TSTP Solution File: KLE003+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KLE003+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 : n015.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 02:10:44 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 152 ( 136 unt; 6 typ; 0 def)
% Number of atoms : 488 ( 305 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 844 ( 76 ~; 46 |; 7 &; 706 @)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 266 ( 0 ^ 266 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $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_zero,type,
zero: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(2,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(4,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(5,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(6,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(8,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(9,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(11,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(12,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(13,conjecture,
( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
<=> ( ( addition @ one @ one )
= one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(14,negated_conjecture,
( ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
<=> ( ( addition @ one @ one )
= one ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
<=> ( ( addition @ one @ one )
= one ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,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)],[4]) ).
thf(20,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)],[5]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
=> ( ( addition @ one @ one )
= one ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(29,plain,
( ( ( ( addition @ one @ one )
= one )
=> ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(30,plain,
( ( ~ ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
=> ( ( addition @ one @ one )
= one ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ( ( ( addition @ one @ one )
= one )
=> ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
& ( ( addition @ one @ one )
!= one ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(33,plain,
( ( ( ( addition @ one @ one )
= one )
& ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(34,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)],[16]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(36,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(46,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)],[34]) ).
thf(47,plain,
( ( ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 )
& ( ( addition @ one @ one )
!= one ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,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)],[46]) ).
thf(49,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( addition @ SX0 @ SX0 )
= SX0 )
| ~ ( ( ( addition @ one @ one )
!= one ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ( addition @ SV1 @ SY23 )
= ( addition @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( addition @ SY25 @ ( addition @ SY24 @ SV2 ) )
= ( addition @ ( addition @ SY25 @ SY24 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SY26 @ SY27 ) )
= ( multiplication @ ( multiplication @ SV5 @ SY26 ) @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV7: $i] :
( ( ( multiplication @ one @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV8: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( multiplication @ SV8 @ ( addition @ SY28 @ SY29 ) )
= ( addition @ ( multiplication @ SV8 @ SY28 ) @ ( multiplication @ SV8 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV9: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( multiplication @ ( addition @ SV9 @ SY30 ) @ SY31 )
= ( addition @ ( multiplication @ SV9 @ SY31 ) @ ( multiplication @ SY30 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV10: $i] :
( ( ( multiplication @ SV10 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV11: $i] :
( ( ( multiplication @ zero @ SV11 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,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)],[48]) ).
thf(62,plain,
( ( ~ ! [SX0: $i] :
( ( addition @ SX0 @ SX0 )
= SX0 )
| ~ ( ( ( addition @ one @ one )
!= one ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(63,plain,
! [SV12: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV12 )
= ( addition @ SV12 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV2: $i,SV13: $i] :
( ( ! [SY32: $i] :
( ( addition @ SY32 @ ( addition @ SV13 @ SV2 ) )
= ( addition @ ( addition @ SY32 @ SV13 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY33: $i] :
( ( multiplication @ SV5 @ ( multiplication @ SV14 @ SY33 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV14 ) @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY34: $i] :
( ( multiplication @ SV8 @ ( addition @ SV15 @ SY34 ) )
= ( addition @ ( multiplication @ SV8 @ SV15 ) @ ( multiplication @ SV8 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY35: $i] :
