TSTP Solution File: GRP703+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP703+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 : n032.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 : Sat Jul 16 10:19:39 EDT 2022
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 168 ( 157 unt; 10 typ; 0 def)
% Number of atoms : 454 ( 307 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 1080 ( 6 ~; 0 |; 10 &;1064 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 271 ( 0 ^ 271 !; 0 ?; 271 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_c,type,
op_c: $i ).
thf(tp_op_d,type,
op_d: $i ).
thf(tp_op_e,type,
op_e: $i ).
thf(tp_op_f,type,
op_f: $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_sK1_X2,type,
sK1_X2: $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [B: $i,A: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
thf(2,axiom,
! [B: $i,A: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
thf(3,axiom,
! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(8,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(9,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(14,conjecture,
! [X2: $i,X3: $i] :
( ( ( mult @ op_e @ ( mult @ X2 @ X3 ) )
= ( mult @ ( mult @ op_e @ X2 ) @ X3 ) )
& ( ( mult @ X2 @ ( mult @ X3 @ op_e ) )
= ( mult @ ( mult @ X2 @ X3 ) @ op_e ) )
& ( ( mult @ X2 @ ( mult @ op_e @ X3 ) )
= ( mult @ ( mult @ X2 @ op_e ) @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(15,negated_conjecture,
( ( ! [X2: $i,X3: $i] :
( ( ( mult @ op_e @ ( mult @ X2 @ X3 ) )
= ( mult @ ( mult @ op_e @ X2 ) @ X3 ) )
& ( ( mult @ X2 @ ( mult @ X3 @ op_e ) )
= ( mult @ ( mult @ X2 @ X3 ) @ op_e ) )
& ( ( mult @ X2 @ ( mult @ op_e @ X3 ) )
= ( mult @ ( mult @ X2 @ op_e ) @ X3 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X2: $i,X3: $i] :
( ( ( mult @ op_e @ ( mult @ X2 @ X3 ) )
= ( mult @ ( mult @ op_e @ X2 ) @ X3 ) )
& ( ( mult @ X2 @ ( mult @ X3 @ op_e ) )
= ( mult @ ( mult @ X2 @ X3 ) @ op_e ) )
& ( ( mult @ X2 @ ( mult @ op_e @ X3 ) )
= ( mult @ ( mult @ X2 @ op_e ) @ X3 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [B: $i,A: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [B: $i,A: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [SY26: $i] :
( ( ( mult @ op_e @ ( mult @ sK1_X2 @ SY26 ) )
= ( mult @ ( mult @ op_e @ sK1_X2 ) @ SY26 ) )
& ( ( mult @ sK1_X2 @ ( mult @ SY26 @ op_e ) )
= ( mult @ ( mult @ sK1_X2 @ SY26 ) @ op_e ) )
& ( ( mult @ sK1_X2 @ ( mult @ op_e @ SY26 ) )
= ( mult @ ( mult @ sK1_X2 @ op_e ) @ SY26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ( ( mult @ op_e @ ( mult @ sK1_X2 @ sK2_SY26 ) )
= ( mult @ ( mult @ op_e @ sK1_X2 ) @ sK2_SY26 ) )
& ( ( mult @ sK1_X2 @ ( mult @ sK2_SY26 @ op_e ) )
= ( mult @ ( mult @ sK1_X2 @ sK2_SY26 ) @ op_e ) )
& ( ( mult @ sK1_X2 @ ( mult @ op_e @ sK2_SY26 ) )
= ( mult @ ( mult @ sK1_X2 @ op_e ) @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
( ( ( mult @ op_e @ ( mult @ sK1_X2 @ sK2_SY26 ) )
= ( mult @ ( mult @ op_e @ sK1_X2 ) @ sK2_SY26 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( ( mult @ sK1_X2 @ ( mult @ sK2_SY26 @ op_e ) )
= ( mult @ ( mult @ sK1_X2 @ sK2_SY26 ) @ op_e ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( ( mult @ sK1_X2 @ ( mult @ op_e @ sK2_SY26 ) )
= ( mult @ ( mult @ sK1_X2 @ op_e ) @ sK2_SY26 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(35,plain,
( ( ( ( mult @ op_e @ ( mult @ sK1_X2 @ sK2_SY26 ) )
!= ( mult @ ( mult @ op_e @ sK1_X2 ) @ sK2_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ( mult @ sK1_X2 @ ( mult @ sK2_SY26 @ op_e ) )
!= ( mult @ ( mult @ sK1_X2 @ sK2_SY26 ) @ op_e ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ( mult @ sK1_X2 @ ( mult @ op_e @ sK2_SY26 ) )
