @ sK1_goals_X0 ) ) ) )
!= ( tuple @ true @ true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ( ( tuple @ ( leq @ ( star @ ( addition @ one @ sK2_goals_X0 ) ) @ ( star @ sK2_goals_X0 ) ) @ ( leq @ ( star @ sK1_goals_X0 ) @ ( star @ ( addition @ one @ sK1_goals_X0 ) ) ) )
!= ( tuple @ true @ true ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(48,plain,
( ( ( ( tuple @ ( leq @ ( star @ ( addition @ one @ sK2_goals_X0 ) ) @ ( star @ sK2_goals_X0 ) ) @ ( leq @ ( star @ sK1_goals_X0 ) @ ( star @ ( addition @ one @ sK1_goals_X0 ) ) ) )
!= ( tuple @ true @ true ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq2 @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ifeq3 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B ) @ true @ ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A ) @ true @ ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(69,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ( tuple @ ( leq @ ( star @ ( addition @ one @ sK2_goals_X0 ) ) @ ( star @ sK2_goals_X0 ) ) @ ( leq @ ( star @ sK1_goals_X0 ) @ ( star @ ( addition @ one @ sK1_goals_X0 ) ) ) )
= ( tuple @ true @ true ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV1: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( ifeq3 @ SV1 @ SV1 @ SY41 @ SY42 )
= SY41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV2: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( ifeq2 @ SV2 @ SV2 @ SY43 @ SY44 )
= SY43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV3: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( ifeq @ SV3 @ SV3 @ SY45 @ SY46 )
= SY45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV4: $i] :
( ( ! [SY47: $i] :
( ( addition @ SV4 @ SY47 )
= ( addition @ SY47 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(75,plain,
! [SV5: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ( addition @ SV5 @ ( addition @ SY48 @ SY49 ) )
= ( addition @ ( addition @ SV5 @ SY48 ) @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(76,plain,
! [SV6: $i] :
( ( ( addition @ SV6 @ zero )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( addition @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(78,plain,
! [SV8: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( multiplication @ SV8 @ ( multiplication @ SY50 @ SY51 ) )
= ( multiplication @ ( multiplication @ SV8 @ SY50 ) @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(79,plain,
! [SV9: $i] :
( ( ( multiplication @ SV9 @ one )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(80,plain,
! [SV10: $i] :
( ( ( multiplication @ one @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV11: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ( multiplication @ SV11 @ ( addition @ SY52 @ SY53 ) )
= ( addition @ ( multiplication @ SV11 @ SY52 ) @ ( multiplication @ SV11 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV12: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( multiplication @ ( addition @ SV12 @ SY54 ) @ SY55 )
= ( addition @ ( multiplication @ SV12 @ SY55 ) @ ( multiplication @ SY54 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV13: $i] :
( ( ( multiplication @ SV13 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV14: $i] :
( ( ( multiplication @ zero @ SV14 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV15: $i] :
( ( ! [SY56: $i] :
( ( ifeq2 @ ( leq @ SV15 @ SY56 ) @ true @ ( addition @ SV15 @ SY56 ) @ SY56 )
= SY56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV16: $i] :
( ( ! [SY57: $i] :
( ( ifeq3 @ ( addition @ SV16 @ SY57 ) @ SY57 @ ( leq @ SV16 @ SY57 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV17: $i] :
( ( ( leq @ ( addition @ one @ ( multiplication @ SV17 @ ( star @ SV17 ) ) ) @ ( star @ SV17 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV18: $i] :
( ( ( leq @ ( addition @ one @ ( multiplication @ ( star @ SV18 ) @ SV18 ) ) @ ( star @ SV18 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV19: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV19 @ SY58 ) @ SY59 ) @ SY58 ) @ true @ ( leq @ ( multiplication @ ( star @ SV19 ) @ SY59 ) @ SY58 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV20: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV20 @ SY60 ) @ SY61 ) @ SV20 ) @ true @ ( leq @ ( multiplication @ SY61 @ ( star @ SY60 ) ) @ SV20 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV21: $i,SV1: $i] :
( ( ! [SY62: $i] :
( ( ifeq3 @ SV1 @ SV1 @ SV21 @ SY62 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY63: $i] :
( ( ifeq2 @ SV2 @ SV2 @ SV22 @ SY63 )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV23: $i,SV3: $i] :