( ( multiplication @ ( addition @ SV9 @ SV16 ) @ SY35 )
= ( addition @ ( multiplication @ SV9 @ SY35 ) @ ( multiplication @ SV16 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
( ( ~ ! [SX0: $i] :
( ( addition @ SX0 @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ( ( ( addition @ one @ one )
!= one ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV2: $i,SV13: $i,SV17: $i] :
( ( ( addition @ SV17 @ ( addition @ SV13 @ SV2 ) )
= ( addition @ ( addition @ SV17 @ SV13 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( multiplication @ SV14 @ SV18 ) )
= ( multiplication @ ( multiplication @ SV5 @ SV14 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ( multiplication @ SV8 @ ( addition @ SV15 @ SV19 ) )
= ( addition @ ( multiplication @ SV8 @ SV15 ) @ ( multiplication @ SV8 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV20: $i,SV16: $i,SV9: $i] :
( ( ( multiplication @ ( addition @ SV9 @ SV16 ) @ SV20 )
= ( addition @ ( multiplication @ SV9 @ SV20 ) @ ( multiplication @ SV16 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ( addition @ SX0 @ SX0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(79,plain,
( ( ( ( addition @ one @ one )
!= one ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV21: $i] :
( ( ! [SY36: $i] :
( ( ( addition @ SV21 @ SY36 )
!= SY36 )
| ( leq @ SV21 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV22: $i] :
( ( ! [SY37: $i] :
( ~ ( leq @ SV22 @ SY37 )
| ( ( addition @ SV22 @ SY37 )
= SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV23: $i] :
( ( ( addition @ SV23 @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
( ( ( addition @ one @ one )
= one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV24: $i,SV21: $i] :
( ( ( ( addition @ SV21 @ SV24 )
!= SV24 )
| ( leq @ SV21 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV25: $i,SV22: $i] :
( ( ~ ( leq @ SV22 @ SV25 )
| ( ( addition @ SV22 @ SV25 )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV24: $i,SV21: $i] :
( ( ( ( ( addition @ SV21 @ SV24 )
!= SV24 ) )
= $true )
| ( ( leq @ SV21 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(87,plain,
! [SV25: $i,SV22: $i] :
( ( ( ~ ( leq @ SV22 @ SV25 ) )
= $true )
| ( ( ( addition @ SV22 @ SV25 )
= SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(88,plain,
! [SV24: $i,SV21: $i] :
( ( ( ( addition @ SV21 @ SV24 )
= SV24 )
= $false )
| ( ( leq @ SV21 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV25: $i,SV22: $i] :
( ( ( leq @ SV22 @ SV25 )
= $false )
| ( ( ( addition @ SV22 @ SV25 )
= SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,89,88,83,82,75,74,73,72,63,60,59,56,55,53]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(92,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(94,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(97,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(101,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(102,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)],[34]) ).
thf(103,plain,
( ( ( ( addition @ one @ one )
= one )
& ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(104,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)],[102]) ).
thf(105,plain,
( ( ~ ( ( ( addition @ one @ one )
!= one )
| ~ ( ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(106,plain,
! [SV26: $i] :
( ( ! [SY38: $i] :
( ( addition @ SV26 @ SY38 )
= ( addition @ SY38 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV27: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( addition @ SY40 @ ( addition @ SY39 @ SV27 ) )
= ( addition @ ( addition @ SY40 @ SY39 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV28: $i] :
( ( ( addition @ SV28 @ zero )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV29: $i] :
( ( ( addition @ SV29 @ SV29 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV30: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( multiplication @ SV30 @ ( multiplication @ SY41 @ SY42 ) )
= ( multiplication @ ( multiplication @ SV30 @ SY41 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV31: $i] :
( ( ( multiplication @ SV31 @ one )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV32: $i] :
( ( ( multiplication @ one @ SV32 )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV33: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( multiplication @ SV33 @ ( addition @ SY43 @ SY44 ) )
= ( addition @ ( multiplication @ SV33 @ SY43 ) @ ( multiplication @ SV33 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV34: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( multiplication @ ( addition @ SV34 @ SY45 ) @ SY46 )
= ( addition @ ( multiplication @ SV34 @ SY46 ) @ ( multiplication @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV35: $i] :
( ( ( multiplication @ SV35 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV36: $i] :
( ( ( multiplication @ zero @ SV36 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,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)],[104]) ).