!= ( mult @ ( mult @ sK1_X2 @ op_e ) @ sK2_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(39,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(44,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(46,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [B: $i,A: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [B: $i,A: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(51,plain,
( ( ( ( mult @ op_e @ ( mult @ sK1_X2 @ sK2_SY26 ) )
!= ( mult @ ( mult @ op_e @ sK1_X2 ) @ sK2_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(52,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ( mult @ SY27 @ ( ld @ SY27 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
( ( ld @ SY28 @ ( mult @ SY28 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV3: $i] :
( ( ! [SY29: $i] :
( ( mult @ ( rd @ SY29 @ SV3 ) @ SV3 )
= SY29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV4: $i] :
( ( ! [SY30: $i] :
( ( rd @ ( mult @ SY30 @ SV4 ) @ SV4 )
= SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ( mult @ SY32 @ ( mult @ SY31 @ ( mult @ SY31 @ SV7 ) ) )
= ( mult @ ( mult @ ( mult @ SY32 @ SY31 ) @ SY31 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV8: $i] :
( ( ! [SY33: $i] :
( ( mult @ op_c @ ( mult @ SY33 @ SV8 ) )
= ( mult @ ( mult @ op_c @ SY33 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV9: $i] :
( ( ! [SY34: $i] :
( ( mult @ SY34 @ ( mult @ SV9 @ op_c ) )
= ( mult @ ( mult @ SY34 @ SV9 ) @ op_c ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV10: $i] :
( ( ! [SY35: $i] :
( ( mult @ SY35 @ ( mult @ op_c @ SV10 ) )
= ( mult @ ( mult @ SY35 @ op_c ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV11: $i] :
( ( op_d
= ( ld @ SV11 @ ( mult @ op_c @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV12: $i] :
( ( ! [SY36: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SY36 @ SV12 ) ) @ SV12 ) @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV13: $i] :
( ( ! [SY37: $i] :
( op_f
= ( mult @ SY37 @ ( mult @ SV13 @ ( ld @ ( mult @ SY37 @ SV13 ) @ op_c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
( ( ( mult @ op_e @ ( mult @ sK1_X2 @ sK2_SY26 ) )
= ( mult @ ( mult @ op_e @ sK1_X2 ) @ sK2_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV1: $i,SV14: $i] :
( ( ( mult @ SV14 @ ( ld @ SV14 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV2: $i,SV15: $i] :
( ( ( ld @ SV15 @ ( mult @ SV15 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV3: $i,SV16: $i] :
( ( ( mult @ ( rd @ SV16 @ SV3 ) @ SV3 )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(69,plain,
! [SV4: $i,SV17: $i] :
( ( ( rd @ ( mult @ SV17 @ SV4 ) @ SV4 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(70,plain,
! [SV7: $i,SV18: $i] :
( ( ! [SY38: $i] :
( ( mult @ SY38 @ ( mult @ SV18 @ ( mult @ SV18 @ SV7 ) ) )
= ( mult @ ( mult @ ( mult @ SY38 @ SV18 ) @ SV18 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV8: $i,SV19: $i] :
( ( ( mult @ op_c @ ( mult @ SV19 @ SV8 ) )
= ( mult @ ( mult @ op_c @ SV19 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV9: $i,SV20: $i] :
( ( ( mult @ SV20 @ ( mult @ SV9 @ op_c ) )
= ( mult @ ( mult @ SV20 @ SV9 ) @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(73,plain,
! [SV10: $i,SV21: $i] :
( ( ( mult @ SV21 @ ( mult @ op_c @ SV10 ) )
= ( mult @ ( mult @ SV21 @ op_c ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV12: $i,SV22: $i] :
( ( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SV22 @ SV12 ) ) @ SV12 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(75,plain,
! [SV13: $i,SV23: $i] :
( ( op_f
= ( mult @ SV23 @ ( mult @ SV13 @ ( ld @ ( mult @ SV23 @ SV13 ) @ op_c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(76,plain,
! [SV7: $i,SV18: $i,SV24: $i] :
( ( ( mult @ SV24 @ ( mult @ SV18 @ ( mult @ SV18 @ SV7 ) ) )
= ( mult @ ( mult @ ( mult @ SV24 @ SV18 ) @ SV18 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,76,75,74,73,72,71,69,68,67,66,65,62,57]) ).