( ( ! [SY64: $i] :
( ( ifeq @ SV3 @ SV3 @ SV23 @ SY64 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV24: $i,SV4: $i] :
( ( ( addition @ SV4 @ SV24 )
= ( addition @ SV24 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY65: $i] :
( ( addition @ SV5 @ ( addition @ SV25 @ SY65 ) )
= ( addition @ ( addition @ SV5 @ SV25 ) @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY66: $i] :
( ( multiplication @ SV8 @ ( multiplication @ SV26 @ SY66 ) )
= ( multiplication @ ( multiplication @ SV8 @ SV26 ) @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV27: $i,SV11: $i] :
( ( ! [SY67: $i] :
( ( multiplication @ SV11 @ ( addition @ SV27 @ SY67 ) )
= ( addition @ ( multiplication @ SV11 @ SV27 ) @ ( multiplication @ SV11 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
! [SV28: $i,SV12: $i] :
( ( ! [SY68: $i] :
( ( multiplication @ ( addition @ SV12 @ SV28 ) @ SY68 )
= ( addition @ ( multiplication @ SV12 @ SY68 ) @ ( multiplication @ SV28 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(100,plain,
! [SV29: $i,SV15: $i] :
( ( ( ifeq2 @ ( leq @ SV15 @ SV29 ) @ true @ ( addition @ SV15 @ SV29 ) @ SV29 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV30: $i,SV16: $i] :
( ( ( ifeq3 @ ( addition @ SV16 @ SV30 ) @ SV30 @ ( leq @ SV16 @ SV30 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV31: $i,SV19: $i] :
( ( ! [SY69: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV19 @ SV31 ) @ SY69 ) @ SV31 ) @ true @ ( leq @ ( multiplication @ ( star @ SV19 ) @ SY69 ) @ SV31 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV32: $i,SV20: $i] :
( ( ! [SY70: $i] :
( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV20 @ SV32 ) @ SY70 ) @ SV20 ) @ true @ ( leq @ ( multiplication @ SY70 @ ( star @ SV32 ) ) @ SV20 ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV33: $i,SV21: $i,SV1: $i] :
( ( ( ifeq3 @ SV1 @ SV1 @ SV21 @ SV33 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV34: $i,SV22: $i,SV2: $i] :
( ( ( ifeq2 @ SV2 @ SV2 @ SV22 @ SV34 )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV35: $i,SV23: $i,SV3: $i] :
( ( ( ifeq @ SV3 @ SV3 @ SV23 @ SV35 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV36: $i,SV25: $i,SV5: $i] :
( ( ( addition @ SV5 @ ( addition @ SV25 @ SV36 ) )
= ( addition @ ( addition @ SV5 @ SV25 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV37: $i,SV26: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( multiplication @ SV26 @ SV37 ) )
= ( multiplication @ ( multiplication @ SV8 @ SV26 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV38: $i,SV27: $i,SV11: $i] :
( ( ( multiplication @ SV11 @ ( addition @ SV27 @ SV38 ) )
= ( addition @ ( multiplication @ SV11 @ SV27 ) @ ( multiplication @ SV11 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV39: $i,SV28: $i,SV12: $i] :
( ( ( multiplication @ ( addition @ SV12 @ SV28 ) @ SV39 )
= ( addition @ ( multiplication @ SV12 @ SV39 ) @ ( multiplication @ SV28 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV40: $i,SV31: $i,SV19: $i] :
( ( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV19 @ SV31 ) @ SV40 ) @ SV31 ) @ true @ ( leq @ ( multiplication @ ( star @ SV19 ) @ SV40 ) @ SV31 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV41: $i,SV32: $i,SV20: $i] :
( ( ( ifeq @ ( leq @ ( addition @ ( multiplication @ SV20 @ SV32 ) @ SV41 ) @ SV20 ) @ true @ ( leq @ ( multiplication @ SV41 @ ( star @ SV32 ) ) @ SV20 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,112,111,110,109,108,107,106,105,104,101,100,95,91,88,87,84,83,80,79,77,76]) ).
thf(114,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : KLE044-10 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36 % Computer : n020.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 13:32:04 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.38
% 0.15/0.38 No.of.Axioms: 21
% 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 .
% 0.15/0.39 (rf:0,axioms:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full).....
% 43.71/43.91
% 43.71/43.91 ********************************
% 43.71/43.91 * All subproblems solved! *
% 43.71/43.91 ********************************
% 43.71/43.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 43.71/43.91
% 43.71/43.91 %**** Beginning of derivation protocol ****
% 43.71/43.91 % SZS output start CNFRefutation
% See solution above
% 43.71/43.91
% 43.71/43.91 %**** End of derivation protocol ****
% 43.71/43.91 %**** no. of clauses in derivation: 114 ****
% 43.71/43.91 %**** clause counter: 113 ****
% 43.71/43.91
% 43.71/43.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------