thf(118,plain,
( ( ( ( addition @ one @ one )
!= one )
| ~ ( ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV37: $i,SV26: $i] :
( ( ( addition @ SV26 @ SV37 )
= ( addition @ SV37 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV27: $i,SV38: $i] :
( ( ! [SY47: $i] :
( ( addition @ SY47 @ ( addition @ SV38 @ SV27 ) )
= ( addition @ ( addition @ SY47 @ SV38 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV39: $i,SV30: $i] :
( ( ! [SY48: $i] :
( ( multiplication @ SV30 @ ( multiplication @ SV39 @ SY48 ) )
= ( multiplication @ ( multiplication @ SV30 @ SV39 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV40: $i,SV33: $i] :
( ( ! [SY49: $i] :
( ( multiplication @ SV33 @ ( addition @ SV40 @ SY49 ) )
= ( addition @ ( multiplication @ SV33 @ SV40 ) @ ( multiplication @ SV33 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV41: $i,SV34: $i] :
( ( ! [SY50: $i] :
( ( multiplication @ ( addition @ SV34 @ SV41 ) @ SY50 )
= ( addition @ ( multiplication @ SV34 @ SY50 ) @ ( multiplication @ SV41 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(124,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(126,plain,
( ( ( ( addition @ one @ one )
!= one ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(127,plain,
( ( ~ ( ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV27: $i,SV38: $i,SV42: $i] :
( ( ( addition @ SV42 @ ( addition @ SV38 @ SV27 ) )
= ( addition @ ( addition @ SV42 @ SV38 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV43: $i,SV39: $i,SV30: $i] :
( ( ( multiplication @ SV30 @ ( multiplication @ SV39 @ SV43 ) )
= ( multiplication @ ( multiplication @ SV30 @ SV39 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV44: $i,SV40: $i,SV33: $i] :
( ( ( multiplication @ SV33 @ ( addition @ SV40 @ SV44 ) )
= ( addition @ ( multiplication @ SV33 @ SV40 ) @ ( multiplication @ SV33 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV45: $i,SV41: $i,SV34: $i] :
( ( ( multiplication @ ( addition @ SV34 @ SV41 ) @ SV45 )
= ( addition @ ( multiplication @ SV34 @ SV45 ) @ ( multiplication @ SV41 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(134,plain,
( ( ( addition @ one @ one )
= one )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(135,plain,
( ( ( ( addition @ sK1_X0 @ sK1_X0 )
!= sK1_X0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(136,plain,
! [SV46: $i] :
( ( ! [SY51: $i] :
( ( ( addition @ SV46 @ SY51 )
!= SY51 )
| ( leq @ SV46 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV47: $i] :
( ( ! [SY52: $i] :
( ~ ( leq @ SV47 @ SY52 )
| ( ( addition @ SV47 @ SY52 )
= SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(138,plain,
( ( ( addition @ sK1_X0 @ sK1_X0 )
= sK1_X0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV48: $i,SV46: $i] :
( ( ( ( addition @ SV46 @ SV48 )
!= SV48 )
| ( leq @ SV46 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV49: $i,SV47: $i] :
( ( ~ ( leq @ SV47 @ SV49 )
| ( ( addition @ SV47 @ SV49 )
= SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV48: $i,SV46: $i] :
( ( ( ( ( addition @ SV46 @ SV48 )
!= SV48 ) )
= $true )
| ( ( leq @ SV46 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(142,plain,
! [SV49: $i,SV47: $i] :
( ( ( ~ ( leq @ SV47 @ SV49 ) )
= $true )
| ( ( ( addition @ SV47 @ SV49 )
= SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV48: $i,SV46: $i] :
( ( ( ( addition @ SV46 @ SV48 )
= SV48 )
= $false )
| ( ( leq @ SV46 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV49: $i,SV47: $i] :
( ( ( leq @ SV47 @ SV49 )
= $false )
| ( ( ( addition @ SV47 @ SV49 )
= SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(145,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[108,144,143,138,134,131,130,129,128,119,116,115,112,111,109]) ).
thf(146,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[145,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE003+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:46:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 12
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:145,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44
% 0.20/0.44 %**** Beginning of derivation protocol ****
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 146 ****
% 0.20/0.44 %**** clause counter: 145 ****
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:145,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------