thf(78,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(79,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(80,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(81,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(84,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(85,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(86,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(87,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(88,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(89,plain,
( ( ! [B: $i,A: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(90,plain,
( ( ! [B: $i,A: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(91,plain,
( ( ( ( mult @ sK1_X2 @ ( mult @ sK2_SY26 @ op_e ) )
!= ( mult @ ( mult @ sK1_X2 @ sK2_SY26 ) @ op_e ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(92,plain,
! [SV25: $i] :
( ( ! [SY39: $i] :
( ( mult @ SY39 @ ( ld @ SY39 @ SV25 ) )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV26: $i] :
( ( ! [SY40: $i] :
( ( ld @ SY40 @ ( mult @ SY40 @ SV26 ) )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV27: $i] :
( ( ! [SY41: $i] :
( ( mult @ ( rd @ SY41 @ SV27 ) @ SV27 )
= SY41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV28: $i] :
( ( ! [SY42: $i] :
( ( rd @ ( mult @ SY42 @ SV28 ) @ SV28 )
= SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV29: $i] :
( ( ( mult @ SV29 @ unit )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV30: $i] :
( ( ( mult @ unit @ SV30 )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV31: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( mult @ SY44 @ ( mult @ SY43 @ ( mult @ SY43 @ SV31 ) ) )
= ( mult @ ( mult @ ( mult @ SY44 @ SY43 ) @ SY43 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV32: $i] :
( ( ! [SY45: $i] :
( ( mult @ op_c @ ( mult @ SY45 @ SV32 ) )
= ( mult @ ( mult @ op_c @ SY45 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV33: $i] :
( ( ! [SY46: $i] :
( ( mult @ SY46 @ ( mult @ SV33 @ op_c ) )
= ( mult @ ( mult @ SY46 @ SV33 ) @ op_c ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV34: $i] :
( ( ! [SY47: $i] :
( ( mult @ SY47 @ ( mult @ op_c @ SV34 ) )
= ( mult @ ( mult @ SY47 @ op_c ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV35: $i] :
( ( op_d
= ( ld @ SV35 @ ( mult @ op_c @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV36: $i] :
( ( ! [SY48: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SY48 @ SV36 ) ) @ SV36 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV37: $i] :
( ( ! [SY49: $i] :
( op_f
= ( mult @ SY49 @ ( mult @ SV37 @ ( ld @ ( mult @ SY49 @ SV37 ) @ op_c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
( ( ( mult @ sK1_X2 @ ( mult @ sK2_SY26 @ op_e ) )
= ( mult @ ( mult @ sK1_X2 @ sK2_SY26 ) @ op_e ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV25: $i,SV38: $i] :
( ( ( mult @ SV38 @ ( ld @ SV38 @ SV25 ) )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV26: $i,SV39: $i] :
( ( ( ld @ SV39 @ ( mult @ SV39 @ SV26 ) )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV27: $i,SV40: $i] :
( ( ( mult @ ( rd @ SV40 @ SV27 ) @ SV27 )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV28: $i,SV41: $i] :
( ( ( rd @ ( mult @ SV41 @ SV28 ) @ SV28 )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV31: $i,SV42: $i] :
( ( ! [SY50: $i] :
( ( mult @ SY50 @ ( mult @ SV42 @ ( mult @ SV42 @ SV31 ) ) )
= ( mult @ ( mult @ ( mult @ SY50 @ SV42 ) @ SV42 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV32: $i,SV43: $i] :
( ( ( mult @ op_c @ ( mult @ SV43 @ SV32 ) )
= ( mult @ ( mult @ op_c @ SV43 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV33: $i,SV44: $i] :
( ( ( mult @ SV44 @ ( mult @ SV33 @ op_c ) )
= ( mult @ ( mult @ SV44 @ SV33 ) @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV34: $i,SV45: $i] :
( ( ( mult @ SV45 @ ( mult @ op_c @ SV34 ) )
= ( mult @ ( mult @ SV45 @ op_c ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV36: $i,SV46: $i] :
( ( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SV46 @ SV36 ) ) @ SV36 ) @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV37: $i,SV47: $i] :
( ( op_f
= ( mult @ SV47 @ ( mult @ SV37 @ ( ld @ ( mult @ SV47 @ SV37 ) @ op_c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV31: $i,SV42: $i,SV48: $i] :
( ( ( mult @ SV48 @ ( mult @ SV42 @ ( mult @ SV42 @ SV31 ) ) )
= ( mult @ ( mult @ ( mult @ SV48 @ SV42 ) @ SV42 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(117,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,116,115,114,113,112,111,109,108,107,106,105,102,97]) ).
thf(118,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(119,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(120,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(121,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(122,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(123,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(124,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(125,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ op_c @ ( mult @ A @ B ) )
= ( mult @ ( mult @ op_c @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(126,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ op_c ) )
= ( mult @ ( mult @ A @ B ) @ op_c ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(127,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ op_c @ B ) )
= ( mult @ ( mult @ A @ op_c ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(128,plain,
( ( ! [A: $i] :
( op_d
= ( ld @ A @ ( mult @ op_c @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(129,plain,
( ( ! [B: $i,A: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ A @ B ) ) @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(130,plain,
( ( ! [B: $i,A: $i] :
( op_f
= ( mult @ A @ ( mult @ B @ ( ld @ ( mult @ A @ B ) @ op_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(131,plain,
( ( ( ( mult @ sK1_X2 @ ( mult @ op_e @ sK2_SY26 ) )
!= ( mult @ ( mult @ sK1_X2 @ op_e ) @ sK2_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(132,plain,
! [SV49: $i] :
( ( ! [SY51: $i] :
( ( mult @ SY51 @ ( ld @ SY51 @ SV49 ) )
= SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV50: $i] :
( ( ! [SY52: $i] :
( ( ld @ SY52 @ ( mult @ SY52 @ SV50 ) )
= SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV51: $i] :
( ( ! [SY53: $i] :
( ( mult @ ( rd @ SY53 @ SV51 ) @ SV51 )
= SY53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV52: $i] :
( ( ! [SY54: $i] :
( ( rd @ ( mult @ SY54 @ SV52 ) @ SV52 )
= SY54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV53: $i] :
( ( ( mult @ SV53 @ unit )
= SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV54: $i] :
( ( ( mult @ unit @ SV54 )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV55: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( mult @ SY56 @ ( mult @ SY55 @ ( mult @ SY55 @ SV55 ) ) )
= ( mult @ ( mult @ ( mult @ SY56 @ SY55 ) @ SY55 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV56: $i] :
( ( ! [SY57: $i] :
( ( mult @ op_c @ ( mult @ SY57 @ SV56 ) )
= ( mult @ ( mult @ op_c @ SY57 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV57: $i] :
( ( ! [SY58: $i] :
( ( mult @ SY58 @ ( mult @ SV57 @ op_c ) )
= ( mult @ ( mult @ SY58 @ SV57 ) @ op_c ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV58: $i] :
( ( ! [SY59: $i] :
( ( mult @ SY59 @ ( mult @ op_c @ SV58 ) )
= ( mult @ ( mult @ SY59 @ op_c ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV59: $i] :
( ( op_d
= ( ld @ SV59 @ ( mult @ op_c @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV60: $i] :
( ( ! [SY60: $i] :
( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SY60 @ SV60 ) ) @ SV60 ) @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV61: $i] :
( ( ! [SY61: $i] :
( op_f
= ( mult @ SY61 @ ( mult @ SV61 @ ( ld @ ( mult @ SY61 @ SV61 ) @ op_c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
( ( ( mult @ sK1_X2 @ ( mult @ op_e @ sK2_SY26 ) )
= ( mult @ ( mult @ sK1_X2 @ op_e ) @ sK2_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV49: $i,SV62: $i] :
( ( ( mult @ SV62 @ ( ld @ SV62 @ SV49 ) )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV50: $i,SV63: $i] :
( ( ( ld @ SV63 @ ( mult @ SV63 @ SV50 ) )
= SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV51: $i,SV64: $i] :
( ( ( mult @ ( rd @ SV64 @ SV51 ) @ SV51 )
= SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV52: $i,SV65: $i] :
( ( ( rd @ ( mult @ SV65 @ SV52 ) @ SV52 )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV55: $i,SV66: $i] :
( ( ! [SY62: $i] :
( ( mult @ SY62 @ ( mult @ SV66 @ ( mult @ SV66 @ SV55 ) ) )
= ( mult @ ( mult @ ( mult @ SY62 @ SV66 ) @ SV66 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV56: $i,SV67: $i] :
( ( ( mult @ op_c @ ( mult @ SV67 @ SV56 ) )
= ( mult @ ( mult @ op_c @ SV67 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV57: $i,SV68: $i] :
( ( ( mult @ SV68 @ ( mult @ SV57 @ op_c ) )
= ( mult @ ( mult @ SV68 @ SV57 ) @ op_c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV58: $i,SV69: $i] :
( ( ( mult @ SV69 @ ( mult @ op_c @ SV58 ) )
= ( mult @ ( mult @ SV69 @ op_c ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV60: $i,SV70: $i] :
( ( op_e
= ( mult @ ( mult @ ( rd @ op_c @ ( mult @ SV70 @ SV60 ) ) @ SV60 ) @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV61: $i,SV71: $i] :
( ( op_f
= ( mult @ SV71 @ ( mult @ SV61 @ ( ld @ ( mult @ SV71 @ SV61 ) @ op_c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV55: $i,SV66: $i,SV72: $i] :
( ( ( mult @ SV72 @ ( mult @ SV66 @ ( mult @ SV66 @ SV55 ) ) )
= ( mult @ ( mult @ ( mult @ SV72 @ SV66 ) @ SV66 ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(157,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[136,156,155,154,153,152,151,149,148,147,146,145,142,137]) ).
thf(158,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[157,77,117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GRP703+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Tue Jun 14 01:50:27 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30
% 0.10/0.30 No.of.Axioms: 13
% 0.10/0.30
% 0.10/0.30 Length.of.Defs: 0
% 0.10/0.30
% 0.10/0.30 Contains.Choice.Funs: false
% 0.10/0.31 (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.14/0.42
% 0.14/0.42 ********************************
% 0.14/0.42 * All subproblems solved! *
% 0.14/0.42 ********************************
% 0.14/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:157,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.43
% 0.14/0.43 %**** Beginning of derivation protocol ****
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43
% 0.14/0.43 %**** End of derivation protocol ****
% 0.14/0.43 %**** no. of clauses in derivation: 158 ****
% 0.14/0.43 %**** clause counter: 157 ****
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:157,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------